CN118604854B - Method for selecting pseudolite base station - Google Patents
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- G—PHYSICS
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Abstract
The invention relates to a method for selecting pseudolite base stations, comprising the step of determining the number K of base stations to be selected. The impact Δmn of each base station on WPDOP is calculated. And determining the minimum value and simultaneously removing the corresponding base station. The calculation of the impact Δmn of each base station on WPDOP is repeated for the remaining base stations. And determining the minimum value, and simultaneously removing the corresponding base stations until the number of the rest base stations is equal to K. The optimal criterion of WPDOP weighted position precision factors is led out on the basis of WDOP weighted factors, a station selecting method based on the contribution to WPDOP is provided, the calculated amount of a base station selecting algorithm is effectively reduced, the selecting speed of a base station is faster, and the real-time performance of positioning is improved.
Description
Technical Field
The invention relates to the field of navigation and positioning, in particular to a method for selecting a pseudolite base station.
Background
On key facilities built in the society in the past, the safety of the facilities is often ensured in real time through monitoring and control. However, due to the poor visibility of the GNSS satellites caused by the environment of some facilities, it is difficult to provide reliable, accurate and continuous navigation positioning services for the receiver through the GNSS satellite system, and how to realize high-precision real-time monitoring becomes a difficult problem. With the progress of technological development, the foundation pseudolite positioning system with independent networking can reasonably deploy base stations according to actual demands and terrains to provide high-precision and reliable positioning services for receivers, but a certain number of redundant base stations are usually distributed, so that the positioning continuity is improved, and the positioning blind area is reduced. Based on the traditional satellite navigation positioning algorithm, the calculation amount of a receiver can be increased, the hardware cost is increased, the observation value with larger pseudo-range measurement error can participate in the positioning calculation, and the positioning precision of the system is reduced. In order to reduce the computational burden of the receiver and improve the positioning accuracy, a base station combination with higher positioning accuracy is selected from the visible base stations to perform signal receiving and positioning calculation.
The base station combination of the traditional GNSS system is selected by adopting DOP precision factor optimal standard. However, in the case of the ground-based pseudolite system, since the distances from the receiver to each base station are different, there is a significant difference in the range error, and thus the DOP precision factor is not applied. Therefore, WDOP weighting precision factor optimal standards are provided as the basis of receiver positioning satellite selection, and influence of different pseudo-range measurement errors on satellite selection and positioning results is weakened.
Disclosure of Invention
In view of the foregoing shortcomings of the prior art, it is an object of the present invention to provide a method of selecting a pseudolite base station that solves one or more of the problems of the prior art.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
a method of selecting a pseudolite base station comprising the steps of:
Determining the number K of base stations needing to be selected;
Calculating delta Mn of each base station;
determining the minimum delta Mn value, and eliminating the base station corresponding to the minimum delta Mn value;
and judging whether the number P of the rest base stations is larger than the number K of the base stations, if so, returning to recalculate the delta Mn of each base station, and if not, finishing the selection of the base stations.
Further, the calculating Δmn of each base station includes the following steps:
An observation matrix H of the system is introduced to calculate a positioning error covariance matrix, and a PDOP position precision factor is calculated according to the definition of the DOP precision factor;
A weighting matrix W of the system ranging error is introduced to calculate a measurement error covariance matrix of the satellite, and a WPDOP weighting position precision factor is obtained according to the definition of the DOP precision factor;
Calculating a pseudo-range measurement error to obtain a direct ratio of the ranging error to the measurement error;
and (3) solving a range error covariance matrix of the satellite, and introducing a weighting matrix W and an observation matrix H to obtain a relation between the weighting position precision factors and delta Mn of the adjacent number of base stations WPDOP.
Further, the calculation of the pseudo-range measurement error includes the following steps:
Obtaining a root mean square expression of the measurement error according to a coherent DLL discriminator used by the receiver;
And further obtaining the relation between the measurement error of the pseudo satellite receiver and the distance between the receiver and the base station by introducing the relation between the received signal power and the free space attenuation model of the signal and combining the wavelength and the power of the transmitted signal of the base station.
