CN104950315A - Broadcast ephemeris data quality detection method, electronic device and system - Google Patents

Abstract

The embodiment of the present invention provides a broadcast ephemeris data quality detection method, electronic equipment and system, which belong to the field of satellite navigation. The method includes: acquiring at least one piece of broadcast ephemeris data sent by satellites; is detected, and a detection result indicating whether at least one piece of broadcast ephemeris data is available is generated. The position of the satellite obtained by broadcast ephemeris data is verified by the satellite position calculated by m reference receivers and n data quality monitoring receivers, which further avoids satellite navigation based on wrong broadcast ephemeris data, thereby improving the Accuracy of navigation. And because the broadcast ephemeris is detected through the satellite broadcast signal, no third party is required to provide the support of satellite in-orbit data, it can effectively shield the ephemeris and almanac broadcast by the system itself from man-made interference, and improve the autonomy of the system. Further improved the accuracy of navigation.

Description

A broadcast ephemeris data quality detection method, electronic equipment and system

technical field

The invention relates to the field of satellite navigation, in particular to a broadcast ephemeris data quality detection method, electronic equipment and a system.

Background technique

With the development of the BeiDou Navigation Satellite System (BeiDou Navigation Satellite System), the wide application of the BeiDou Satellite Navigation System, the BeiDou-based Ground Based Augmentation System (Ground Based Augmentation System, GBAS) is gradually being researched and applied, making it necessary to provide a ground-based Enhance the system's broadcast ephemeris data quality detection method to improve the integrity and accuracy of the Beidou GBAS system.

The existing technology provides a method for detecting the quality of broadcast ephemeris data. The method calculates the satellite on-orbit position through the satellite orbit parameters contained in the satellite broadcast ephemeris, and compares the obtained position with the satellite orbit contained in the satellite broadcast almanac. The satellite orbit calculated by the parameters or the satellite orbit position calculated by the satellite orbit parameters contained in the previous broadcast ephemeris is compared, and the quality detection of the broadcast ephemeris data is realized according to the comparison result.

However, due to the low accuracy of the almanac of the satellite navigation system, when using the satellite orbit parameters in the almanac to calculate the satellite orbit position, the error between the obtained position and the real position will increase rapidly over time, so when using the existing technology The method provided reduces the accuracy of satellite navigation.

Contents of the invention

In order to improve the accuracy of satellite navigation, an embodiment of the present invention provides a broadcast ephemeris data quality detection method, electronic equipment and a system. Described technical scheme is as follows:

In a first aspect, a method for detecting the quality of broadcast ephemeris data is provided, the method comprising:

Obtain at least one piece of broadcast ephemeris data sent by satellites received by m reference receivers and n data quality monitoring receivers;

Detecting the at least one piece of broadcast ephemeris data to generate a detection result, where the detection result is used to indicate whether the at least one piece of broadcast ephemeris data is available.

In a second aspect, an electronic device is provided, and the device includes:

The acquisition module is used for acquiring at least one piece of broadcast ephemeris data sent by satellites received by m reference receivers and n data quality monitoring receivers;

A satellite orbit data processing module, configured to detect the at least one piece of broadcast ephemeris data and generate a detection result, the detection result being used to indicate whether the at least one piece of broadcast ephemeris data is available;

An information publishing module, configured to send the detection result to the ground subsystem of the ground-based augmentation system.

In a third aspect, a broadcast ephemeris data quality detection system is provided, and the system includes a satellite, the electronic device described in the second aspect, and a ground subsystem of a ground-based augmentation system.

The embodiment of the present invention provides a broadcast ephemeris data quality detection method, electronic equipment and system, and the satellite position calculated by m reference receivers and n data quality monitoring receivers is compared to the satellite position acquired by broadcast ephemeris data Compared with the traditional ephemeris-almanac check and old and new ephemeris check, it further avoids satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation. And because the broadcast ephemeris is detected through the satellite broadcast signal, no third party is required to provide the support of satellite in-orbit data, it can effectively shield the ephemeris and almanac broadcast by the system itself from man-made interference, and improve the autonomy of the system. Further improved the accuracy of navigation.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings that need to be used in the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those skilled in the art, other drawings can also be obtained based on these drawings without creative effort.

Fig. 1 is a flow chart of a method for detecting the quality of broadcast ephemeris data provided by an embodiment of the present invention;

Fig. 2 is a schematic structural diagram of an electronic device provided by an embodiment of the present invention;

FIG. 3 is a signal interaction diagram provided by an embodiment of the present invention;

Fig. 4 is a schematic diagram of signal interaction within a device provided by an embodiment of the present invention.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only Some, but not all, embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

