Beidou space signal integrity determination method based on non-Gaussian characteristic

Abstract

The invention provides a Beidou spatial signal integrity determination method based on non-Gaussian characteristics, which comprises the following steps of: firstly, calculating two-step Gaussian over-bound envelope distribution by using long-term empirical data according to a two-step Gaussian over-bound envelope method, then estimating a scale factor K according to a predefined integrity risk, and substituting each parameter into a spatial signal integrity standard; uREworst in a period of time is substituted into an integrity standard formula to be compared with a threshold value to judge whether a space signal is abnormal or not, and finally, the integrity standard is used for calculating the integrity risk of the satellite navigation system so as to verify whether the calculated integrity risk meets the integrity risk committed by a system manager or not. Meanwhile, an integrity index is provided for civil aviation and other navigation applications related to life safety. Aiming at the non-Gaussian characteristic of the Beidou space signal error, a two-step over-bound Gaussian envelope method is adopted to replace the traditional single-peak probability density function envelope, the feasibility and integrity are strictly proved and are tighter, and the method can be suitable for any empirical distribution.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and particularly to a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics. Background Art

[0002] The space signal error of GNSS is caused by the orbit and clock errors of broadcast ephemeris, and is considered to be the main factor endangering the positioning accuracy and integrity of the system. The manifestation of the space signal error reflects the basic service performance of the satellite, and the space signal ranging error is an important index for evaluating the service performance of GNSS. The user ranging accuracy is used to characterize the integrity of the space signal. Long-term statistical results show that the user ranging accuracy provided by BDS is somewhat conservative compared to the actual space signal performance. Directly using the broadcast user ranging accuracy as the space signal integrity threshold to monitor anomalies may not be the best choice. It is necessary to derive the monitoring threshold for BDS space signal anomalies by meeting the predefined integrity risk.

[0003] Due to the existence of systematic errors, the empirical distribution of BDS space signal errors does not strictly follow the standard Gaussian distribution. Using the standard Gaussian distribution to envelope the empirical distribution of BDS space signal errors that does not strictly follow the Gaussian distribution may cause problems such as missed detection risks or being overly conservative. In addition, the traditional symmetric unimodal cumulative probability density function envelope and bilateral envelope methods respectively have the disadvantages of only being applicable to symmetric unimodal distributions and having overly strict envelope requirements. The two-step Gaussian crossing envelope method effectively overcomes the disadvantages of the above two methods. The feasibility and integrity of this method have been strictly proven, and it can be applied to any empirical distribution.

[0004] Since there is currently no officially announced space signal integrity standard for BDS, current research mainly uses the integrity standard of GPS determined by the envelope distribution assuming the standard normal distribution for BDS. Traditional error envelope methods may not be applicable to empirical distributions with non-Gaussian distributions. Therefore, studying the integrity performance of space signal errors is of great significance for understanding the system operation status, anomaly monitoring, improving the system service performance, and developing future integrity algorithms related to life safety. Summary of the Invention

[0005] The present invention is to solve the problem of Beidou space signal judgment, and provides a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics, which can fit an envelope distribution for the non-Gaussian characteristics of Beidou space signal errors, proposes a space signal integrity standard more suitable for Beidou, and can more accurately detect Beidou space signal anomalies.

[0006] The present invention provides a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics, including the following steps:

[0007] S1. Calculate the worst-case space signal error probability density function and distribution based on the historical worst space signal error URE of Beidou satellites. The worst-case space signal error probability density distribution is a bimodal asymmetric thick-tailed distribution with significant non-Gaussian distribution characteristics. worst S2. Adjust the distribution of the worst-case space signal error probability density function to be approximately uniform by segmenting, defining forced adjustment according to unimodal distribution, symmetric distribution, and based on the regularized sample set, so that a symmetric unimodal probability density distribution f

[0008] satisfies: su

[0009]

[0010] where ε is the excess value.

[0011] That is, determine an empirical distribution of the Gaussian envelope of a symmetric unimodal distribution.

[0012] S3. Determine a unimodal symmetric Gaussian envelope distribution f ob The envelope probability density distribution f su , so that

[0013]

[0014] where f ob is a symmetric unimodal Gaussian envelope distribution, m is the mean value, and σ is the standard deviation.

[0015] S4. Return to step S2, and use the methods of steps S2 and S3 to obtain the symmetric unimodal Gaussian distribution on the other side for the unimodal on the other side.

[0016] That is: Determine a unimodal symmetric Gaussian distribution on each side of greater than zero and less than zero to envelope the greater than zero part and less than zero part of the unimodal symmetric Gaussian distribution determined in the first step respectively; and use the two distributions of (σ, -m) and (σ, m) on the left and right as the final envelope distributions, σ ob = max(σ ob right , σ ob left ) m = max(m right , m left ), σ ob left and σ ob right are the standard deviations of the left and right Gaussian envelope distributions respectively, and m left and m right are the mean values of the left and right Gaussian envelope distributions respectively.