Further, the positioning error covariance matrix is shown as follows:
Wherein H is the observation matrix of the system The directional cosine of the ith satellite), n represents the number of visible satellites,For the pseudorange measurement variance, D is a coefficient matrix, cov (dx) is a positioning error covariance matrix;
The PDOP position accuracy factor may be expressed as:
The PDOP position precision factor is mainly used for measuring the precision of three-dimensional positioning, including longitude, latitude and height of the position, and the smaller the PDOP is, the higher the positioning precision is.
Further, the covariance matrix of the measurement error may be represented as follows:
Wherein W n is a weighting matrix of the system ranging error, and dx is used for indicating the net error of the positioning system position/time estimation, the covariance matrix of the ranging error is:
the WPDOP weighted precision factor may be represented as follows:
And taking WPDOP optimal standards as the basis of the selection of the base station of the pseudo satellite positioning system.
Further, the receiver measures the root mean square of the error using a coherent DLL discriminator as follows:
Where B n denotes the noise bandwidth of the code tracking loop, F denotes the pitch of the lead-lag correlator, and C/N 0 denotes the carrier-to-noise ratio, which is the ratio of the RF signal to the noise power before demodulation.
Further, the following relationship exists between the standard deviation σ i and σ 0 of each base station measurement error:
In the middle of For the ranging error when the receiver is 1m from the base station, C 0 is the radio frequency signal power when the receiver is 1m from the base station, C i is the received signal power;
the magnitude of the observed quantity error is primarily dependent on the received signal power, which is determined from the free space attenuation model of the signal.
Further, the relation between the received signal power and the free space attenuation model of the signal is as follows:
Where C R (d) is the received power from the antenna at the source dm, C T is the transmitted power of the signal, G T and G R are the gains of the transmitting and receiving antennas, λ is the signal wavelength, and L is the hardware loss factor, and sigma i 2 can be simplified as:
the pseudolite receiver observance error is approximately proportional to the square of the distance between the receiver and the base station.
Further, according to the covariance matrix of the ranging error of the pseudo satellite system and the weighting matrix W of the pseudo satellite system, the relation between the adjacent base stations is as follows:
Wherein, H is the observed quantity of the removed base stations, w is the corresponding weight value thereof, H n is the observed matrix when the number of the visible base stations is n, one base station is removed therefrom, and the observed matrix of the remaining n-1 base stations is H n-1;
the following formula can be further derived from the Sherman-Morrison-Woodbury identity:
where r= (1/w-hM nhT)-1 is a scalar.
Further, the weighted position accuracy factors of the geometric configuration formed by the remaining n-1 base stations and the receiver are as follows:
The effect of the removed base station on WPDOP n is:
△Mn＝L11+L22+L33
The smaller Δm n, the smaller WPDOP of the remaining base stations after removal, and the higher the positioning accuracy.
Compared with the prior art, the invention has the following beneficial technical effects:
The optimal criterion of WPDOP weighted position precision factors is led out on the basis of WDOP weighted factors, a station selecting method based on the contribution to WPDOP is provided, the calculated amount of a base station selecting algorithm is effectively reduced, the selecting speed of a base station is faster, and the real-time performance of positioning is improved.
Drawings
Fig. 1 shows a pseudo satellite base station selection strategy flowchart of a method for selecting a pseudo satellite base station according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, a method for selecting a pseudolite base station according to the present invention will be described in further detail with reference to the accompanying drawings and detailed description. The advantages and features of the present invention will become more apparent from the following description. It should be noted that the drawings are in a very simplified form and are all to a non-precise scale, merely for the purpose of facilitating and clearly aiding in the description of embodiments of the invention. For a better understanding of the invention with objects, features and advantages, refer to the drawings. It should be understood that the structures, proportions, sizes, etc. shown in the drawings are for illustration purposes only and should not be construed as limiting the invention to the extent that any modifications, changes in the proportions, or adjustments of the sizes of structures, proportions, or otherwise, used in the practice of the invention, are included in the spirit and scope of the invention which is otherwise, without departing from the spirit or essential characteristics thereof.
