Robust positioning method considering correlation between satellites

Abstract

The present invention proposes a robust positioning method that takes correlation into account, which effectively solves the problem of erroneous positioning failures caused by strong correlation between observation values ​​and improves positioning accuracy. Based on numerical simulation and result analysis, when there are many observable satellites, the correlation between satellites is weak; as the number of observed satellites decreases, the correlation between satellites becomes stronger. The chi-square global test and the w local test can effectively detect and identify faults; the correlation between satellites is weak, and the fault identification method has a high probability of correctly identifying the fault location; as the correlation between satellites becomes stronger, the probability of erroneously locating the fault location becomes higher. The robust positioning method that takes satellite correlation into account proposed by the present invention adopts a weight function processing strategy for adaptive robustness in a satellite strong correlation environment, which effectively improves positioning accuracy.

Description

Technical Field

[0001] The invention relates to the field of satellite navigation technology, and in particular to an anti-error positioning method taking into account the correlation between satellites. Background Art

[0002] The Global Navigation Satellite System (GNSS) can provide accurate position, speed and time information to users around the world. It is widely used in military and civilian fields such as geodesy, deformation monitoring, urban rail transit and unmanned driving, and is an important layout for national strategic development. With the official launch of the BeiDou-3 global satellite navigation system, applications based on "BeiDou+" and "+ BeiDou" will flourish. However, satellite signals are susceptible to external interference, such as high-rise buildings, tree-lined areas and tunnels. Abnormal observations will cause a sharp drop in positioning performance. These abnormal values ​​must be detected and eliminated in a timely manner. Therefore, the study of positioning methods with robustness is an important way to improve positioning reliability.

[0003] Many scholars have conducted extensive research on fault detection and isolation methods for satellite navigation. Receiver Autonomous Integrity Monitoring (RAIM) based on least squares residual is the most important fault detection and isolation method (FDE), which is widely used in the aviation field. It mainly includes pseudorange comparison method, least squares residual method and parity vector method. This method classifies the fault into a function model. Another method classifies the fault into a random model and improves the RAIM algorithm by using robust estimation methods, retaining all observations but down-weighting potential observations, such as the Danish method, R estimation, M estimation, S estimation and multi-segment method (Institute of Geodesy & Geophysics III, IGGIII) weight method, etc., to adaptively improve the robustness of the positioning method. By considering the relationship between different statistical parameters, an optimized FDE scheme is proposed to reduce the false alarm rate of the FDE algorithm. In order to improve the performance of RAIM and FDE, multi-GNSS constellation fusion can significantly improve the performance of single / dual constellation system fusion. In addition, for decades, many scholars have used the Kalman filter method (KF) to study FDE in GNSS integrity monitoring, and statistical tests are usually based on the new information vector. However, due to the relatively low accuracy of pseudorange observations, autonomous integrity monitoring based on pseudorange is limited to meter-level accuracy. With the integrity requirements for high-precision positioning, the KF-based FDE method has been further studied using carrier phase as the main observation data. However, both the least squares residual-based and KF-based FDE methods assume that the GNSS observations are uncorrelated. In practical applications, GNSS observations are correlated, especially in restricted observation environments, where satellites show strong correlation. Affected by the correlation, GNSS observations will reduce the reliability and accuracy of standard KF positioning, as well as the performance of the FDE algorithm, including the determination of the test statistic and the minimum detectable bias (MDB). One of the reasons is that fault value detection sometimes mistakenly identifies a normal measurement value as a fault value, that is, retains the fault value and eliminates the normal observation value. This type of event is called the third type of error, which will have a serious impact on the positioning results.

[0004] The strong correlation between abnormal satellite observations will cause the positioning performance of the traditional FDE method to drop sharply. In order to overcome the limitations of the existing methods discussed above.

[0005] Based on the above problems, the present invention proposes a robust estimation method which takes into account the correlation between satellites on the basis of the existing FDE. The faults are detected by the chi-square global test and identified by the w local test. If there is a strong correlation between the satellites, the weight function is used to adaptively process the outliers. The method is applied to the GNSS positioning example, and the robust method proposed in this paper is analyzed and verified. Summary of the invention

[0006] In order to solve the above technical problems, the present invention proposes a robust estimation method that takes into account the correlation between satellites. Faults are detected by chi-square global test and identified by w local test. If there is a strong correlation between satellites, the weight function is used to adaptively process outliers, which effectively solves the problem of erroneous positioning failures caused by strong correlation between observations and improves positioning accuracy.