[0017] S5. Take σ ob , m​left , m right Substitute it into the space signal integrity standard, calculate the cumulative probability density of the envelope distribution, and obtain the size factor K under different integrity risks left , K right ;

[0018] The space signal integrity standard is:

[0019]

[0020] Among them, URE worst,negative is the negative worst space signal ranging error, URE worst,positive is the positive worst space signal ranging error, P(*) is the probability, and ψ IR is the integrity risk level;

[0021] S6. Substitute the calculated worst space signal error URE worst,T to be determined within the specified period into the space signal integrity standard, compare it with the integrity risk threshold, and then determine whether there is an abnormal space signal;

[0022] If the worst space signal error URE worst,T to be determined is positive and less than the positive integrity risk threshold K right σ ob +m right , the space signal is normal; if the worst space signal error URE worst,T to be determined is positive and greater than or equal to the positive integrity risk threshold K right σ ob +m right , the space signal is abnormal;

[0023] If the worst space signal error URE worst,T to be determined is negative and greater than the negative integrity risk threshold K left σ ob +m left , the space signal is normal; if the worst space signal error URE worst,T to be determined is negative and less than or equal to the negative integrity risk threshold K left σ ob +m left , the space signal is abnormal;

[0024] Finally, the actual integrity risk of the satellite navigation system can be obtained based on the determined abnormal space signal, so as to determine whether the integrity risk promised by the constellation management party is met.

[0025] A Beidou space signal integrity determination method based on non-Gaussian characteristics is completed.

[0026] A method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to the present invention, as a preferred method, step S1 includes the following steps:

[0027] S11. Obtain long-term Beidou historical broadcast ephemeris and precise ephemeris;

[0028] S12. Calculate the orbit error and clock error after unifying the time and coordinate systems of the broadcast ephemeris and the precise ephemeris;

[0029] S13. Obtain the historical worst space signal error URE of the Beidou satellite according to the orbit error and clock error worst data, calculate the probability density function and distribution of the worst-case space signal error, and the probability density function distribution of the worst-case space signal error is a bimodal asymmetric tail distribution with significant non-Gaussian distribution characteristics.

[0030] A method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to the present invention, as a preferred method, step S12 includes:

[0031] S121. Unify the time system and coordinate system;

[0032] S122. Perform antenna phase center correction, and then subtract the satellite coordinates calculated from the broadcast ephemeris in the geocentric inertial coordinate system from the satellite coordinates given by the precise ephemeris and convert them to the orbit coordinate system to obtain the orbit error;

[0033] S123. Perform group delay correction, and then subtract the average value of the differences between the satellite broadcast clock errors and the precise clock errors of all satellites in the constellation from the difference between the satellite broadcast clock error and the precise clock error to obtain the clock error by taking the second difference.

[0034] A method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to the present invention, as a preferred method, in step S121, convert the Beidou time referenced by the Beidou broadcast ephemeris to the GPS time referenced by the precise ephemeris;

[0035] In step S122, modify the antenna reference centroid position of the precise ephemeris to the antenna phase center for phase center correction:

[0036]

[0037] where, [X CoM Y CoM Z CoM T and [X APC Y APC Z APC T are the satellite centroid and antenna phase center coordinates in the earth-centered earth-fixed coordinate system, respectively, [δX δY δZ]​​T is the phase center correction vector in the satellite-fixed coordinate system, and matrix A is the satellite attitude transformation matrix between the Earth-centered Earth-fixed coordinate system and the satellite-fixed coordinate system;

[0038] In step S122, the orbit error includes a radial vector, a tangential vector, and a normal vector, and the orbit error is: p = (δ R , δ A , δ C ):

[0039] where, δ R = e R ·δr, δ A = e A ·δr, δ C = e C ·δr;

[0040] δr = (ΔX, ΔY, ΔZ) is the difference between the satellite coordinates of the broadcast ephemeris after antenna center offset correction and the satellite coordinates of the precise ephemeris, and "·" represents the dot product;

[0041] e A = e' R ×e C , e R = e C ×e A ;

[0042] where, e R , e C and e A are the radial, tangential, and normal vectors, and "×" represents the cross product, and the result is still a vector;

[0043]

[0044] where, p brd = (p x , p y , p z ) is the satellite coordinate calculated from the broadcast ephemeris, and v brd = (v x , v y , v z ) is the instantaneous velocity of the satellite;

[0045] The obtained radial, normal, and tangential orbit errors are used to statistically analyze the accuracy using the root mean square error;