The embodiment of the present invention provides a method for detecting the quality of broadcast ephemeris data, the method is applied in a ground-based augmentation system, the ground-based augmentation system includes a satellite subsystem, a ground subsystem and an airborne subsystem; the satellite subsystem includes a BDS A navigation satellite, the BDS navigation satellite is used to generate ranging signals; generate broadcast ephemeris data according to the ranging information number, and send the broadcast ephemeris data to the ground subsystem and the airborne subsystem. The ground subsystem includes at least one reference receiver, a data processor and a set of VHF data link; the at least one reference receiver is used to receive broadcast ephemeris data sent by BDS navigation satellites, and the data processor generates instructions for The test results of the quality of the ephemeris data are broadcast, and the pseudo-range correction value of the satellite position is calculated; the VHF data link is used to send the test results and the pseudo-range correction value to the airborne subsystem. The airborne subsystem includes a multi-mode receiver, which is used to receive the broadcast ephemeris data sent by the BDS navigation satellite and the detection result and the pseudorange correction value of the satellite position sent by the ground subsystem to indicate the quality of the broadcast ephemeris data, and output Corrected satellite positions and integrity alerts indicating the quality of the broadcast ephemeris data.

The embodiment of the present invention provides a kind of broadcast ephemeris data quality detection method, as shown in Fig. 1, this method comprises:

101. Acquire at least one piece of broadcast ephemeris data sent by satellites received by m reference receivers and n data quality monitoring receivers.

Specifically, at least one navigation message at least including broadcast ephemeris data is received from the same BDS constellation navigation satellite.

The embodiment of the present invention does not limit the specific receiving manner.

Among them, m≥3, m+n≥4.

102. Determine whether the data of each subframe in any one of the navigation texts at least including the broadcast ephemeris data is complete; if yes, perform step 103; if not, perform step 110.

Specifically, whether each subframe is complete can be judged by detecting the start identifier and end identifier of the data of each subframe in the navigation message, specifically:

If the start identifier and the end identifier of the data of each subframe in the navigation message are detected, it is determined that each subframe is complete;

If any one of the start identifier and the end identifier of the data of each subframe in the navigation message cannot be detected, it is determined that each subframe is incomplete.

In addition, other methods can also be used to judge whether the data of each subframe in the navigation message is complete, and the embodiment of the present invention does not limit the specific judgment process.

Due to transmission errors, data loss, etc., the data of each subframe in the broadcast ephemeris data will be incomplete, and the broadcast ephemeris data with incomplete data in each subframe will deduce the wrong satellite position, thereby reducing the satellite position. The accuracy of navigation, so, by judging whether the data of each subframe in the at least one piece of broadcast ephemeris data is complete, the accuracy of broadcast satellite data quality detection can be further improved, and further avoiding the error based on the wrong broadcast ephemeris Data for satellite navigation, thereby improving the accuracy of navigation.

103. Determine whether the subframe synchronization code is correct; if yes, execute step 104; if not, execute step 110.

Specifically, it may be determined whether the subframe synchronization code is correct by comparing the subframe synchronization code with the pre-stored subframe synchronization code, specifically:

If the subframe synchronization code is the same as the pre-stored subframe synchronization code, it is determined that the subframe synchronization code is correct; otherwise, it is determined that the subframe synchronization code is wrong.

In addition, other methods may also be used to determine whether the subframe synchronization code is correct, and this embodiment of the present invention does not limit the specific method.

Since the correct broadcast ephemeris data includes at least the correct subframe synchronization code, it is possible to further improve the accuracy of broadcast satellite data quality detection by judging whether the subframe synchronization code included in the broadcast ephemeris data is correct, and further Satellite navigation based on erroneous broadcast ephemeris data is avoided, thereby improving navigation accuracy.

It is worth noting that steps 102 to 103 are the process of judging whether any one of the at least one piece of broadcast ephemeris data is complete. In addition to the methods described in the above steps, this process can also be realized by means. The embodiment of the invention does not limit the specific process.

Because transmission errors, data loss, etc. will lead to incomplete broadcast ephemeris data, and incomplete broadcast ephemeris data will deduce wrong satellite positions, thereby reducing the accuracy of satellite navigation, therefore, by judging the at least one Whether any one of the broadcast ephemeris data is complete, further improves the accuracy of broadcast satellite data quality detection, and further avoids satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation.

It should be noted that, in practical applications, step 109 may also be directly performed after it is determined that the subframe synchronization code is verified to be correct.

Since incomplete broadcast ephemeris data will deduce wrong satellite positions, thereby reducing the accuracy of satellite navigation, when it is determined that any one of at least one piece of broadcast ephemeris data is complete, the incomplete broadcast ephemeris can be directly determined The data is available, thereby further improving the accuracy of broadcast satellite data quality detection, and further avoiding satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation.

104. Determine whether any one of the broadcast ephemeris data passes the cyclic redundancy check; if yes, execute step 105; if not, execute step 110.

Specifically, the embodiment of the present invention does not limit the specific judgment process.

Since the correct broadcast ephemeris data can pass the cyclic redundancy check, it is possible to further improve the accuracy of broadcast satellite data quality detection by judging whether any one of the broadcast ephemeris data passes the cyclic redundancy check, and further avoid Wrong broadcast ephemeris data for satellite navigation, thus improving the accuracy of navigation.

105. Determine whether the age of the clock data included in the broadcast ephemeris data is correct; if yes, execute step 106; if not, execute step 110.