[0007] To achieve the above object, the technical solution adopted by the present invention is:

[0008] The robust positioning method taking into account the correlation between satellites is characterized by comprising the following steps:

[0009] S1: Anti-differential positioning analysis:

[0010] First, the number of satellites is determined based on satellite signals, and then a global inspection is performed to detect faults. If the fault does not exist, that is, the fault detection is invalid, positioning and solving are performed. If the fault does exist, local inspection is used to identify the fault.

[0011] If the correlation coefficient ρ between the observation values ​​of the fault is less than the set threshold, the observation value corresponding to the maximum test value is directly eliminated and the positioning solution is performed again.

[0012] If the correlation coefficient ρ between the observations with faults is greater than the set threshold, the identified fault may occur on the i-th or k-th observation. The weight function is used to adaptively process the fault value. Therefore, a specific weight function needs to be selected to reduce the weight of the i-th and k-th observations.

[0013] The IGGIII weight function expression is:

[0014]

[0015] Where: k 0 and k 1 is a constant threshold parameter, k 0 Take 1.345, k 1 Take 3, v i Standardize the residual for the ith element, and use the equivalent weight function to adaptively reduce or set the weight of the abnormal measurement to zero, thereby obtaining an estimated value;

[0016] S2: Verification and Analysis:

[0017] The simulation data of Beidou satellite navigation system is used for calculation, the dynamic running trajectory of ground vehicles is simulated, and the visible satellites are simulated to be blocked, which will deteriorate the spatial geometric structure of the observed satellites and cause strong correlation in the observed values. Single faults and multiple faults are added respectively, and the positioning solution results of the robust positioning method that takes into account the correlation between satellites are compared and analyzed;

[0018] S21: When a single fault is added:

[0019] When the correlation between satellites is weak or strong, a single fault value is added to the pseudorange respectively, and then the performance of fault detection and isolation is compared and analyzed when the correlation between satellites is weak or strong.

[0020] When the correlation between satellites is weak: when a fault is detected, the fault location can be correctly located and eliminated.

[0021] When the satellite correlation is strong: When a fault is detected, adaptive processing can be performed based on the correlation, and robust processing can be performed to locate the fault.

[0022] S22: When multiple failures are added:

[0023] When the correlation between satellites is weak and when the correlation between satellites is strong, single fault values ​​are continuously added to their pseudoranges, and then the performance of fault detection and isolation when the correlation between satellites is weak and when the correlation between satellites is strong is compared and analyzed.

[0024] When the correlation between satellites is weak: it is possible to detect and identify faults occurring in all epochs and locate the faults.

[0025] When the satellite correlation is strong: The stronger the satellite correlation is, the lower the correct recognition rate is. The correct rates of fault detection and recognition are 81.756% and 66.780%. The positioning accuracy is improved through adaptive anti-error.

[0026] As a preferred technical solution of the present invention: in step S1, assuming that there is no fault value in the measurement, the least squares estimation of the unknown parameters in the measurement can be based on the following function model and random model:

[0027] v=Ax-l (2)

[0028] Σ=σ 0 2 Q=σ 0 2 P -1 (3)

[0029] Where: x is a t×1 unknown parameter vector; v is an n×1 residual vector; A is an n×t design matrix; l is an n×1 measurement vector; Σ is the positive definite variance covariance matrix of the measured values; σ 0 2 is the prior variance factor; Q is the covariance matrix; P is the weight matrix,

[0030] The estimated and solved variance for the unknown parameters is:

[0031]

[0032]

[0033] The corresponding residual vector and its covariance are solved as follows:

[0034] v=(I-(A T PA) -1 A T Pl)l (6)

[0035] Q v =P -1 -A(A T PA) -1 A T (7)

[0036] As a preferred technical solution of the present invention: in step S1, the global inspection is specifically as follows:

[0037] The satellite system is tested for gross errors by using the residual as a hypothesis test statistic, and the variance factor for constructing the detection fault is determined as:

[0038]

[0039] in: is the posterior variance factor, t is the number of unknown parameters,

[0040] When the satellite system has no faults, the function follows a centralized chi-square distribution:

[0041]

[0042] Where: nt is the degree of freedom, α is the significance level,

[0043] If the variance factor ratio exceeds a given threshold, it is determined that a fault exists; otherwise, it is determined that no fault occurs.