Step 1 referring to fig. 1, in the method for selecting a pseudolite base station of the present embodiment, the number K of base stations to be selected is first determined.
Step 2, please continue to refer to fig. 1, the influence Δmn of each base station on WPDOP is calculated.
In step 2.1, further, in the positioning navigation system, the positioning error may be expressed as a product of the ranging error and the DOP precision factor, where DOP represents a composite effect of the relative geometrical layout of the satellite/user on the positioning error, and the smaller the value, the higher the positioning precision. The DOP precision factor is defined by the ratio of the sum of the components of the error covariance matrix to the reference root mean square pseudorange error σp2. DOP represents the composite effect of the relative geometry of the satellite/user on the positioning error, with the smaller the value, the higher the positioning accuracy.
Further, the error covariance matrix and the observation matrix of the system are shown in the following formulas 1 and 2, respectively:
In the above formulas 1 and 2, H is the observation matrix of the system The directional cosine of the ith satellite), n represents the number of visible satellites,For pseudorange measurement variance, D is the coefficient matrix and cov (dx) is the positioning error covariance matrix.
According to the definition of DOP precision factor, the commonly used precision factor can be expressed as the following formulas 3 to 5:
In the above formulas 3 to 5, the GDOP geometric precision factor comprehensively considers the influence of satellite position geometric structure on positioning precision, including the number, the position and the distribution of satellites. It represents the accuracy of the position and time solutions, which is a comprehensive index. The PDOP position accuracy factor is mainly used for measuring the accuracy of three-dimensional positioning, including longitude, latitude and altitude of the position. The smaller the PDOP, the higher the positioning accuracy. The HDOP horizontal accuracy factor only considers the horizontal positioning accuracy of the system, and does not include the height. It measures mainly the horizontal accuracy of the position solution, i.e. the accuracy of longitude and latitude.
Further, because the satellites in a single system of satellite navigation are at the same orbit altitude and are far from the user's location, the range error is relatively small and similar. Ordinary DOP is feasible as an evaluation index of the positioning accuracy of the system.
In step 2.2, further, in a pseudolite positioning system, a common DOP value may not accurately reflect the positioning capability of the system. Considering WDOP the weighting precision factors, the method can more comprehensively consider the error magnitude and uncertainty of each observed quantity, more accurately evaluate the positioning precision of the system, and assist in selecting the optimal base station combination to improve the positioning accuracy and reliability. WDOP the essence of the weighted precision factor is to give each observation a different weight, weakening the effect of the large error on the system assuming that the pseudorange measurement errors for each satellite are independent, normal distribution with zero mean, the covariance matrix of the measurement errors for n satellites can be represented as shown in equation 6 below:
in equation 6 above, W n is the weighting matrix of the system range error, and dx is used to represent the net error of the positioning system position/time estimate, the range error covariance matrix is shown in equation 7 below:
According to the definition of DOP precision factor, WPDOP the weighted precision factor can be expressed as shown in equation 8 below:
the pseudo-range measurement errors according to the observables of the pseudo-satellite positioning system 7 are independent and have normal distribution with zero mean value, and the assumption made on the observables when WDOP is defined is satisfied. And finally, taking WPDOP optimal standards as the basis for selecting the base station of the pseudo satellite positioning system.
In step 2.3, further, the influence Δmn of each base station on WPDOP is derived from the relation of WPDOP weighted position accuracy factors of the number of neighboring base stations, and the derivation of the relation of the weighted position accuracy factors relates to the pseudo-range measurement error.
Step 2.3.1, on the basis of not considering multipath errors and troposphere demonstration, the pseudo-range measurement errors mainly comprise thermal noise distance error tremors and dynamic stress errors, and when the receiver uses a coherent DLL discriminator to measure the root mean square of the errors is shown as follows:
Where B n denotes the noise bandwidth of the code tracking loop, F denotes the pitch of the lead-lag correlator, and C/N 0 denotes the carrier-to-noise ratio, which is the ratio of the RF signal to the noise power before demodulation.