[0046] In step S123, the broadcast satellite clock error is based on the observation value of the B3I signal, and the precise satellite clock error is based on the dual-frequency ionospheric-free combined observation values of B1I and B3I to correct the time deviation caused by the antenna phase center deviation related to the frequency:

[0047]

[0048] Among them, δZ brd，3 is the phase center offset in the Z direction of the B3I signal used to determine the broadcast ephemeris and clock bias. δZ pre,1 and δZ pre,3 are the phase center offsets in the Z direction of B1I and B3I used to determine the precise ephemeris and clock bias respectively. f1 is the frequency of the B1I signal, f2 is the frequency of the B2I signal, and f3 is the frequency of the B3I signal;

[0049] The hardware delay is corrected by the following formula:

[0050]

[0051] Among them, δ tgd is the group delay parameter of the B1I signal in the broadcast ephemeris;

[0052] The broadcast clock bias considering the group delay and phase center offset correction is:

[0053] τ brd = τ brd,3 - δ′ tgd - δ PCO

[0054] Among them, τ brd,3 and τ brd are the satellite broadcast clock bias and the corrected satellite broadcast clock bias respectively.

[0055] For a BeiDou space signal integrity determination method based on non-Gaussian characteristics according to the present invention, as a preferred method, in step S1, the worst-case space signal error URE worst is:

[0056]

[0057] Among them, θ is the nadir angle of the line of sight of the satellite service area, γ is the nadir angle threshold at the edge of the satellite service area depending on the satellite orbital altitude, the function max(x) returns the x with the largest absolute value, δ R , δ A , δ C are the orbit error, and δτ is the clock bias.

[0058] For a BeiDou space signal integrity determination method based on non-Gaussian characteristics according to the present invention, as a preferred method, step S2 includes the following steps:

[0059] S21. Segment the probability density function of the worst-case space signal error;

[0060] S22. Modify the data distribution of each interval one by one starting from the left, ensuring that the data in each interval is equal to or greater than that in the previous interval to conform to the Gaussian unimodal distribution;

[0061] S23. Symmetrize the determined distribution on the left side to the right side as the right side distribution, set the probability q of the one-sided tail between the left tail and the right tail, and the middle data interval contains a probability of 1 - 2q, to obtain a data interval with a probability exceeding 50%;

[0062] S24. Define a regularized sample set so that the regularized sample set is approximately uniformly distributed with the same number of samples in each partition;

[0063] S25. Modify the probability density distribution f su , so that all scalars x satisfy the unimodal distribution, and

[0064]

[0065] S26.

[0066] Determine a unimodal symmetric Gaussian envelope distribution f ob envelope probability density distribution f su , so that

[0067]

[0068] where f ob is a symmetric unimodal Gaussian envelope distribution.

[0069] In a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to the present invention, as a preferred mode, in step S3, the Gaussian distribution N(m,σ) is a super-boundary distribution, and f ob can be used to replace the actual distribution.

[0070] In a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to the present invention, as a preferred mode, in step S5, the integrity risks 10 -7 , 10 -6 , 10 -5 , 10 -4 and 10 -3 of the MEO and IGSO size factors K left , K right .

[0071] In a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to the present invention, as a preferred mode, the Beidou satellite navigation system uses the integrity risk ψ IR of 10 -5 as the final judgment benchmark.

[0072] This method includes: calculating the ranging error of the space signal at the worst position based on the Beidou broadcast ephemeris, precise ephemeris, and precise clock offset products, and statistically obtaining the probability distribution of the signal ranging error at the worst position in the long-term history. The probability density of the worst space signal error of Beidou exhibits non-Gaussian characteristics of double peaks, symmetry, and thick tails. Using the long-term historical data as samples, the parameters of the overbound envelope distribution are calculated by the two-step overbound Gaussian envelope method. After substituting the fitted distribution coefficients into the space signal integrity standard, the scale factors of MEO and IGSO are estimated respectively with integrity risks of 10 -7 、10 -6 、10 -5 、10 -4 and 10 -3 ; Finally, the scale factors and distribution coefficients are substituted into the integrity standard formula as the final integrity standard.

[0073] Obtain the long-term Beidou historical broadcast ephemeris and precise ephemeris;

[0074] Unify the time system and coordinate system. Convert the Beidou Time referenced by the Beidou broadcast ephemeris to the GPS Time referenced by the precise ephemeris. Since the maximum gap between the reference frames of the broadcast ephemeris and the precise ephemeris is centimeter-level, considering the accuracy of the broadcast ephemeris approaching meter-level, the influence caused by the different reference frames is ignored when evaluating the accuracy of the broadcast ephemeris.

[0075] Phase center correction. The satellite positions calculated from the broadcast ephemeris and the precise ephemeris refer to the antenna phase center and the satellite centroid respectively. Before calculating the orbit error, the antenna reference centroid position of the precise ephemeris should be transformed to the antenna phase center.