[0044] As a preferred technical solution of the present invention: in step S1, the local inspection is specifically as follows:

[0045] To test whether there are outliers in the measurements, the following hypotheses need to be tested:

[0046]

[0047] Assume that the fault occurs at the i-th observation value, h i is a vector whose i-th element is equal to 1 and other elements are equal to 0. Fault detection and identification can be derived from the mean shift model:

[0048]

[0049] Using the block matrix, the fault size can be obtained as:

[0050]

[0051] The variance of the estimated fault value can be expressed by the error propagation law:

[0052]

[0053] Therefore, the fault test statistic on the i-th observation can be expressed as:

[0054]

[0055] When there is no fault on the observed value, that is, Then i It should obey the standard normal distribution. In this case, the null hypothesis H 0 On the contrary, when there is a fault, Then i The expectation is no longer zero, so the alternative hypothesis H 1 Established,

[0056] The expected occurrence size of the i-th fault value statistic is δ d Offset:

[0057]

[0058] Where: d =N 1-α / 2 (0,1)+N 1-β (0,1) is the non-centralization parameter,

[0059] If the expected offset of the fault value statistic is δ d , then the MDB of the i-th observation is:

[0060]

[0061] The correlation coefficient between the i-th and k-th observations is:

[0062]

[0063] Where: |ρik |=|ρ ki |≤1.

[0064] As a preferred technical solution of the present invention: in step S2,

[0065] When simulating through the Beidou satellite navigation system, 35 satellites and a simulated vehicle are set in the simulation process. The 35 satellites include 5 geostationary orbit satellites, 3 inclined geosynchronous orbit satellites and 27 medium earth orbit satellites, among which 01-27, 28-32 and 33-35 are the numbers of medium earth orbit satellites, geostationary orbit satellites and inclined geosynchronous orbit satellites respectively. The simulated vehicle running time is 4476s in total, and the simulated vehicle travels on north-south or east-west streets.

[0066] As a preferred technical solution of the present invention: at the four epochs of observation time 1000s, 1500s, 2000s and 3000s, the numbers of visible satellites are 8, 7, 6 and 5 respectively.

[0067] As a preferred technical solution of the present invention: in step S21, when the number of observed satellites is equal to 5, fault detection can be performed, but fault identification cannot be performed. When the number of observed satellites is greater than 6, fault detection and identification can be performed.

[0068] There are 8 satellites in 1000s, and the correlation between satellites is weak. There are 6 satellites in 2011s, and the correlation between satellites is strong. A fault value of 15m is added to the pseudoranges of satellite No. 20 in 1000s and satellite No. 19 in 2011s, respectively. When calculating, the false alarm rate is set to α as 1%, the missed detection rate is set to β as 20%, the threshold of the w statistic is 3.291, and the correlation coefficient threshold ρ is set to 0.9.

[0069] As a preferred technical solution of the present invention: when the pseudorange of satellite No. 20 at epoch 1000s contains a fault value of 15m,

[0070] When the fault is not eliminated: the global test threshold is 3.715, and the measured statistic is 24.537. After the fault is eliminated: the global test threshold is 4.279, and the measured statistic is 0.180.

[0071] When the pseudorange of satellite No. 19 in 2011s epoch contains a fault value of 15m,

[0072] Before the fault is eliminated: the chi-square test threshold is 5.298, and the measured statistic is 27.234. After the fault is eliminated: the global test threshold is 0.721, and the measured statistic is 7.879.

[0073] As a preferred technical solution of the present invention: in step S22, a 15m fault value is continuously added to the single satellite pseudorange in the three time periods of 0-1300s, 1644-2372s, and 3589-3883s, respectively. There are 8 visible satellites in the 0-1300s time period, and the satellite numbers are [01, 08, 14, 19, 20, 21, 29, 30] respectively. The 0-1300s time period is the correlation between the 20th satellite and other satellites, and the correlation coefficients are all below 0.6. Therefore, a 15m fault is continuously added to the pseudorange of the 20th satellite. There are 6 visible satellites in the 1644-2372s time period, and the satellite numbers are [01, 08, 14, 19, 20, 21, 29, 30] respectively. 9, 20, 29, 30], the 1644-2372s time period is the correlation between satellite No. 19 and other satellites, and the correlation coefficients between two satellites and satellite No. 19 are greater than 0.9. Therefore, a 15m fault value is continuously added to the pseudorange observation value of satellite No. 19. In the 3589-3883s time period, there are 6 visible satellites, and the satellite numbers are [07, 08, 19, 20, 29, 30] respectively. The 3589-3883s time period is the correlation between satellite No. 19 and other satellites, among which the correlation coefficients between satellite No. 19 and satellites 07 and 20 are as high as 0.99. Therefore, a 15m fault value is continuously added to the pseudorange observation value of satellite No. 19.

[0074] As a preferred technical solution of the present invention: in the time period of 0-1300s, all faults can be correctly identified;

[0075] In the time periods of 1644-2372s and 3589-3883s, the actual fault was added to the 19th satellite, while the identified faults were in the three positions of the 07th, 20th and 30th satellites.