Specifically, the embodiment of the present invention does not limit the specific judgment process.

Since the correct broadcast ephemeris data includes at least the correct clock data age, it is possible to further improve the accuracy of broadcast satellite data quality detection by judging whether the clock data age included in the broadcast ephemeris data is correct, and further Satellite navigation based on erroneous broadcast ephemeris data is avoided, thereby improving navigation accuracy.

It is worth noting that steps 104 to 105 are a process of judging whether any one of the at least one piece of broadcast ephemeris data is valid. In addition to the methods described in the above steps, this process can also be realized in other ways, The embodiment of the present invention does not limit the specific manner.

By judging whether any one of the at least one piece of broadcast ephemeris data is valid, it is ensured that all the broadcast ephemeris data in the at least one piece of broadcast ephemeris data are valid, further improving the accuracy of broadcast satellite data quality detection , further avoiding satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation.

It should be noted that, in practical applications, step 109 may be directly executed after it is determined that the age of the clock data included in the broadcast ephemeris data is correct.

Since invalid broadcast ephemeris data will deduce wrong satellite positions, thereby reducing the accuracy of satellite navigation, when it is determined that any one of at least one piece of broadcast ephemeris data is valid, it can be directly determined that the valid broadcast ephemeris data is available , so as to further improve the accuracy of broadcast satellite data quality detection, and further avoid satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation. In addition, on the basis of judging whether any one of the at least one piece of broadcast ephemeris data is complete, further judging whether any one of the at least one piece of broadcast ephemeris data is valid, further improving the accuracy of broadcast satellite data quality detection, It further avoids satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation.

106. Determine whether the at least one piece of broadcast ephemeris data is consistent, if yes, perform step 107, and if not, perform step 110.

Specifically, if it is determined that any one of the at least one piece of broadcast ephemeris data is valid, the at least one piece of broadcast ephemeris data is cyclically compared to obtain the same number of broadcast ephemeris data;

It is judged whether the number of the same broadcast ephemeris data satisfies a preset condition, and if so, it is judged that the at least one piece of broadcast ephemeris data is consistent.

The preset condition may be that the number of the same broadcast ephemeris data is half or more than half of the total number of broadcast ephemeris data.

Since the broadcast ephemeris data with more frequent occurrences is the correct broadcast satellite data within the allowable range of error, it is possible to further improve the accuracy of broadcast satellite data quality detection by judging whether the at least one piece of broadcast ephemeris data is consistent. Accuracy, further avoiding satellite navigation based on erroneous broadcast ephemeris data, thereby improving the accuracy of navigation.

It should be noted that, after it is determined that the at least one piece of broadcast ephemeris data is consistent, step 109 may be directly executed.

Because the wrong broadcast ephemeris data will deduce the wrong satellite position, thereby reducing the accuracy of satellite navigation, when it is determined that the at least one piece of broadcast ephemeris data is consistent, it can be directly determined that the broadcast ephemeris data is available, thereby further improving The accuracy of broadcast satellite data quality detection further avoids satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation. In addition, on the basis of judging whether any one of the at least one piece of broadcast ephemeris data is complete and judging whether any one of the at least one piece of broadcast ephemeris data is valid, further judging whether the at least one piece of broadcast ephemeris data Consistent, further improving the accuracy of broadcast satellite data quality detection, and further avoiding satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation.

107. Acquire the position of the satellite according to the at least one piece of broadcast ephemeris data.

Specifically, calculate the satellite orbit position according to the broadcast ephemeris parameters;

Among them, the broadcast ephemeris parameters and almanac parameters are shown in Table 1.

Table 1

The process of estimating the satellite orbit position according to the broadcast ephemeris parameters can be as follows:

a. According to the first algorithm, obtain the semi-major axis A of the satellite orbit, the average angular velocity n of the satellite running on the orbit, and the anomaly M _k of the satellite on the moving orbit at the current epoch time t, the first algorithm can be :

$\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\sqrt{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>$

$\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;n</span>}<span\; class="notranslate">\; ,</span>$

M _k =M ₀ +n×(tt _oe ),

Among them, μ=3.986004418×10 ¹⁴ m ³ /s ² is the gravitational constant of the earth in the CGCS2000 coordinate system;

b. On the basis of the second algorithm, according to the semi-major axis A of the satellite orbit, obtain the intermediate parameter E _k , the true anomaly V _k of the satellite on the orbit, and the angular distance Φ _k of the ascending node of the orbit of the satellite, the second The second algorithm can be:

E _k =M _k +e×cosE _k ,

$\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>}$

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctg</span>}<span\; class="notranslate">\; [</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span>$