Step 2.3.2, further, setting the mean square error of the reference ranging error of the pseudo satellite system as the ranging error when the receiver is 1m away from the base station, and then each base station measuring error standard deviation σ i and σ 0 have the following relationship, as shown in the following formula 10:
In the middle of For the range error when the receiver is 1m from the base station, C 0 is the radio frequency signal power when the receiver is 1m from the base station, and C i is the received signal power.
From equation 10 above, it can be seen that the magnitude of the observed error is primarily dependent on the received signal power, which can be determined from the free-space attenuation model of the signal.
Step 2.3.3, further, the relation between the received signal power and the free space attenuation model of the signal is shown in the following formula 11:
Wherein C R (d) is the received power from the antenna at the transmission source dm, C T is the transmitted power of the signal, G T and G R are the gains of the transmission and reception antennas, lambda is the signal wavelength, L is the hardware loss factor, and because the hardware equipment used by the base station and the transmitted signal wavelength and power are identical The following formula 12 can be simplified:
From equation 12 above, it follows that the observed error of a pseudolite receiver is approximately proportional to the square of the distance between the receiver and the base station.
Step 2.4, further, assuming that the observed errors of the pseudo satellite system are mutually independent and zero-mean gaussian distributions, the base station relationship of the adjacent number can be obtained according to the covariance matrix of the ranging errors of the pseudo satellite system and the weighting matrix W n of the pseudo satellite system as shown in the following formula 13:
Where h is the observed quantity of the removed base station and w is the corresponding weight. H n is the observation matrix for the number of visible base stations n, from which one base station is removed, and the observation matrix for the remaining n-1 base stations is H n-1.
Further, the following formula 14 can be further obtained according to the Sherman-Morrison-Woodbury identity:
where r= (1/w-hM nhT)-1 is a scalar.
The weighted position accuracy factors of the geometric configuration formed by the remaining n-1 base stations and the receiver are shown in the following formula 15 according to the definition of the weighted position accuracy factors:
Step 3, please continue to refer to fig. 1, the effect of the removed base station on WPDOP n is given by the following expression of Δmn 16:
△Mn＝L11+L22+L33 (16)
The smaller Δm n, the smaller WPDOP of the remaining base stations after removal, and the higher the positioning accuracy.
Step 4, please continue to refer to fig. 1, the diagram P represents the remaining number of base stations. Setting the total number of visible base stations of the receiver as N, selecting K base stations from the N base stations, and performing a traversal methodThe WPDOP solution process, which involves matrix multiplication and matrix inversion, is performed. Base station selection method based on contribution of base station to WPDOP needs to be executed N-K times WPDOP andThe secondary involves only the ΔM n solving process of matrix multiplication. As the number of the visual base stations N increases, compared with a traversal method, the calculation amount of the station selection method based on the contribution of the base stations to WPDOP is smaller, the selection speed of the base stations is faster, and the positioning instantaneity is obviously improved.