[0076] Group delay correction. The BDS broadcast satellite clock offset is based on the observations of the B3I signal, but the precise satellite clock offset provided by the analysis center of Wuhan University is based on the dual-frequency ionospheric-free combination observations of B1I and B3I. The antenna phase center deviation and hardware delay deviation related to the frequency should be corrected. In addition, the hardware delay related to the frequency will also cause inconsistencies between the satellite clocks determined by different frequencies, and this inconsistency can be corrected by the group delay parameter in the broadcast ephemeris file.

[0077] After subtracting the satellite coordinates calculated from the broadcast ephemeris in the geocentric inertial coordinate system from the satellite coordinates given by the precise ephemeris and converting them to the orbital coordinate system, the orbit error is obtained. The orbit error is represented by three vectors: radial, tangential, and normal.

[0078] Calculate the average value of the differences between the broadcast clock offsets and the precise clock offsets of all satellites in the constellation, and then subtract this average value from the differences between the satellite broadcast clock offsets and the precise clock offsets to obtain the second difference as the clock offset.

[0079] Calculate the orbit error and clock error after unifying the time and coordinates of broadcast ephemeris and precise ephemeris. Calculate the worst-case space signal error based on the orbit error and clock error; assuming that the Earth is an ideal sphere, the worst-case space signal error can be expressed as:

[0080]

[0081] where θ is the nadir angle of the line of sight of the satellite service area, γ is the nadir angle threshold at the edge of the satellite service area depending on the satellite orbit altitude, and the function max(x) returns the x with the largest absolute value. Assuming that the user altitude cutoff angle is 0°, according to the satellite orbit altitude of the navigation system, γ for MEO is 13.2°, and γ for IGSO is 8.69°.

[0082] Analyze the statistical characteristics of the worst-case space signal error, and construct a mathematical model of the space signal integrity standard according to the statistical characteristics of the worst-case space signal error;

[0083] Calculate the model parameters according to the mathematical model of the space signal integrity standard;

[0084] The worst-case space signal ranging error is the maximum value of the instantaneous space signal ranging error of the satellite within the service area, and it is an important index for evaluating the integrity of the space signal.

[0085] Calculate the probability density function of the long-term worst-case space signal error and analyze its distribution characteristics.

[0086] Use the left and right Gaussian distributions to envelope the left and right sides of the empirical distribution of the worst-case space signal ranging error respectively, and its space signal integrity standard can be expressed as:

[0087] (1 + ε)[P(URE worst,negative ≤K left σ ob +μ left )

[0088] +P(URE worst,positive ≥K right σ ob +μ right )]≤ψ IR ;

[0089] In the formula, URE worst,negative and URE worst,positive represent the negative and positive worst-case space signal ranging errors respectively, ψ IR is the integrity risk of a certain level, m left and m right are the means of the left and right envelope distributions, σ ob is the standard deviation of the envelope distribution, ε is the excess value of the envelope distribution, and the scale factor Kob,left / right Highly dependent on parameters σ ob and m left and m right .

[0090] Use the two-step Gaussian envelope method to envelope the empirical distribution of the ranging error of the worst space signal, and calculate the distribution parameters σ ob and m left and m right , calculate the cumulative probability density of the envelope distribution, and determine the integrity risk of 10 -7 10 -6 10 -5 10 -4 10 -3 scale factors K of MEO and IGSO ob,left / right .

[0091] The present invention has the following advantages:

[0092] (1) Utilize the ranging error of the worst-case space signal of Beidou statistically over a long period, and adopt the error envelope method to construct a space signal integrity standard applicable to Beidou, filling the gap in the related field.

[0093] (2) Aiming at the non-Gaussian characteristics of the Beidou space signal error, adopt the two-step over-bound Gaussian envelope method to replace the traditional single-peak probability density function envelope. The two-step Gaussian over-bound envelope method overcomes the shortcomings of the traditional method, and its feasibility and integrity have been strictly proven, and it can be applied to any empirical distribution. The space signal integrity standard obtained by using this envelope method is also more rigorous theoretically. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 is a flowchart of a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics;

[0095] Figure 2 is a flowchart of the two-step Gaussian over-bound envelope method involved in a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics;

[0096] Figure 3 is a right-side two-step Gaussian envelope probability density distribution diagram obtained from steps S2 and S3 in a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics;

[0097] Figure 4 is a right-side two-step Gaussian envelope cumulative probability density distribution diagram obtained from steps S2 and S3 in a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics. DETAILED DESCRIPTION OF THE INVENTION

[0098] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0099] Embodiment 1

[0100] As Figures 1 to 4 shown, a method for determining the integrity of Beidou space signals based on non-Gaussian characteristics, the method includes the following steps:

[0101] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0102] S1. In this embodiment, the Beidou broadcast ephemeris from January 1, 2019 to June 2, 2021 is used, and the precise products provided by the IGS Analysis Center of Wuhan University during the corresponding period are selected.