[0076] A total of 729 fault values ​​were added to the 19th satellite in the time period of 1644-2372s, of which 596 faults were correctly identified and 133 fault values ​​were incorrectly located.

[0077] A total of 295 fault values ​​were added to the 19th satellite in the time period of 3589-3883s, of which 197 fault values ​​were correctly identified and 98 fault values ​​were incorrectly located.

[0078] Compared with the prior art, the present invention has the following beneficial effects:

[0079] The invention proposes a robust positioning method taking into account correlation, which effectively solves the problem of erroneous positioning failure caused by strong correlation between observation values ​​and improves positioning accuracy.

[0080] (1) When there are many observable satellites, the correlation between satellites is weak; as the number of observable satellites decreases, the correlation between satellites becomes stronger.

[0081] (2) The chi-square global test and the w local test can effectively detect and identify faults. When the correlation between satellites is weak, the probability that the fault identification method can correctly identify the fault location is high. As the correlation between satellites becomes stronger, the probability of incorrectly locating the fault location increases.

[0082] (3) In a strong correlation environment, traditional fault detection and isolation methods are prone to incorrectly locate the fault location, retaining the faulty observations while eliminating the correct observations, resulting in a sharp drop in positioning accuracy. The robust positioning method that takes satellite correlation into account uses a weight function processing strategy for adaptive robustness in a strong satellite correlation environment, effectively improving positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is the technical roadmap of robust positioning algorithm;

[0084] Figure 2 is the motion trajectory diagram;

[0085] Figure 3 It is the visible image of the sky in the occluded environment;

[0086] Figure 4 is the number of visible satellites and the change of PDOP value;

[0087] Figure 5 is the correlation coefficient of the five satellites at the 3000s epoch;

[0088] Figure 6 is the correlation coefficient of the six satellites in the 2011s epoch;

[0089] Figure 7 is the correlation coefficient of 7 satellites at 1500s epoch;

[0090] Figure 8 is the correlation coefficient of 8 satellites at 1000s epoch;

[0091] Fig. 9 Add the fault chi-square fault test plot for both epochs;

[0092] Fig.10 is the w fault identification diagram;

[0093] Fig.11 Added fault measurement statistics table for 1000s;

[0094] Fig.12 Added fault measurement statistics table for 2011s;

[0095] Fig.13 It is the least square solution positioning error map;

[0096] Fig.14 localize error maps for traditional fault detection and isolation methods;

[0097] Fig.15 It is the correlation coefficient variation diagram between satellites;

[0098] Fig.16 is the chi-square fault test plot for each epoch;

[0099] Fig.17 is the w fault identification diagram;

[0100] Fig.18 Identify location maps of faults for existing methods;

[0101] Fig.19 This is a comparison of the positioning results of the three methods;

[0102] Fig. 20 To identify the statistical table of faults;

[0103] Fig.21 This is the position error statistical result table. DETAILED DESCRIPTION

[0104] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0105] like Figure 1 As shown, the present invention proposes a robust positioning method taking into account the correlation between satellites, comprising the following steps:

[0106] S1: Anti-differential positioning analysis:

[0107] First, the number of satellites is determined based on satellite signals, and then a global inspection is performed to detect faults. If the fault does not exist, that is, the fault detection is invalid, positioning and solving are performed. If the fault does exist, local inspection is used to identify the fault.

[0108] If the correlation coefficient ρ between the observation values ​​of the fault is less than the set threshold, the observation value corresponding to the maximum test value is directly eliminated and the positioning solution is performed again.

[0109] If the correlation coefficient ρ between the observations with faults is greater than the set threshold, the identified fault may occur on the i-th or k-th observation. The weight function is used to adaptively process the fault value. Therefore, a specific weight function needs to be selected to reduce the weight of the i-th and k-th observations.

[0110] The IGGIII weight function expression is:

[0111]

[0112] Where: k 0 and k 1 is a constant threshold parameter, k 0 Take 1.345, k 1 Take 3, v i Standardize the residual for the ith element, and use the equivalent weight function to adaptively reduce or set the weight of the abnormal measurement to zero, thereby obtaining an estimated value;

[0113] S2: Verification and Analysis:

[0114] The simulation data of Beidou satellite navigation system is used for calculation, the dynamic running trajectory of ground vehicles is simulated, and the visible satellites are simulated to be blocked, which will deteriorate the spatial geometric structure of the observed satellites and cause strong correlation in the observed values. Single faults and multiple faults are added respectively, and the positioning solution results of the robust positioning method that takes into account the correlation between satellites are compared and analyzed;

[0115] S21: When a single fault is added:

[0116] When the correlation between satellites is weak or strong, a single fault value is added to the pseudorange respectively, and then the performance of fault detection and isolation is compared and analyzed when the correlation between satellites is weak or strong.

