CN104898140B - Error Envelope Method for Satellite Navigation Ground-Based Augmentation System Based on Extreme Value Theory - Google Patents

Abstract

The present invention provides an error envelope method for a satellite navigation ground-based augmentation system based on the extreme value theory, comprising: acquiring at least two sets of pseudorange error correction sample values, and determining the corresponding risk of each set of pseudorange error correction sample values The first quantile and the first standard deviation, and then according to the total operational risk of the ground-based augmentation system GBAS to determine the second quantile corresponding to the total operational risk of GBAS under the standard Gaussian distribution, and then according to the first quantile, the second The quantile and the first standard deviation determine the amplification factor corresponding to the sample value of the pseudorange error correction in this group. The amplification factor can be accurately calculated through the above method, so that the calculated pseudorange correction value can envelope the actual error and effectively improve the continuous performance of the system. sex.

Description

Error Envelope Method for Satellite Navigation Ground-Based Augmentation System Based on Extreme Value Theory

technical field

The invention relates to satellite navigation technology, in particular to an error envelope method of a satellite navigation ground-based augmentation system based on extreme value theory.

Background technique

Ground-Based Augmentation Systems (GBAS for short) use differential technology to improve aircraft positioning accuracy. At present, GBAS can meet the requirements of civil aviation operations up to CAT I, and can be used as the main or even the only navigation system, thus making it possible for the satellite navigation system to replace the traditional land-based radio navigation system.

In order to ensure flight safety, while the airborne equipment of GBAS performs differential positioning in real time, it also needs to calculate the upper limit of the positioning error under the specified risk probability, which is called the protection level. In GBAS, the ground station calculates the pseudorange correction value of each satellite in the horizon in real time. At the same time, the ground station assumes that the pseudorange correction error obeys a zero-mean Gaussian distribution and estimates its standard deviation σ _{pr_gnd} . The pseudorange corrections and standard deviations of the correction errors for each satellite are broadcast to the aircraft. The aircraft assumes that the error of the pseudorange correction value sent by the ground station is Gaussian distribution with zero mean value, and the standard deviation is σ _{pr_gnd} , so as to calculate the protection level.

But in practice, the error caused by ground reflection multipath may be non-Gaussian, non-zero mean, or there is not enough data to verify that the actual error is Gaussian distributed, resulting in the standard deviation of the actual error exceeding the σ _{pr_gnd} value, resulting in Potential integrity risk. Therefore, in order to compensate for the difference between the assumed error probability distribution and the real error probability distribution, a certain method must be found to deal with these distribution characteristics of the error to ensure the reliability of the protection level, and this method does not require that the error must be a Gaussian distribution , the variance is known.

A technique called envelope is widely used in the current GBAS to solve this problem. Firstly, the estimated value of the error standard deviation σ _{pr_gnd_est} is calculated based on the actual observation value, and then the amplification factor (Inflation Factor) k _inf is calculated, and according to the formula: σ _{pr_gnd} = k _inf × σ _{pr_gnd_est} , so that the calculated value of σ _{pr_gnd} can envelope (Overbound) the actual error, so that the protection level calculated by the airborne receiver according to σ _{pr_gnd} can meet the integrity requirement.

However, in practice, the number of independent samples that can be used to calculate the error envelope is extremely limited compared with the risk probability that the error envelope is intended to protect. Even under the condition that the real error satisfies the zero-mean Gaussian distribution, it is still necessary to consider the number of samples used Uncertainty due to limitations. In addition, because the real error comes from the overall distribution with different standard deviations, the error mixture caused by the processing process, and the correlation between different reference receiver data, etc., the real error presents a thick-tailed distribution, and its real distribution is unknown, while Existing methods make conservative assumptions about the tails of the distribution, leading to excessively large calculated amplification factors, which lead to a reduction in the continuity of the system.

Contents of the invention

An embodiment of the present invention provides an error envelope method for a satellite navigation ground-based augmentation system based on the extreme value theory to overcome the conservative assumption of the distribution tail in the existing method, resulting in the calculated amplification factor being too large, resulting in a system The problem of reduced continuity.

The first aspect of the present invention provides an error envelope method for a satellite navigation ground-based augmentation system based on extreme value theory, including:

Obtaining at least two sets of pseudorange error correction sample values;

Do the following for each set of pseudorange error correction sample values:

Determine the first quantile and the first standard deviation with the specified risk corresponding to the pseudorange error correction sample value of this group;

The second quantile corresponding to the total operational risk of the GBAS under the standard Gaussian distribution according to the total operational risk of the ground-based augmentation system GBAS;

An amplification factor corresponding to the set of pseudorange error correction sample values is determined according to the first quantile, the second quantile and the first standard deviation.