Φ _k = v _k + ω;

c. On the basis of the third algorithm, according to the semi-major axis A of the satellite orbit, the intermediate parameter E _k and the angular distance Φ _k of the ascending node of the satellite motion orbit, obtain the corrected satellite motion orbit ascending node angular distance u _k , satellite vector r _k and satellite orbit inclination i _k , the third algorithm can be:

u _k =Φ _k +C _us sin(2Φ _k )+C _us cos(2Φ _k ),

r _k ＝A(1-ecosE _k )+C _rs sin(2Φ _k )+C _rs cos(2Φ _k ),

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; is</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&Phi;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; is</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&Phi;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

d. On the basis of the fourth algorithm, the position (x _p , y _p ) of the satellite in the orbital plane coordinate system is obtained according to the corrected satellite motion orbit ascending node angular distance u _k and satellite vector r _k :

x _p =r _k cosu _k ,

y _p =r _k sinu _k ;

Optionally, if the satellite is a MEO/IGSO satellite, the process of estimating the orbital position of the satellite according to the broadcast ephemeris parameters also includes:

e. According to the fifth algorithm, the time t _k calculated from the ephemeris reference epoch of the MEO/IGSO satellite and the corrected longitude Ω _k of the ascending node of the satellite orbit are obtained. The fifth algorithm can be:

t _k = tt _oe ,

${\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; oe</span>}}<span\; class="notranslate">\; ,</span>$

in, ${\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_e=7.2921150\&times;{10}^{-5}\mathrm{rad}/\mathrm{the\; s}$ is the angular velocity of the Earth's rotation.

f. On the basis of the sixth algorithm, according to the position (x _p , y _p ) of the satellite in the orbit plane coordinate system and the corrected ascending node longitude Ω _k of the satellite motion orbit, obtain the MEO/IGSO satellite in the CGCS2000 coordinate system coordinates (x _s , y _s , z _s ), the sixth algorithm can be:

x _s = x _p cos Ω _k -y _p cosi _k sin Ω _k ,

y _s = x _p sinΩ _k -y _p cosi _k cosΩ _k ,

z _s =y _p sini _k .

If the satellite is a GEO satellite, the process of estimating the orbital position of the satellite based on the broadcast ephemeris parameters also includes:

g. According to the seventh algorithm, the time t _k calculated from the ephemeris reference epoch of the GEO satellite and the corrected ascending node longitude Ω _k of the satellite motion orbit are obtained. The seventh algorithm can be:

t _k = tt _oe ,

${\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; oe</span>}}<span\; class="notranslate">\; .</span>$

h. On the basis of the eighth algorithm, according to the position (x _p , y _p ) of the satellite in the orbit plane coordinate system and the corrected ascending node longitude Ω _k of the satellite motion orbit, obtain the GEO satellite in the self-defined three-dimensional coordinate system Coordinates (x _z , y _z , z _z ) in the system, the eighth algorithm can be:

x _z = x _p cos Ω _k -y _p cosi _k sin Ω _k ,

y _z = x _p sin Ω _k - y _p cosi _k cos Ω _k ,

z _z =y _p sini _k .

i. On the basis of the ninth algorithm, according to the coordinates (x _z , y _z , z _z ) of the GEO satellite in the self-defined three-dimensional coordinate system, the coordinates of the GEO satellite in the self-defined spherical coordinate system ( x _z , y _z , z _z ), the ninth algorithm can be:

in:

108. Determine whether the position of the satellite satisfies a preset condition; if yes, execute step 109; if not, execute step 110.

Specifically, if the position of the satellite meets the following conditions, it is determined that the position of the satellite meets the preset condition.

The difference between the position of the satellite and the position of the satellite calculated by the multi-receiver positioning is less than the first threshold value;

The difference between the satellite's position and the satellite's orbital position at the same moment calculated according to the satellite orbital parameters in the last consecutive ephemeris that has passed the detection is less than the second threshold value;

The difference between the satellite's position and the satellite's orbital position at the same moment calculated according to the satellite's orbital parameters in the almanac is smaller than the third threshold value.

Wherein, the process of judging whether the difference between the position of the satellite and the satellite position calculated by multi-receiver positioning is less than the first threshold value may be:

The satellite combination is recorded as: SAT _PRN = {PRN ₁ , PRN ₂ , L, PRN _N }, N is the number of satellites that passed the test in step 2;

Use the observed pseudoranges of the same BDS constellation navigation satellite received by m reference receivers and n data quality monitoring receivers to calculate the position of SAT _PRNi (1≤i≤N) satellites:

j. Record each receiver pair The observation pseudorange combination of is;

${\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\\ {\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\end{array}\right\}$

Suppose the coordinate value of SAT _PRNi is X=(x,y,z), the known reference position coordinates of each receiver are (x ^l ,y ^l ,z ^l ), (x ^(l) ,y ^(l) , z ^(l) ), 1≤l≤m+n then:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\\ {\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\end{array}\right\}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; \&delta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ \sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ \sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}}\end{array}\right\}$

Among them, δt _u(k) , 1≤k≤m+ _n , is the known local clock offset of the K-th receiver, δt is the satellite clock offset of SAT _PRNi , I is the ionospheric delay, T is the tropospheric Delay, ε is receiver noise.