[0117] When the correlation between satellites is weak: when a fault is detected, the fault location can be correctly located and eliminated.

[0118] When the satellite correlation is strong: When a fault is detected, adaptive processing can be performed based on the correlation, and robust processing can be performed to locate the fault.

[0119] S22: When multiple failures are added:

[0120] When the correlation between satellites is weak and when the correlation between satellites is strong, single fault values ​​are continuously added to their pseudoranges, and then the performance of fault detection and isolation when the correlation between satellites is weak and when the correlation between satellites is strong is compared and analyzed.

[0121] When the correlation between satellites is weak: it is possible to detect and identify faults occurring in all epochs and locate the faults.

[0122] When the satellite correlation is strong: When the satellite correlation is extremely strong and the satellite correlation is relatively strong, the fault location is achieved through adaptive anti-error, and the accuracy of fault detection and identification rate is 81.756% and 66.780%.

[0123] In step S1, assuming that there are no fault values ​​in the measurement, the least squares estimation of the unknown parameters in the measurement can be based on the following function model and random model:

[0124]

[0125] Σ=σ 0 2 Q=σ 0 2 P -1 (3)

[0126] Where: x is a t×1 unknown parameter vector; v is an n×1 residual vector; A is an n×t design matrix; l is an n×1 measurement vector; Σ is the positive definite variance covariance matrix of the measured values; σ 0 2 is the prior variance factor; Q is the covariance matrix; P is the weight matrix,

[0127] The estimated and solved variance for the unknown parameters is:

[0128]

[0129]

[0130] The corresponding residual vector and its covariance are solved as follows:

[0131] v=(I-(A T PA) -1 A T Pl)l (6)

[0132] Q v =P -1 -A(A T PA) -1 A T (7)

[0133] In step S1, the global inspection is specifically as follows:

[0134] The satellite system is tested for gross errors by using the residual as a hypothesis test statistic, and the variance factor for constructing the detection fault is determined as:

[0135]

[0136] in: is the posterior variance factor, t is the number of unknown parameters,

[0137] When the satellite system has no faults, the function follows a centralized chi-square distribution:

[0138]

[0139] Where: nt is the degree of freedom, α is the significance level,

[0140] If the variance factor ratio exceeds a given threshold, it is determined that a fault exists; otherwise, it is determined that no fault occurs.

[0141] In step S1, the local inspection is specifically as follows:

[0142] To test whether there are outliers in the measurements, the following hypotheses need to be tested:

[0143]

[0144] Assume that the fault occurs at the i-th observation value, h i is a vector whose i-th element is equal to 1 and other elements are equal to 0. Fault detection and identification can be derived from the mean shift model:

[0145]

[0146] Using the block matrix, the fault size can be obtained as:

[0147]

[0148] The variance of the estimated fault value can be expressed by the error propagation law:

[0149]

[0150] Therefore, the fault test statistic on the i-th observation can be expressed as:

[0151]

[0152] When there is no fault on the observed value, that is, Then i It should obey the standard normal distribution. In this case, the null hypothesis H 0 On the contrary, when there is a fault, Then i The expectation is no longer zero, so the alternative hypothesis H 1 Established,

[0153] The expected occurrence size of the i-th fault value statistic is δ d Offset:

[0154]

[0155] Where: d =N 1-α / 2 (0,1)+N 1-β (0,1) is the non-centralization parameter,

[0156] If the expected offset of the fault value statistic is δ d , then the MDB of the i-th observation is:

[0157]

[0158] The correlation coefficient between the i-th and k-th observations is:

[0159]

[0160] Where: |ρ ik |=|ρ ki |≤1.

[0161] In order to verify the method of the present invention, the simulation data of Beidou satellite navigation system is used for calculation, the dynamic running trajectory of ground vehicles is simulated, and the visible satellites are simulated to be blocked, which will deteriorate the spatial geometric structure of the observed satellite, resulting in a strong correlation in the observed values. Single faults and multiple faults are added respectively, and the positioning solution results of the least squares positioning solution, the traditional fault detection and isolation method positioning solution and the anti-error positioning method taking into account the correlation between satellites are compared and analyzed. There are 35 satellites in the simulation process, including 5 geostationary orbits (Geosychronons Earth Orbit, GEO) satellites, 3 inclined geosynchronous orbits (Inclined GeoSynchronous Orbit, IGSO) satellites and 27 medium earth orbits (Medium Earth Orbit, MEO) satellites. Among them, 01-27, 28-32 and 33-35 are the satellite numbers (Satellite Number, SN) of MEO, GEO and IGSO respectively. Figure 2 To simulate the vehicle's motion trajectory, the running time is 4476 seconds. Severe occlusion often occurs in real urban environments. For example, if one side of the vehicle is completely blocked by high-rise buildings, half of the sky will be blocked; if the vehicle is traveling on a north-south or east-west street, two-way street occlusion will occur. Figure 3 To simulate the satellite distribution sky visible view under the two-way street occlusion environment, the number of observed satellites is reduced and the geometric structure is deteriorated, resulting in a strong correlation between the observation values. The satellites in the azimuth [-45°-45°] and [-135°-135°] directions are completely blocked, and the visible stars are numbered [01, 07, 08, 14, 19, 20, 21, 29, 30]. During the calculation process, the pseudorange accuracy is 1m, the sampling time interval is 1s, and the cut-off elevation angle is 10°.