With reference to the first aspect, in the first possible implementation of the first aspect, the determining the first quantile with a specified risk corresponding to the set of pseudorange error correction sample values includes:

Determine the threshold corresponding to the set of pseudorange error correction sample values;

Obtain at least two groups of resampling sample values corresponding to the group of pseudorange error correction sample values according to the resampling method;

Determine each set of resampling samples according to the threshold corresponding to the set of pseudorange error correction sample values and each set of resampling sample values in the at least two sets of resampling sample values corresponding to the set of pseudorange error correction sample values The excess sample value in the value, the excess sample value is the difference between the value greater than the threshold and the threshold in each set of resampled sample values;

The first quantile is determined based on the excess sample value.

With reference to the first possible implementation of the first aspect, in the second possible implementation of the first aspect, the determining the first quantile according to the excess sample value includes:

determining a first probability that the set of resampled sample values exceeds the threshold according to the excess sample value corresponding to the set of resampled sample values;

Determine the second standard deviation of the excess sample value corresponding to the group of resampled sample values;

The first quantile is determined based on the first probability and the second standard deviation.

With reference to the second possible implementation of the first aspect, in a third possible implementation of the first aspect, the determining the first quantile according to the first probability and the second standard deviation ,include:

determining a first parametric confidence limit for a specified confidence level based on the first probability;

determining a second parametric confidence limit for a specified confidence level based on said second standard deviation;

The first quantile is determined based on the first parameter confidence limit and the second parameter confidence limit.

With reference to the first possible implementation of the first aspect, in the fourth possible implementation of the first aspect, the determining the threshold corresponding to the set of pseudorange error correction sample values includes:

The threshold corresponding to the set of pseudorange error correction sample values is determined according to the mean excess function MEF.

With reference to the first aspect, in a fifth possible implementation manner of the first aspect, the acquiring at least two sets of pseudorange error correction sample values includes:

Acquiring at least two pseudorange error correction sample values according to a preset time interval;

Grouping the at least two pseudorange error correction sample values to obtain at least two groups of pseudorange error correction sample values.

In the present invention, at least two groups of pseudorange error correction sample values are obtained, and the first quantile and the first standard deviation corresponding to each group of pseudorange error correction sample values corresponding to the specified risk are determined, and then according to the total The operational risk determines the second quantile corresponding to the total operational risk of GBAS under the standard Gaussian distribution, and then determines the amplification factor according to the first quantile, the second quantile and the first standard deviation, and finally, determines the current quantile according to the amplification factor. The pseudorange correction value corresponding to the group pseudorange error correction sample value can accurately calculate the amplification factor through the above method, so that the calculated pseudorange correction value can envelope the actual error and effectively improve the continuity of the system.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description These are some embodiments of the present invention. For those skilled in the art, other drawings can also be obtained according to these drawings without any creative effort.

FIG. 1 is a flowchart of an error envelope method for a satellite navigation ground-based augmentation system based on extreme value theory provided by an embodiment of the present invention.

detailed description

In order to make the purpose, technical solutions and advantages of the embodiments 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 drawings in the embodiments of the present invention. Obviously, the described embodiments It is a part of embodiments of the present invention, but not all embodiments. 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.

Fig. 1 is the flow chart of the error envelope method of the satellite navigation ground-based augmentation system based on extreme value theory provided by the embodiment of the present invention, as shown in Fig. 1, the method of the present embodiment may include:

Step 101: Obtain at least two groups of pseudorange error correction sample values.

Specifically, at least two pseudorange error correction sample values are acquired according to a preset time interval, and then at least two pseudorange error correction sample values are grouped to obtain at least two groups of pseudorange error correction sample values.

In practical applications, usually, the GBAS ground reference station calculates a pseudorange difference correction value at the current moment every 0.5 seconds, and correspondingly obtains a sample value of the pseudorange correction error. Then obtain at least two sample values of pseudorange correction errors at all times, and filter the sample values of pseudorange correction errors at all times to obtain independent sample values of pseudorange correction errors.

A typical screening method is as follows: first, sample the pseudorange correction error sample values at all times at a time interval of 100 seconds, and then group the sampled pseudorange correction error sample values according to their corresponding elevation angles, that is, the elevation angle is 0 The pseudorange correction error sample values from 5° to 5° are one group, the pseudorange correction error sample values from 5° to 10° are one group, and so on, and a total of 18 groups of pseudorange correction error sample values are obtained.

Step 102: Perform the following operations on each set of pseudorange error correction sample values: that is, perform the methods in steps 103 to 105 on each set of pseudorange correction error sample values.

For example: at least 50000 pseudorange error correction sample values are obtained according to a preset time interval, and then at least 50000 pseudorange error correction sample values are grouped to obtain 18 groups of pseudorange error correction sample values.

Step 103: Determine the first quantile and the first standard deviation corresponding to each group of pseudorange error correction sample values with specified risk.