At this time, it can be considered that ε ₁ ≈ε ₂ ≈…≈ε _m+n , then the above formula can be calculated as:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\\ {\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\end{array}\right\}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; \&delta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}\\ \sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ \sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}\end{array}\right\}$

Wherein, δ= _-δt +I+T+ε.

k. According to the method of least squares method, the position coordinates of the satellite are obtained; the least square method iteratively calculates: the positioning algorithm is to solve the following four-element nonlinear equations:

$\left\{\begin{array}{c}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}\\ \sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}\\ <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\\ \sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; PSR</span>}}_{{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; SAT</span>}}_{{\mathrm{<span\; class="notranslate">\; PRN</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

l. Prepare data and set initial solution.

Set the initial estimated value of the current position coordinates to X=[0 0 0] ^T , and calculate the pseudo-range measurement value after difference correction.

m. Linearization of nonlinear equations.

Geometric distance from receiver to satellite:

${\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Find the partial derivative of the function r ^(k) with respect to x, and get:

$\frac{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Similar to the partial derivative of the function r ^(k) to y, z, that is:

$\left[\begin{array}{c}\frac{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; x</span>}}\\ \frac{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}\\ \frac{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; z</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

The matrix equation of formula (1) after linearization at [X _k-1 , δ _k-1 ] ^T is:

$\mathrm{<span\; class="notranslate">\; G</span>}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;y</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;z</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;\&delta;</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; b</span>}$

in:

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\\ <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right]$

n. Solve linear equations.

Apply the solution formula of the least squares method:

$\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;y</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;z</span>}\\ \mathrm{<span\; class="notranslate">\; \&Delta;\&delta;</span>}\end{array}\right]<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; b</span>}$

o. Update the roots of nonlinear equations.

X _k ＝X _k-1 +ΔX

δ _k = δ _k-1 + Δδ

p. Finally, judge the convergence of the iteration: calculate the length of the displacement vector Δx:

$<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Delta;X</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span>\sqrt{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; ;</span>$

q. Obtain the final satellite position result X.

Because the difference between the position of the satellite obtained according to the correct broadcast ephemeris data and the satellite position calculated by multi-receiver positioning is less than the first threshold value; the position of the satellite obtained according to the correct broadcast ephemeris data The satellite orbit parameters in the last ephemeris that have passed the test calculate that the difference between the satellite orbit positions at the same time is less than the second threshold value; The difference between the satellite orbit positions at the same moment calculated by the satellite orbit parameters is less than the third threshold value; Satellite orbital position and satellite orbital position calculation at the same time based on satellite orbital parameters in the almanac In addition to verifying the satellite position obtained from broadcast ephemeris data, positioning can also be performed through m reference receivers and n data quality monitoring receivers The calculated satellite position verifies the position of the satellite acquired by broadcast ephemeris data, thereby further improving the accuracy of broadcast satellite data quality detection, and further avoiding satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation .

In the embodiment of the present invention, the difference between the position of the judging satellite and the satellite orbit position estimated at the same time according to the satellite orbit parameters in the last ephemeris that has passed the detection is less than the second threshold value; The specific manner in which the difference between the position and the satellite orbit position at the same time calculated according to the satellite orbit parameters in the almanac is smaller than the third threshold is not limited.

It is worth noting that steps 107 to 108 are the process of judging whether the at least one piece of broadcast ephemeris data is available. In addition to the methods described in the above steps, this process can also be realized in other ways. The embodiment of the present invention The specific method is not limited.

By judging whether at least one piece of broadcast ephemeris data is available, satellite navigation based on wrong broadcast ephemeris data is further avoided, thereby improving the accuracy of navigation. In addition, on the basis of judging whether any one of the at least one piece of broadcast ephemeris data is complete, judging whether any one of the at least one piece of broadcast ephemeris data is valid, and judging whether the at least one piece of broadcast ephemeris data is consistent , judging whether at least one piece of broadcast ephemeris data is available, further improving the accuracy of broadcast satellite data quality detection, and further avoiding satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation.

It is worth noting that in practical applications, only when the difference between the satellite position obtained according to broadcast ephemeris data and the satellite position calculated by multi-receiver positioning is less than the first threshold; The difference between the satellite orbital positions at the same moment calculated by the satellite orbit parameters in the ephemeris that has passed the detection is less than the second threshold value; value is less than the third threshold value, it can be determined that the broadcast ephemeris data is available, so correspondingly, in the process of judging whether at least one piece of broadcast ephemeris data is available, it is necessary to perform steps to determine the position of the satellite and the multi-receiver positioning calculation. The difference between the satellite positions is less than the first threshold value, and the step judges that the difference between the position of the satellite and the satellite orbit position at the same time according to the satellite orbit parameters in the last ephemeris that has passed the detection is less than The second threshold value sums the step of judging that the difference between the position of the satellite and the satellite orbit position estimated at the same time according to the satellite orbit parameters in the almanac is smaller than the third threshold value.

109. Generate a first detection result for indicating that the at least one piece of broadcast ephemeris data is available.

Specifically, the embodiment of the present invention does not limit the specific generating process.