[0103] Unification of time system and coordinate system. Convert the Beidou time referenced by the Beidou broadcast ephemeris to the GPS time referenced by the precise ephemeris. Since the maximum difference between the reference frames of the broadcast ephemeris and the precise ephemeris is centimeter-level, considering the accuracy of the broadcast ephemeris approaching meter-level, the influence caused by different reference frames is ignored when evaluating the accuracy of the broadcast ephemeris.

[0104] Phase center correction. The satellite positions calculated by the broadcast ephemeris and the precise ephemeris refer to the antenna phase center and the satellite centroid respectively. Before calculating the orbit error, the antenna reference centroid position of the precise ephemeris should be transformed to the antenna phase center. For each satellite, the coordinates of these two reference points can be converted to:

[0105]

[0106] In the above formula, [X CoM Y CoM Z CoM T and [X APC Y APC Z APC T are the satellite centroid and antenna phase center coordinates in the Earth-centered Earth-fixed coordinate system respectively, [δX δY δZ] T is the phase center correction vector in the satellite-fixed coordinate system, and the matrix A represents the satellite attitude conversion matrix between the Earth-centered Earth-fixed coordinate system and the satellite-fixed coordinate system.

[0107] ​​Group delay correction. The BDS broadcast satellite clock offset is based on the observations of the B3I signal, while the precise satellite clock offset provided by the analysis center of Wuhan University is based on the dual-frequency ionospheric-free combination observations of B1I and B3I. The time offset caused by the antenna phase center deviation and hardware delay related to frequency should be corrected.

[0108]

[0109] In the formula, δZ brd，3 is the phase center offset in the Z direction of the B3I signal used to determine the broadcast ephemeris and clock offset, δZ pre,1 and δZ pre,3 are the phase center offsets in the Z direction of B1I and B3I used to determine the precise ephemeris and clock offset respectively, and f1, f2, f3 represent different frequencies. In addition, the hardware delay related to frequency will also cause inconsistencies between the satellite clocks determined by different frequencies, and this inconsistency can be corrected by the group delay parameter in the broadcast ephemeris file. For BDS, the 3rd and 4th parameters of the 6th orbit in the broadcast ephemeris represent the hardware delays between B1I and B3I, and between B2I and B3I respectively. The hardware delay can be corrected by the following formula:

[0110]

[0111] In the formula, δ tgd is the group delay parameter of the B1I signal in the broadcast ephemeris. Therefore, the broadcast clock offset considering the group delay and phase center offset correction can be expressed as:

[0112] τ brd =τ brd,3 -δ′ tgd -δ PCO ;

[0113] In the formula, τ brd,3 and τ brd are the broadcast satellite clock offset and the corrected broadcast satellite clock offset respectively.

[0114] The difference between the satellite coordinates calculated from the broadcast ephemeris in the geocentric inertial coordinate system and the satellite coordinates given by the precise ephemeris is converted to the orbital coordinate system to obtain the orbital error. The orbital error is represented by three vectors: radial, tangential, and normal. The conversion process can be expressed as:

[0115]

[0116] p brd =(p x ,p y ,p z ) is the satellite coordinate calculated from the broadcast ephemeris, v brd =(v x ,v y, v z ) represents the instantaneous velocity of the satellite.

[0117] e A = e' R × e C , e R = e C × e A ;

[0118] e R , e C and e A represent the radial, tangential and normal vectors. "×" represents the cross product, and the result is still a vector. The orbit error can be expressed as:

[0119] δ R = e R · δr, δ A = e A · δr, δ C = e C · δr;

[0120] δr = (ΔX, ΔY, ΔZ) represents the difference between the satellite coordinates of the broadcast ephemeris after antenna center offset correction and the satellite coordinates of the precise ephemeris. "." represents the dot product, and the result is a number. Finally, the orbit error can be expressed as p = (δ R , δ A , δ C ). After calculating the radial, normal and tangential orbit errors, the root mean square error is used to statistically analyze the accuracy.

[0121] Calculate the average value of the difference between the broadcast clock error and the precise clock error of all satellites in the constellation, and subtract this average value from the difference between the broadcast clock error and the precise clock error of the satellite to obtain the clock error as the second difference.

[0122] The worst-case space signal ranging error is the maximum value of the instantaneous space signal ranging error of the satellite in the service area, and it is an important indicator for evaluating the integrity of the space signal. Assuming that the earth is an ideal sphere, the worst-case space signal error can be expressed as:

[0123]

[0124] θ is the nadir angle of the line of sight of the satellite service area, γ is the nadir angle threshold at the edge of the satellite service area depending on the satellite orbit altitude, and the function max(x) returns the x with the largest absolute value. Assuming that the user altitude cut-off angle is 0°, according to the satellite orbit altitude of the navigation system, γ for MEO is 13.2°, and γ for IGSO is 8.69°.