Specifically, it is first necessary to determine the threshold corresponding to the pseudo-range error correction sample value of this group. Let {X _i }, i=1, ..., N be the pseudo-range error sample value of a group after screening, and N be the pseudo-range error correction sample value of this group. For the number of range error sample values, a mean excess function (Mean Excess Function, MEF for short) is used to determine the threshold corresponding to the group of pseudo-range error correction sample values.

The specific method to determine the threshold is:

Arrange the pseudorange error sample values in {X _i } in descending order to obtain the order statistics X ₁ ≤X ₂ ≤…≤X _N , where MEF is defined as:

Where N _u is the number of samples exceeding the threshold _u , Xi ′ is the sample value greater than u among the pseudorange error sample values, and E(u) represents the mathematical expectation of the exceeding amount of the samples greater than the threshold.

Draw a curve composed of points (u, E(u)) in the two-dimensional coordinate axis according to the above formula of MEF. By selecting sufficiently large u ₀ , E(x) is a linear function with approximately positive slope when x≥u ₀ , and u ₀ is taken as the threshold.

It is worth noting that the threshold u ₀ usually selected is between 1.96 and 2.58 times the sample standard deviation σ _samp .

Then, according to the resampling method, at least two groups of resampled sample values corresponding to each group of pseudorange error correction sample values are obtained.

According to the GBAS pseudo-range error samples, the re-sampling method is used to obtain re-sampled samples of multiple sets of pseudo-range errors;

The resampling method can adopt methods such as bootstrap.

Taking the bootstrap method as an example, B resampling is performed on {X _i } to obtain B groups of resampling samples:

{X ^* _bi }, i=1,...,N; b=1,...,B.

Furthermore, according to the threshold corresponding to the group of pseudorange error correction sample values and each group of resampled sample values, the excess sample value in each group of resampled sample values is determined, and the excess sample value is greater than the threshold in each group of resampled sample values The difference between the value and the threshold,

The excess sample value can be calculated according to the following formula, Y=X ^* _a -u ₀ , (X ^* _a ∈ X ^* _bi )>u ₀ , where Y is the excess sample value.

Finally, the first quantile is determined from the excess sample values.

Optionally, determine the first quantile based on the excess sample value, including:

Determine the first probability of exceeding the threshold in this group of resampling sample values according to the excess sample value corresponding to this group of resampling sample values;

Determine the second standard deviation of the excess sample value corresponding to this group of resampled sample values;

According to the existing research on the GBAS pseudorange error, the kernel of the probability distribution of the GBAS pseudorange error obeys the Gaussian distribution, and the tail of the probability distribution is unknown, but it is between the Gaussian distribution and the Laplace distribution. According to the extremum theory, no matter what form the distribution of GBAS pseudorange error X is, its maximum value obeys type I extreme value distribution (Gumbel distribution). Further, its excess Y obeys the type I Pareto (Pareto) distribution:

F _e (y) = G ₁ (y) = 1-exp{-y/σ ₁ }

Wherein, F _e (y) is the probability distribution of the excess amount Y, and σ ₁ is the second standard deviation of the excess amount Y.

The relationship between the probability distribution F _e (y) of the excess amount Y and the probability distribution F _r (x) of the pseudo-range error X is:

Therefore: According to the above formula, it can be seen that:

F _r (x)＝(1-P _tail )+P _tail F _e (xu),x>u

where P _tail =1-F _r (u).

The parameters that need to be estimated in the above model are the first probability P _tail and σ ₁ .

The parameter estimate of P _tail is the empirical distribution of each resampling sample:

That is, P _tail =m/n

The maximum likelihood method is used to estimate σ ₁ , and its estimated value is:

σ ₁ =E(Y)

That is, the first quantile can be determined according to the estimated _first probability _Ptail and the second standard deviation σ1.

Optionally, the first quantile is determined according to the first probability and the second standard deviation, including:

Confidence tests were performed on the estimated upper bounds of P _tail and σ.

Let the empirical α quantiles of the parameter values {P ^* _tail,b } and {σ ^* _b } estimated from the resampled samples of Group B be the upper bounds of α for the confidence of _Ptail and σ.

According to parameter confidence limits and parameter confidence limits Determine the magnification factor k _inf .

Further, the first parameter confidence limit P ^* _tail,B (α) corresponding to the estimated first probability P _tail and the first parameter confidence limit σ ^* _B (α) corresponding to the second standard deviation σ ₁ are banded enter:

F _r (x)＝(1-P _tail )+P _tail F _e (xu),x>u

The probability distribution of the GBAS pseudorange error is obtained:

Finally, the first quantile is determined according to the first parameter confidence limit P ^* _tail,B (α) and the second parameter confidence limit σ ^* _B (α).