Since the first detection result is used to indicate that the at least one piece of broadcast ephemeris data is available, according to the second detection result, the available broadcast ephemeris data can be obtained, and satellite navigation can be performed based on the available broadcast ephemeris data, avoiding Wrong broadcast ephemeris data for satellite navigation, thus improving the accuracy of navigation.

110. Generate a second detection result for indicating that the at least one piece of broadcast ephemeris data is unavailable.

Specifically, the embodiment of the present invention does not limit the specific generating process.

Since the second detection result is used to indicate that the at least one piece of broadcast ephemeris data is unavailable, according to the second detection result, satellite navigation based on wrong broadcast ephemeris data can be avoided, thereby improving the accuracy of navigation.

Optionally, can also include:

111. According to the first detection result, generate an availability matrix corresponding to the at least one piece of broadcast ephemeris data, where the availability matrix is used to describe the availability of the at least one piece of broadcast ephemeris data;

Specifically, the first monitoring result is input into the broadcast ephemeris data availability matrix, and the broadcast ephemeris data availability matrix can be:

Among them, SN is the number of satellites in the navigation system, PRN _k (1≤k≤SN) represents the satellite number, PER _k (1≤k≤SN) represents the consistency check result of multi-reference receiver broadcast ephemeris data, EER _k (1 ≤k≤SN) represents the detection results of the old and new ephemeris detection methods, EAR _k (1≤k≤SN) represents the detection results of the ephemeris-almanac detection method, and each row in this matrix represents a satellite detected by the three detection methods The broadcast ephemeris availability of , the entire matrix describes the availability status of all satellite broadcast ephemeris of the satellite navigation system, which is used for ground-based augmentation system integrity monitoring.

Generate an availability matrix for describing the at least one piece of broadcast ephemeris data corresponding to the at least one piece of broadcast ephemeris data according to the first detection result, so that at least one piece of broadcast ephemeris data is obtained according to the availability matrix The quality of the ephemeris data, thereby further avoiding satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation.

112. Acquire an availability broadcast ephemeris array according to the availability matrix.

Specifically, the embodiment of the present invention does not limit the specific process.

The method provided by the embodiment of the present invention is compatible with the traditional data quality monitoring method, and eliminates the reference receiver and the corresponding broadcast ephemeris that have broadcast ephemeris data errors in the receiving and analyzing process; Accurate positioning and calculation of orbit position; and due to the use of ground-based multi-receiver monitoring satellite broadcast ephemeris data detection, the accuracy of satellite orbit position prediction is improved, the problem of low accuracy in traditional methods is solved, and the data in the ground-based augmentation system is reduced. Integrity risk caused by quality monitoring; since the broadcast ephemeris is detected through the satellite broadcast signal, no third party is required to provide satellite in-orbit data support, which can effectively shield the ephemeris and almanac broadcast by the system itself from man-made interference problems, The autonomy of the system is improved, and at the same time, the invention is applied to the field of Beidou system ground-based enhancement to monitor the quality of satellite data of the Beidou satellite navigation system; and the accuracy of satellite navigation is improved. At the same time, when using satellites for positioning or navigation, at least four receivers are required to locate the satellite positions, so that when at least one of the four receivers fails, the positioning of the satellite positions cannot be completed, and thus cannot Realize the use of satellites for positioning or navigation, and the method provided by the embodiment of the present invention uses m reference receivers and n data quality monitoring receivers to position the satellites, and since m≥3, m+n≥4, thus The situation that the positioning of the satellite position cannot be completed due to failure of at least one of the four receivers can be reduced, thereby realizing the reliability of navigation.

The embodiment of the present invention provides a method for detecting the quality of broadcast ephemeris data. The position of the satellite obtained by the broadcast ephemeris data is verified by the satellite position calculated by m reference receivers and n data quality monitoring receivers. Compared with traditional ephemeris-almanac inspection and old and new ephemeris inspection, it further avoids satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation. And because the broadcast ephemeris is detected through the satellite broadcast signal, no third party is required to provide the support of satellite in-orbit data, it can effectively shield the ephemeris and almanac broadcast by the system itself from man-made interference, and improve the autonomy of the system. Further improved the accuracy of navigation.

Embodiment 2 is an electronic device 2 provided by an embodiment of the present invention. Referring to FIG. 2 , the electronic device 2 includes:

Obtaining module 21, for obtaining at least one piece of broadcast ephemeris data sent by satellites received by m reference receivers and n data quality monitoring receivers;

A satellite orbit data processing module 22, configured to detect the at least one piece of broadcast ephemeris data and generate a detection result, the detection result being used to indicate whether the at least one piece of broadcast ephemeris data is available;

The information publishing module 23 is configured to send the detection result to the ground subsystem of the ground-based augmentation system.

Wherein, the acquisition module includes four data quality monitoring receivers, respectively data quality monitoring receiver 211, data quality monitoring receiver 212, data quality monitoring receiver 213 and data quality monitoring receiver 214, the four data quality monitoring receivers The antenna of the receiver is in a precise position;

The electronic book device also includes a rubidium atomic frequency standard providing module 24: used to provide time and frequency standards for data quality monitoring receivers, so that each receiver can maintain clock synchronization.