[0125] Calculate the long-term worst-case spatial signal error probability density function and analyze its distribution characteristics. The probability distribution presents a bimodal asymmetric heavy-tailed distribution with significant non-Gaussian distribution characteristics as Figure 3 shown, showing obvious non-Gaussian characteristics.

[0126] Use the two-step Gaussian overbound envelope to calculate the envelope distribution parameters to envelope the empirical distribution of the worst-case spatial signal error, as Figure 3 、 4 shown.

[0127] Specifically, it includes: first, determine a symmetric unimodal envelope distribution as the intermediate distribution, and then determine the left and right Gaussian distributions to envelope the left and right sides of the intermediate distribution respectively.

[0128] S2. As Figure 3 、 4 shown, taking the right distribution as an example, determine a symmetric unimodal distribution f su satisfying:

[0129]

[0130] where ε is the excess value, which is used to solve the problem that the process of determining f su is too conservative.

[0131] Specifically, determine f su according to the following steps:

[0132] (1) Divide the empirical distribution into intervals of a certain size. The size of the segments is a parameter that can be adjusted according to the required accuracy, and it can effectively smooth the empirical distribution.

[0133] (2) Forcefully adjust the data distribution of each interval according to the definition of the unimodal distribution. Specifically, start from the left and modify the data distribution of each interval one by one to ensure that the data in each interval is equal to or greater than that in the previous interval.

[0134] (3) Stop (2) when the left side of the distribution is determined, and then add a data interval with a probability exceeding 50%. Symmetrize the distribution determined on the left side to the right side as the right distribution. Set the probability of the one-sided tail to q between the left tail and the right tail, then the middle data interval contains a probability of 1 - 2q. The middle data interval is set to ensure that the distribution is unimodal, and the median and mean of the obtained distribution are also different from the empirical distribution.

[0135] (4) Assume a uniform distribution within each partition. Then define a regularized sample set so that it can approximate the uniform distribution with the same number of samples within each partition.

[0136] (5) Modify f su so that (3) holds for all x.

[0137] S3. As shown in, taking the right - hand distribution as an example, determine a symmetric unimodal Gaussian envelope distribution \(f\) Figure 3 , 4 such that: ob ,

[0138]

[0139] If these two conditions are met, the Gaussian distribution \(N(m,\sigma)\) will be a right - hand super - boundary distribution. That is to say, when calculating the integrity risk, we can use \(f\) ob to replace the actual distribution.

[0140] S4. Then, after determining the symmetric unimodal Gaussian distribution on the left - hand side in the same way, the maximum values of the standard deviations and means of the two left - hand and right - hand distributions should be taken as the final Gaussian distribution parameters, \(\sigma=\max(\sigma\) right ,\(\sigma\) left ) and \(m = \max(m\) right ,m\) left ).

[0141] S5. Taking the two left - hand and right - hand distributions of \((\sigma,-m)\) and \((\sigma,m)\) as the final envelope distribution, finally, determine the space - signal integrity standard by combining the predefined integrity risk and envelope - distribution parameters.

[0142] Its space - signal integrity standard can be expressed as:

[0143]

[0144] where URE worst,negative and URE worst,positive represent the negative and positive worst - case space - signal ranging errors, \(\psi\) IR is an integrity risk of a certain level, \(\mu\) left and \(\mu\) right are the means of the left - hand and right - hand envelope distributions, \(\sigma\) ob is the standard deviation of the envelope distribution, \(\varepsilon\) is the excess value of the envelope distribution, and the scale factor \(K\) ob,left / right is highly dependent on the parameters \(\sigma\) ob ,\(\mu\) left and \(\mu\) right .

[0145] S6. Use the two - step Gaussian - envelope method to envelope the empirical distribution of the worst - case space - signal ranging error, calculate the distribution parameters \(\sigma\) ob and \(\mu\) left and \(\mu\) right , calculate the cumulative probability density of the envelope distribution, and determine the integrity risks \(10\) -7 , \(10\) -6 , \(10\) -5 , \(10\)-4 and 10 -3 scale factors K of MEO and IGSO for ob,left / right 。