[0162] Figure 4The figure shows the change of the number of visible satellites and the Position Dilution of Precision (PDOP) value over time during the entire movement. The maximum number of visible satellites is 8, and the minimum number of visible satellites is 5. In the period of 2373-3588s, the number of visible satellites is small, only 5. Due to the poor spatial geometric distribution of satellites in the occluded environment, the PDOP value varies in the range of 10-14, which will make the positioning accuracy poor during this period.

[0163] Depend on Figure 4 It can be seen that at the four epochs of observation time 1000s, 1500s, 2000s and 3000s, the number of visible satellites is 8, 7, 6 and 5 respectively, corresponding to Figure 4 The correlation coefficients between satellites in a single epoch are given by Figure 5-8 It can be seen that when there are 5 visible satellites, the correlation between each satellite is 1, that is, completely correlated. As the number of satellites increases, the correlation between each satellite will tend to decrease. In a restricted observation environment, the obstruction of high-rise buildings causes a decrease in the number of visible satellites, and the satellites are strongly correlated.

[0164] Add a single fault:

[0165] When the number of observed satellites is equal to 5, fault detection can be performed, but fault identification cannot be performed because the 5 satellites are completely correlated. Fault detection and identification can only be performed when the number of observed satellites is greater than 6.

[0166] Depend on Figure 4 It can be seen that there are 8 satellites in 1000s, and the correlation between satellites is weak; there are 6 satellites in 2011s, and the correlation between satellites is strong. A 15m fault value is added to the pseudorange of satellite No. 20 in 1000s and satellite No. 19 in 2011s, respectively, to compare and analyze the performance of fault detection and isolation in these two cases. During the calculation, the false alarm rate α is set to 1%, the missed detection rate β is set to 20%, the threshold of the w statistic is 3.291, and the correlation coefficient threshold ρ is set to 0.9. Fig.11 The MDB, w test quantity, correlation coefficient ρ, and chi-square test statistic measured at 1000s for the unremoved faults and after removing the faults are shown. Fig. 9 and Fig.10 Distributions of the chi-square test statistic and the w test statistic for adding faults at two epochs, respectively.

[0167] The pseudorange of satellite No. 20 at epoch 1000s contains a fault value of 15m. Fig.11It can be seen that the chi-square global test threshold is 3.715, the measured statistic is 24.537, and the detection fault exists. The w test statistics of satellites 19, 20 and 21 did not pass the local test due to correlation, and the w test value was greater than the threshold of 3.291. Since the traditional fault detection and isolation method only excludes the largest w test value as the fault value, satellite 20 is eliminated. After eliminating the fault value, the chi-square global test threshold is 4.279, and the measured statistic is 0.180, which passes the test and the fault does not exist. Since the fault is accurately identified and eliminated, all w statistics are lower than the threshold value and pass the test.

[0168] The pseudorange of the satellite at epoch 19 in 2011 contains a fault value of 15m. Fig.12 It can be seen that the chi-square global test threshold is 5.298, and the measured statistic is 27.234, indicating that the detection fault exists.

[0169] The w test statistics of the four satellites 01, 19, 20 and 30 failed the test due to high correlation, which was greater than the threshold of 3.291. Since the traditional fault detection and isolation method identifies the satellite corresponding to the largest statistic as the fault value, the actual fault added is in satellite 19, and the fault is located in satellite 30. This is because the correlation between satellite 30 and satellite 19 is high, reaching 0.933, and the fault value is incorrectly identified. Fig.12 It also shows that the w statistics of the pseudoranges of each satellite are equal after satellite 30 is removed. Since there are only 5 observed satellites left, they are perfectly correlated with each other and the correlation coefficients are all 1. In this case, it is impossible to identify the remaining or any further faults.