Optionally, the satellite orbit data processing module 22 detects the at least one piece of broadcast ephemeris data at least through the following steps, and generates a detection result:

Positioning the satellite position according to m reference receivers and n data quality monitoring receivers, and obtaining the position of the satellite;

It is judged whether the position of the satellite satisfies a preset condition, and if the position of the satellite satisfies the preset condition, it is determined that the at least one piece of broadcast ephemeris data is available.

Optionally, the satellite orbit data processing module 22 is also configured to perform the following operations:

judging whether any one of the at least one piece of broadcast ephemeris data is complete;

judging whether any one of the at least one piece of broadcast ephemeris data is valid;

It is judged whether the at least one piece of broadcast ephemeris data is consistent.

Optionally, the satellite orbit data processing module 22 is specifically used for:

If it is determined that any one of the at least one piece of broadcast ephemeris data is complete, then judging whether any one of the at least one piece of broadcast ephemeris data is valid;

If it is determined that any one of the at least one piece of broadcast ephemeris data is valid, then judging whether the at least one piece of broadcast ephemeris data is consistent;

If it is determined that the at least one piece of broadcast ephemeris data is consistent, execute the step of locating the position of the satellite according to the m reference receivers and the n data quality monitoring receivers, and obtaining the position of the satellite.

Optionally, the satellite orbit data processing module 22 is specifically used for:

If any data in the at least one broadcast ephemeris is complete, at least one of the at least one broadcast ephemeris data is valid, the at least one broadcast ephemeris data is consistent, and the at least one broadcast ephemeris data If the data is available, generate a first detection result for indicating that the at least one piece of broadcast ephemeris data is available; otherwise, generate a second detection result for indicating that the at least one piece of broadcast ephemeris data is unavailable.

Optionally, the satellite orbit data processing module 22 is specifically used for:

generating an availability matrix corresponding to the at least one piece of broadcast ephemeris data according to the first detection result, where the availability matrix is used to describe the availability of the at least one piece of broadcast ephemeris data;

Obtain an availability broadcast ephemeris array according to the availability matrix.

Optionally, the information release module 23 is also configured to send the availability broadcast ephemeris array to the ground-based augmentation system.

It is worth noting that the data interaction between the electronic equipment and the ground subsystem of the ground-based augmentation system can be shown in Figure 3. In Figure 3,

The data interaction between various modules of the internal data of the electronic device can be shown in Figure 4. In Figure 4, the flow direction of the signal in the electronic device can be:

The ground subsystem A of the ground-based augmentation system sends the navigation observation data including the broadcast ephemeris data of the reference receiver of the ground subsystem to the interface b in the electronic device 2 through the ground network for forwarding. At the same time, the interface b is also used to forward the broadcast ephemeris availability matrix and the available broadcast ephemeris array 10 sent by the information publishing module.

Four data quality integrity monitoring receivers B1 receive BDS signals and output navigation observation data, including pseudorange data, ephemeris, almanac, satellite clock difference and time information, and observation data 1 to 4 are forwarded by interface a .

The satellite orbit data processing module 22 receives the data quality integrity monitoring receiver navigation observation data 5 forwarded by interface a, receives the ground-based augmentation system ground subsystem navigation observation data 7 forwarded by interface b, performs data quality monitoring processing, and completes the ephemeris - Almanac inspection, old and new ephemeris inspection, ground multi-receiver detection of satellite broadcast ephemeris, output broadcast ephemeris availability matrix and available broadcast ephemeris array 6 .

The information release module 23 receives the broadcast ephemeris availability matrix and the available broadcast ephemeris array 6, stores the integrity information, and forwards the data quality integrity judgment result 8 to the ground subsystem A of the ground-based augmentation system through interface b.

The rubidium atomic frequency standard providing module 24 provides the time-frequency reference signal 11 for four data quality integrity monitoring receivers.

An embodiment of the present invention provides an electronic device. By detecting at least one piece of broadcast ephemeris data, the electronic device avoids satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation. And because the broadcast ephemeris is detected through the satellite broadcast signal, no third party is required to provide the support of satellite in-orbit data, it can effectively shield the ephemeris and almanac broadcast by the system itself from man-made interference, and improve the autonomy of the system. Further improved the accuracy of navigation.

Embodiment 3 is a broadcast ephemeris data quality detection system provided by an embodiment of the present invention. Referring to FIG. 3, the system includes a satellite subsystem, a ground subsystem, and an airborne subsystem. The ground subsystem includes at least the embodiment The electronic equipment mentioned in 2.

The embodiment of the present invention provides a broadcast ephemeris data quality detection system, the system verifies the satellite position acquired by the broadcast ephemeris data through the satellite position calculated by m reference receivers and n data quality monitoring receivers , compared with the traditional ephemeris-almanac check and old and new ephemeris check, it further avoids satellite navigation based on wrong broadcast ephemeris data, thereby improving the accuracy of navigation. And because the broadcast ephemeris is detected through the satellite broadcast signal, no third party is required to provide the support of satellite in-orbit data, it can effectively shield the ephemeris and almanac broadcast by the system itself from man-made interference, and improve the autonomy of the system. Further improved the accuracy of navigation.