The technical features of the above-described embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above-described embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (7)
1. A method of selecting a pseudolite base station, comprising the steps of:
Determining the number K of base stations needing to be selected;
the delta Mn of each base station is calculated, comprising the following steps:
An observation matrix H of the system is introduced to calculate a positioning error covariance matrix, a PDOP position precision factor is calculated according to the definition of the DOP precision factor,
A weighting matrix W of the system ranging error is introduced to calculate a measurement error covariance matrix of the satellite, a WPDOP weighting position precision factor is obtained according to the definition of the DOP precision factor,
The range error is proportional to the measurement error by calculation of the pseudo-range measurement error,
Solving a range error covariance matrix of a satellite, and introducing a weighting matrix W and an observation matrix H to obtain a relation between a weighting position precision factor and delta Mn of adjacent number base stations WPDOP, wherein the relation between the adjacent number base stations is shown as follows:
Wherein H is the observed quantity of the removed base station, w is the corresponding weight, H n is the observation matrix when the number of visible base stations is n, one base station is removed from the observed matrix, the observation matrix of the remaining n-1 base stations is H n-1, and the following formula can be further obtained according to the Sherman-Morrison-Woodbury identity:
Where R= (1/w-hM nhT)-1 is a scalar,
And the remaining n-1 base stations and receivers form a geometry with a weighted position accuracy factor of:
The effect of the removed base station on WPDOP n is:
△Mn＝L11+L22+L33
the smaller the DeltaM n is, the smaller WPDOP of the rest base stations is removed, and the higher the positioning precision is;
determining the minimum delta Mn and eliminating the base station corresponding to the minimum delta Mn;
and judging whether the number P of the rest base stations is larger than the number K of the base stations, if so, returning to recalculate the delta Mn of each base station, and if not, finishing the selection of the base stations.
2. A method of selecting a pseudolite base station as set forth in claim 1 wherein said calculation of said pseudorange measurement error comprises the steps of:
Obtaining a root mean square expression of the measurement error according to a coherent DLL discriminator used by the receiver;
according to the range error when the standard range error variance of the pseudo satellite system is set as the range error when the receiver is 1m away from the base station, the relation between the standard deviation of the measuring error of each base station is obtained and related to the power of the received signal;
the relation between the measurement error of the pseudolite receiver and the distance from the receiver to the base station is further obtained by introducing the relation between the received signal power and the free space attenuation model of the signal and combining the wavelength and the power of the transmitted signal of the base station.
3. A method of selecting a pseudolite base station as set forth in claim 2 wherein said positioning error covariance matrix is represented by the formula:
wherein H is the observation matrix of the system, using The directional cosine of the i-th satellite, i=1, 2, 3..n, where n represents the number of visible satellites; for the pseudorange measurement variance, D is a coefficient matrix, cov (dx) is a positioning error covariance matrix;
The PDOP position accuracy factor may be expressed as:
The PDOP position precision factor is mainly used for measuring the precision of three-dimensional positioning, including longitude, latitude and height of the position, and the smaller the PDOP is, the higher the positioning precision is.
4. A method of selecting a pseudolite base station as set forth in claim 3 wherein said covariance matrix of measurement errors is represented by the formula:
Wherein W n is a weighting matrix of system ranging errors when the number of base stations is n, dx is used for representing the net error of positioning system position/time estimation, and the covariance matrix of the ranging errors is as follows:
the WPDOP weighted precision factor may be represented as follows:
And taking WPDOP optimal standards as the basis of the selection of the base station of the pseudo satellite positioning system.
5. A method of selecting a pseudolite base station as set forth in claim 4 wherein said receiver measures the root mean square of the error using a coherent DLL discriminator as follows:
Where B n denotes the noise bandwidth of the code tracking loop, F denotes the pitch of the lead-lag correlator, and C/N 0 denotes the carrier-to-noise ratio, which is the ratio of the RF signal to the noise power before demodulation.
6. A method of selecting a pseudolite base station as set forth in claim 5 wherein each base station measurement error standard deviation σ i and σ 0 has the following relationship:
In the middle of For the ranging error when the receiver is 1m from the base station, C 0 is the radio frequency signal power when the receiver is 1m from the base station, C i is the received signal power;
the magnitude of the observed quantity error is primarily dependent on the received signal power, which is determined from the free space attenuation model of the signal.
7. A method of selecting a pseudolite base station as set forth in claim 6 wherein said received signal power is related to a free space attenuation model of the signal as follows:
Wherein C R (d) is the received power from the antenna at the transmission source dm, C T is the transmitted power of the signal, G T and G R are the gains of the transmission and reception antennas, lambda is the signal wavelength, L is the hardware loss factor, and because the hardware equipment used by the base station and the transmitted signal wavelength and power are identical Can be simplified into:
the pseudolite receiver observance error is approximately proportional to the square of the distance between the receiver and the base station.
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