[0146] In this embodiment, the two-step Gaussian crossing envelope method is used to calculate the two-step Gaussian crossing envelope distribution for the empirical distribution from January 2019 to May 2021. The data from June 2021 to November 2022 is used as the verification distribution to verify the envelope effect of the two-step Gaussian envelope distribution on the empirical distribution and the verification distribution. The two-step crossing Gaussian envelope distribution has a good envelope effect on the empirical distribution and the verification distribution with integrity risk from 10 -3 to 10 -7 The two-step Gaussian crossing distribution has a good envelope effect on the empirical distribution and the verification distribution, and at the same time verifies the conservativeness of the envelope distribution, indicating the effectiveness of the two-step Gaussian crossing envelope method. In actual use, according to the modeling method and process provided by this technical solution, first use long-term empirical data to calculate the two-step Gaussian crossing envelope distribution according to the two-step Gaussian crossing envelope method, then estimate the scale factor K according to the predefined integrity risk, and substitute each parameter into the space signal integrity standard. Then substitute the URE worst，T within the specified period into the integrity standard formula to compare with the threshold and judge whether the space signal is abnormal. Finally, obtain the integrity risk of the satellite navigation system according to the probability of the space signal being abnormal, and at the same time verify whether the integrity risk meets the integrity risk promised by the system management party.

[0147] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and should be covered by the protection scope of the present invention.

Claims

1. A method for determining the integrity of Beidou space signals based on non-Gaussian characteristics, characterized in that: The following steps are involved: S1. Based on the historical worst spatial signal error URE of Beidou satellite worst The worst-case spatial signal error probability density function and distribution are calculated. The worst-case spatial signal error probability density distribution is a bimodal asymmetric thick-tailed distribution with significant non-Gaussian distribution characteristics. S2, by segmentation, forced adjustment according to the unimodal distribution definition, symmetrical distribution and adjusting the distribution of the worst-case spatial signal error probability density function to be approximately uniformly distributed according to the regularized sample set, so that a symmetrical unimodal probability density distribution f su satisfy: Among them, ε is the excess value; S3. Determine a unimodal symmetrical Gaussian envelope distribution f ob Envelope of the probability density distribution f su ,make Where m is the mean value and σ is the standard deviation; S4, return to step S2, use the method of steps S2 and S3 to obtain the symmetrical unimodal Gaussian distribution of the other side, and use the two distributions (σ, -m) and (σ, m) as the final envelope distribution, σ ob =max(σ obright ,σ obleft )m=max(m right ,m left ), σ obleft , σ obright are the standard deviations of the left and right Gaussian envelope distributions, m left 、m right are the means of the left and right Gaussian envelope distributions, respectively; S5, σ ob 、m left 、m right Substituting into the spatial signal integrity standard, the cumulative probability density of the envelope distribution is calculated to obtain the size factor K under different integrity risks. left , K right ; The spatial signal integrity standard is: Among them, URE worst,negative is the negative worst spatial signal ranging error, URE worst,positive is the positive worst spatial signal ranging error, P(*) is the probability, ψ IR is the integrity risk level; S6. The worst spatial signal error URE to be determined calculated within the specified period T is worst,T Substitute the space signal integrity standard into the integrity risk threshold and compare it with the integrity risk threshold to determine whether a space signal anomaly occurs. According to the determined space signal anomaly, the actual integrity risk ψ of the satellite navigation system is obtained. IR ; If the worst spatial signal error URE to be determined worst,T Is a positive number and less than the integrity risk positive threshold K right σ ob +m right When the spatial signal is normal; if the worst spatial signal error URE to be determined worst,T is a positive number and is greater than or equal to the integrity risk positive threshold K right σ ob +m right When the spatial signal is abnormal; If the worst spatial signal error URE to be determined worst,T It is a negative number and is greater than the negative integrity risk threshold K left σ ob +m left When the spatial signal is normal; if the worst spatial signal error URE to be determined worst,T is a negative number and is less than or equal to the integrity risk negative threshold K left σ ob +m left When the spatial signal is abnormal; Finally, the actual integrity risk of the satellite navigation system is obtained based on the determined space signal anomaly, so as to determine whether the integrity risk promised by the constellation management party is met; A method for determining the integrity of Beidou space signals based on non-Gaussian characteristics is completed.

2. The method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to claim 1, characterized in that: Step S1 includes the following steps: S11. Obtain long-term Beidou historical broadcast ephemeris and precise ephemeris; S12, unify the time and coordinate systems of the broadcast ephemeris and the precise ephemeris and calculate the orbit error and clock error; S13, obtaining the historical worst spatial signal error URE of the Beidou satellite according to the orbit error and the clock error worst The worst-case spatial signal error probability density function and distribution are calculated based on the data. The worst-case spatial signal error probability density function distribution is a bimodal asymmetric thick-tailed distribution with significant non-Gaussian distribution characteristics.