All the above optional technical solutions can be combined in any way to form an optional embodiment of the present invention, which will not be repeated here.

It should be noted that: when the electronic equipment and system provided by the above-mentioned embodiments detect the quality of the broadcast ephemeris data, the division of the above-mentioned functional modules is used as an example for illustration. In practical applications, the above-mentioned functions can be allocated by Completion of different functional modules means that the internal structure of the device is divided into different functional modules to complete all or part of the functions described above. In addition, the electronic equipment and system provided in the above embodiments belong to the same idea as the embodiment of the method for detecting the quality of broadcast ephemeris data, and its specific implementation process is detailed in the method embodiment, and will not be repeated here.

Those of ordinary skill in the art can understand that all or part of the steps for implementing the above embodiments can be completed by hardware, and can also be completed by instructing related hardware through a program. The program can be stored in a computer-readable storage medium. The above-mentioned The storage medium mentioned may be a read-only memory, a magnetic disk or an optical disk, and the like.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within range.

Claims (10)

1. A method for detecting quality of broadcast ephemeris data, the method comprising:

acquiring at least one piece of broadcast ephemeris data sent by a satellite and received by m reference receivers and n data quality monitoring receivers;

and detecting the at least one piece of broadcast ephemeris data to generate a detection result, wherein the detection result is used for indicating whether the at least one piece of broadcast ephemeris data is available.

2. The method of claim 1, wherein the at least one piece of broadcast ephemeris data is detected to generate a detection result by at least:

positioning the satellite position according to the m reference receivers and the n data quality monitoring receivers to obtain the position of the satellite;

and judging whether the position of the satellite meets a preset condition, and if the position of the satellite meets the preset condition, judging that the at least one piece of broadcast ephemeris data is available.

3. The method of claim 1, wherein the detecting the at least one piece of broadcast ephemeris data further comprises:

judging whether any one of the at least one piece of broadcast ephemeris data is complete;

judging whether any one of the at least one piece of broadcast ephemeris data is valid;

and judging whether the at least one piece of broadcast ephemeris data is consistent.

4. The method of claim 3,

if any one of the at least one piece of broadcast ephemeris data is judged to be complete, judging whether any one of the at least one piece of broadcast ephemeris data is valid;

if any one of the at least one piece of broadcast ephemeris data is judged to be valid, judging whether the at least one piece of broadcast ephemeris data is consistent;

and if the at least one piece of broadcast ephemeris data is consistent, executing the step of positioning the satellite position according to the m reference receivers and the n data quality monitoring receivers to acquire the position of the satellite.

5. The method of any of claims 1 to 4, wherein the generating the detection result comprises:

if any data in the at least one piece of broadcast ephemeris is complete, at least one piece of ephemeris data is valid, the at least one piece of broadcast ephemeris data is consistent, and the at least one piece of broadcast ephemeris data is available, generating a first detection result for indicating that the at least one piece of broadcast ephemeris data is available; otherwise, generating a second detection result for indicating that the at least one piece of broadcast ephemeris data is unavailable.

6. The method of claim 5, further comprising:

generating an availability matrix corresponding to the at least one piece of broadcast ephemeris data according to the first detection result, wherein the availability matrix is used for describing the availability of the at least one piece of broadcast ephemeris data;

and acquiring an availability broadcast ephemeris array according to the availability matrix.

7. An electronic device, characterized in that the electronic device comprises:

the system comprises an acquisition module, a quality monitoring module and a processing module, wherein the acquisition module is used for acquiring at least one piece of broadcast ephemeris data sent by a satellite and received by m reference receivers and n data quality monitoring receivers;

the satellite orbit data processing module is used for detecting the at least one piece of broadcast ephemeris data and generating a detection result, wherein the detection result is used for indicating whether the at least one piece of broadcast ephemeris data is available;

and the information issuing module is used for sending the detection result to the ground subsystem of the ground-based augmentation system.

8. The apparatus of claim 7, wherein the satellite trajectory data processing module detects the at least one piece of broadcast ephemeris data by at least:

positioning the satellite position according to the m reference receivers and the n data quality monitoring receivers to obtain the position of the satellite;

and judging whether the position of the satellite meets a preset condition, and if the position of the satellite meets the preset condition, judging that the at least one piece of broadcast ephemeris data is available.

9. A broadcast ephemeris data quality detection system, comprising a satellite, an electronic device according to claim 7 or 8 and a ground based augmentation system ground subsystem.

10. The system of claim 9, wherein the electronic device detects the at least one piece of broadcast ephemeris data by at least:

positioning the satellite position according to the m reference receivers and the n data quality monitoring receivers to obtain the position of the satellite;

and judging whether the position of the satellite meets a preset condition, and if the position of the satellite meets the preset condition, judging that the at least one piece of broadcast ephemeris data is available.