[0170] Fig.13 and Fig.14 The positioning results of the least squares positioning solution and the traditional fault detection and isolation method are respectively. After the fault was added at 1000s, the positioning results in the northeastern sky direction were 6.966m, 4.528m and 1.524m respectively; due to the low correlation between satellites, the traditional fault detection and isolation method can accurately identify the fault, and the positioning results in the northeastern sky direction were 1.249m, 0.252m and 1.262m respectively. After the fault was added at 2011s, the positioning results were 12.323m, 4.706m and 1.244m respectively; the traditional fault detection and isolation method was used to mislocate the observation value of the faulty satellite No. 19 to the satellite No. 30, resulting in the positioning results in the northeastern sky direction of 34.571m, 9.774m and 18.489m respectively. Due to the high correlation between satellites in this epoch, the fault position was mislocated, resulting in a positioning result that was worse than the positioning result without removing the fault.

[0171] Add multiple faults:

[0172] There are 9 satellites in the whole movement process, and the satellite numbers are [01, 07, 08, 14, 19, 20, 21, 29, 30]. When there are fewer observed satellites and the geometric structure is not ideal, the correlation between satellites is high, which is prone to misidentification of faults. Fig.15 To account for the change in correlation coefficient between satellites, a 15m fault value is added to the pseudorange of a single satellite in the three time periods of 0-1300s, 1644-2372s, and 3589-3883s. There are 8 visible satellites in the time period of 0-1300s, and the satellite numbers are [01, 08, 14, 19, 20, 21, 29, 30] respectively. Fig.15 The 0-1300s time period is the correlation between satellite No. 20 and other satellites. The correlation coefficients are basically below 0.6, and the possibility of correctly distinguishing the fault is high. A 15m fault is continuously added to the pseudorange of satellite No. 20. There are 6 visible satellites in the 1644-2372s time period, and the satellite numbers are [01, 08, 19, 20, 29, 30]. Fig.15 The time period of 1644-2372s is the correlation between satellite 19 and other satellites. There are two satellites with a correlation coefficient greater than 0.9 with satellite 19. A 15m fault value is continuously added to the pseudorange observation value of satellite 19, and the position of the fault is likely to be wrongly located. There are 6 visible satellites in the time period of 3589-3883s, and the satellite numbers are [07, 08, 19, 20, 29, 30]. Fig.15 The time period of 3589-3883s is the correlation between satellite 19 and other satellites, among which the correlation coefficient between satellite 19 and satellites 07 and 20 is as high as 0.99. A 15m fault value is continuously added to the pseudorange observation value of satellite 19, and the possibility of erroneous positioning of the fault position is high.

[0173] Fig.16 and Fig.17 They are the chi-square test statistic and w test statistic of each epoch, respectively. As can be seen from the figure, all epoch failures can be detected and identified, and some epochs have false alarms.

[0174] Fig.18 Indicates the actual fault location and the identified fault location. Fig. 20 is the statistic of correctly identified and incorrectly identified fault locations. Fig.18 and Fig. 20It can be seen that all faults in the time period of 0-1300s can be correctly identified; in the time periods of 1644-2372s and 3589-3883s, the actual fault was added to the 19th satellite, and the identified faults were at three locations on satellites 07, 20 and 30. In the time period of 1644-2372s, a total of 729 fault values ​​were continuously added to the 19th satellite, of which 596 faults were correctly identified and 133 fault values ​​were incorrectly located. In the time period of 3589-3883s, a total of 295 fault values ​​were added to the 19th satellite, of which 197 fault values ​​were correctly identified and 98 fault values ​​were incorrectly located. Fig. 20 It can be seen that the probability of misidentifying the fault location in the two time periods of 1644-2372s and 3589-3883s is 18.24% and 33.22% respectively. Since the correlation between the two satellites in the time period of 3589-3883s is stronger than that in the time period of 1644-2372s, reaching about 0.99, the probability of mislocating the fault shows a higher trend.

[0175] Fig.19 The comparison of positioning results of the three methods shows that in the 0-1300s time period, the correlation between satellites is low, and the positioning error is small because the fault can be accurately located. Fig.19 It can be seen that traditional fault detection and isolation methods are prone to fault location errors when the correlation between satellites is high, resulting in huge deviations. Fig.21 The average value, standard deviation, root mean square error and maximum value analysis results of the positioning results in the three directions of northeast and sky. The maximum positioning errors of the traditional method are 47.415m, 33.236m, and 131.468m, respectively, and the positioning results of the least squares positioning solution and the proposed method are 16.365m, 14.615m, 41.456m and 9.974m, 9.989m, 41.456m, respectively. This is because the traditional fault detection and isolation method has an incorrect positioning fault, resulting in a huge deviation in the positioning result, which is even worse than the least squares positioning result without fault detection and isolation. The root mean square errors of the positioning results of the fault detection and isolation method taking into account the correlation and the traditional fault detection and isolation method in the three directions of northeast and sky are 2.193m, 1.743m, 6.752m and 6.048m, 4.793m, 12.237m, respectively. Compared with the traditional method, the root mean square error positioning accuracy in the three directions is improved by 63.74%, 63.63% and 44.82% respectively. In addition, the fault detection and isolation method taking into account the correlation is also significantly better than the traditional method in terms of the mean value and standard deviation of the positioning error.