3. The method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to claim 2, characterized in that: Step S12 includes: S121, unified time system and coordinate system; S122, perform antenna phase center correction, then make a difference between the satellite coordinates calculated by the broadcast ephemeris in the geocentric inertial coordinate system and the satellite coordinates given by the precise ephemeris, and then convert them to the orbital coordinate system to obtain the orbital error; S123, perform group delay correction, then deduct the difference between the satellite broadcast clock error and the precise clock error from the average value of the difference between the satellite broadcast clock errors and the precise clock errors in the constellation to obtain the clock error by performing a quadratic difference.

4. The method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to claim 3, characterized in that: In step S121, the Beidou time referenced by the Beidou broadcast ephemeris is converted into the GPS time referenced by the precise ephemeris; In step S122, the antenna reference centroid position of the precise ephemeris is changed to the antenna phase center to perform phase center correction: Among them, [X CoM Y CoM Z CoM ] T and [X APC Y APC Z APC ] T are the satellite center of mass and antenna phase center coordinates in the Earth-centered Earth-fixed coordinate system, [δX δY δZ] T is the phase center correction vector in the satellite-fixed coordinate system, and matrix A is the satellite attitude transformation matrix between the Earth-centered Earth-fixed coordinate system and the satellite-fixed coordinate system; In step S122, the orbit error includes a radial vector, a tangential vector and a normal vector, and the orbit error is: p = (δ R ,δ A ,δ C ): among them,d R =e R ·δr,δ A =e A ·δr,δ C =e C ·δr; δr=(ΔX, ΔY, ΔZ) is the difference between the satellite coordinates of the broadcast ephemeris and the satellite coordinates of the precise ephemeris after the antenna center offset correction, "·" represents the dot product; And A =and′ R ×e C ,And R =and C ×e A ; Among them, e R 、e C and e A are radial, tangential and normal vectors, "×" represents cross product, and the result is still a vector; Among them, p brd =(p x ,p y ,p z ) is the satellite coordinates calculated by broadcast ephemeris, v brd =(v x ,v y ,v z ) is the instantaneous velocity of the satellite; The obtained radial, normal and tangential orbit errors are used to calculate the accuracy using the root mean square error; In step S123, the broadcast satellite clock error is based on the observation value of the B3I signal, and the precise satellite clock error is based on the dual-frequency deionization combined observation value of B1I and B3I to correct the time deviation caused by the frequency-related antenna phase center deviation: Among them, δZ brd，3 is the phase center offset in the Z direction of the B3I signal used to determine the broadcast ephemeris and clock error, δZ pre,1 and δZ pre,3 are the Z-direction phase center offsets of B1I and B3I respectively used to determine precise ephemeris and clock errors, f1 is the frequency of the B1I signal, f2 is the frequency of the B2I signal, and f3 is the frequency of the B3I signal; The hardware delay is corrected by: Among them, δ tgd is the group delay parameter of the B1I signal in the broadcast ephemeris; The broadcast clock error considering group delay and phase center offset correction is: t brd =t brd,3 -d′ tgd -d PCO Among them, τ brd,3 and τ brd They are the satellite broadcast clock error and the corrected satellite broadcast clock error.

5. The method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to claim 1, characterized in that: In step S1, the worst spatial signal error URE worst for: Among them, θ is the nadir angle of the satellite service area line of sight, γ is the nadir angle threshold of the edge of the satellite service area line of sight that depends on the satellite orbit altitude, and the function max(x) returns the x with the largest absolute value, δ R ,δ A ,δ C is the orbit error, and δτ is the clock error.

6. The method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to claim 1, characterized in that: Step S2 includes the following steps: S21, segmenting the worst-case spatial signal error probability density function; S22, starting from the left, modify the data distribution of each interval one by one, ensuring that the data of each interval is equal to or greater than the data of the previous interval to conform to the Gaussian unimodal distribution; S23, symmetrically distribute the distribution determined on the left side to the right side as the right side distribution, set the probability q of the one-sided tail between the left tail and the right tail, and the middle data interval contains the probability of 1-2q, and obtain the data interval with a probability exceeding 50%; S24, defining a regularized sample set so that the regularized sample set is approximately uniformly distributed in each partition using the same number of samples; S25. Modify the probability density distribution f su , so that all scalars x satisfy a unimodal distribution, and S26. Determine a unimodal symmetrical Gaussian envelope distribution f ob Envelope of the probability density distribution f su ,make 7. The method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to claim 1, characterized in that: In step S3, the Gaussian distribution N(m,σ) is a super-boundary distribution and can be obtained by f ob instead of the actual distribution.

8. The method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to claim 1, characterized in that: In step S5, the integrity risk 10 is obtained. -7 , 10 -6 , 10 -5 , 10 -4 and 10 -3 The size factor K of MEO and IGSO left , K right .

9. The method for determining the integrity of Beidou space signals based on non-Gaussian characteristics according to claim 8, characterized in that: BeiDou satellite navigation system with integrity risk IR For 10 -5 as the final basis for judgment.

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