Among them, the first quantile is calculated according to the following formula:

Among them, Q _r,risk is the first quantile, u ₀ is the threshold, P ^* _tail,B (α) is the confidence limit of the first parameter, σ ^* _B (α) is the confidence limit of the second parameter, P _risk It is the specified risk corresponding to GBAS.

Step 104: Determine the second quantile of the standard Gaussian distribution corresponding to the total GBAS operational risk according to the total operational risk of the ground-based augmentation system GBAS.

Step 105: According to the first quantile, the second quantile and the first standard deviation, determine the amplification factor corresponding to the pseudorange error correction sample value of this group.

Specifically, the amplification factor k _inf is determined according to the first quantile, the second quantile and the first standard deviation, including:

Determine the amplification factor k _inf according to the following formula:

k _inf ＝Q _r,risk /k _ffmd /σ _samp

Among them, Q _{r, risk} is the first quantile, k _ffmd is the second quantile, and σ _samp is the first standard deviation.

An embodiment of the present invention provides an error envelope method for a satellite navigation ground-based augmentation system based on extreme value theory, including: obtaining at least two sets of pseudorange error correction sample values, and determining each set of pseudorange error correction sample values corresponding to a specified The first quantile and the first standard deviation of the risk, and then according to the total operational risk of the ground-based augmentation system GBAS to determine the second quantile corresponding to the total operational risk of GBAS under the standard Gaussian distribution, and then according to the first quantile, The second quantile and the first standard deviation determine the amplification factor corresponding to the pseudorange error correction sample value of this group. Finally, the pseudorange correction value corresponding to the pseudorange error correction sample value of this group is determined according to the amplification factor. Through the above method, it can be accurately The amplification factor is calculated, so that the calculated pseudorange correction value can envelope the actual error and effectively improve the continuity of the system.

Those of ordinary skill in the art can understand that all or part of the steps for implementing the above method embodiments can be completed by program instructions and related hardware. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps comprising the above-mentioned method embodiments; and the aforementioned storage medium includes: Read-Only Memory (Read-Only Memory, ROM), Random Access Memory (Random Access Memory, RAM), magnetic Various media that can store program codes such as discs or optical discs.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: It is still possible to modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the various embodiments of the present invention. scope.

Claims (6)

1. a kind of error enveloping method of the satellite navigation foundation strengthening system based on extreme value theory, it is characterised in that including：

Obtain at least two groups pseudorange error calibration samples values；

Operations described below is performed to every group of pseudorange error calibration samples value：

Determining that this group of pseudorange error calibration samples value is corresponding has the first quantile and the first standard deviation for specifying risk；

Total GBAS operation risk under standard gaussian distribution is determined according to operation risk total ground strengthening system GBAS Corresponding second quantile；

This group of pseudorange error calibration samples are determined according to first quantile, second quantile and first standard deviation It is worth corresponding amplification factor；

The corresponding pseudo-range corrections value of this group of pseudorange error calibration samples value is determined according to amplification factor.

2. according to the method described in claim 1, it is characterised in that described to determine that this group of pseudorange error calibration samples value is corresponding The first quantile with specified risk, including：

Determine the corresponding threshold value of described group pseudorange error calibration samples value；

The corresponding at least two groups resampling sample values of described group pseudorange error calibration samples value are obtained according to resampling method；

It is worth corresponding threshold value according to described group pseudorange error calibration samples corresponding with described group pseudorange error calibration samples value At least two groups resampling sample values in every group of resampling sample value determine plussage in every group of resampling sample value Sample value, the plussage sample value is the value and the difference of the threshold value in every group of resampling sample value more than the threshold value Value；

First quantile is determined according to the plussage sample value.

3. method according to claim 2, it is characterised in that described to determine described first according to the plussage sample value Quantile, including：

Determined according to the corresponding plussage sample value of this group of resampling sample value in described group resampling sample value more than described First probability of threshold value；

Determine the second standard deviation of the corresponding plussage sample value of described group resampling sample value；

First quantile is determined according to first probability and second standard deviation.

4. method according to claim 3, it is characterised in that described according to first probability and second standard deviation First quantile is determined, including：

The first parameter confidence limit value of confidence level is specified according to first determine the probability；

Determined to specify the second parameter confidence limit value of confidence level according to second standard deviation；

First quantile is determined according to the first parameter confidence limit value and the second parameter confidence limit value.

5. method according to claim 2, it is characterised in that described described group pseudorange error calibration samples value pair of determination The threshold value answered, including：

According to averagely determining the corresponding threshold value of described group pseudorange error calibration samples value beyond flow function MEF.

6. according to the method described in claim 1, it is characterised in that at least two groups pseudorange error calibration samples values of the acquisition, Including：

At least two pseudorange error calibration samples values are obtained according to prefixed time interval；

At least two groups pseudorange error calibration samples values are grouped at least two pseudorange errors calibration samples value.