[0176] Therefore, there is a strong correlation between satellite observation values ​​in a complex observation environment. The present invention proposes a robust positioning method that takes into account the correlation, which effectively solves the problem of erroneous positioning failure caused by the strong correlation between observation values ​​and improves the positioning accuracy. Based on numerical simulation and result analysis, the following main conclusions are obtained:

[0177] (1) When there are many observable satellites, the correlation between satellites is weak; as the number of observable satellites decreases, the correlation between satellites becomes stronger.

[0178] (2) The chi-square global test and the w local test can effectively detect and identify faults. When the correlation between satellites is weak, the probability that the fault identification method can correctly identify the fault location is high. As the correlation between satellites becomes stronger, the probability of incorrectly locating the fault location increases.

[0179] (3) In a strong correlation environment, traditional fault detection and isolation methods are prone to incorrectly locate the fault location, retaining the faulty observations while eliminating the correct observations, resulting in a sharp drop in positioning accuracy. The robust positioning method that takes satellite correlation into account uses a weight function processing strategy for adaptive robustness in a strong satellite correlation environment, effectively improving positioning accuracy.

[0180] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. A robust positioning method taking into account the correlation between satellites, characterized in that: The following steps are included: S1: Anti-differential positioning analysis: First, the number of satellites is determined based on satellite signals, and then a global inspection is performed to detect faults. If the fault does not exist, that is, the fault detection is invalid, positioning and solving are performed. If the fault does exist, local inspection is used to identify the fault. If the correlation coefficient ρ between the observation values ​​of the fault is less than the set threshold, the observation value corresponding to the maximum test value is directly eliminated and the positioning solution is performed again. If the correlation coefficient ρ between the observations with faults is greater than the set threshold, the identified fault occurs on the i-th or k-th observation, and the weight function is used to adaptively process the fault value. Therefore, a specific weight function needs to be selected to reduce the weight of the i-th and k-th observations. The IGGIII weight function expression is: Where: k0 and k1 are constant threshold parameters, k0 is 1.345, k1 is 3, v i Standardize the residual for the ith element, and use the equivalent weight function to adaptively reduce or set the weight of the abnormal measurement to zero, thereby obtaining an estimated value; S2: Verification and Analysis: The simulation data of Beidou satellite navigation system is used for calculation, the dynamic running trajectory of ground vehicles is simulated, and the visible satellites are simulated to be blocked, which will deteriorate the spatial geometric structure of the observed satellites and cause strong correlation in the observed values. Single faults and multiple faults are added respectively, and the positioning solution results of the robust positioning method that takes into account the correlation between satellites are compared and analyzed; S21: When a single fault is added: When the correlation between satellites is weak or strong, a single fault value is added to the pseudorange respectively, and then the performance of fault detection and isolation is compared and analyzed when the correlation between satellites is weak or strong. When the correlation between satellites is weak: when a fault is detected, the fault location can be correctly located and eliminated. When the satellite correlation is strong: When a fault is detected, adaptive processing can be performed based on the correlation, and robust processing can be performed to locate the fault. S22: When multiple failures are added: When the correlation between satellites is weak and when the correlation between satellites is strong, single fault values ​​are continuously added to their pseudoranges, and then the performance of fault detection and isolation when the correlation between satellites is weak and when the correlation between satellites is strong is compared and analyzed. When the correlation between satellites is weak: it is possible to detect and identify faults occurring in all epochs and locate the faults. When the satellite correlation is strong: When the satellite correlation is extremely strong and the satellite correlation is relatively strong, the fault location is achieved through adaptive anti-error, and the accuracy of fault detection and identification rate is 81.756% and 66.780%; In step S1, assuming that there are no fault values ​​in the measurement, the least squares estimation of the unknown parameters in the measurement can be based on the following function model and random model: v=Ax-l (2) S=σ0 2 Q=σ0 2 P -1 (3) Where: x is a t×1 unknown parameter vector; v is an n×1 residual vector; A is an n×t design matrix; l is an n×1 measurement vector; Σ is the positive definite variance covariance matrix of the measured values; σ0 2 is the prior variance factor; Q is the covariance matrix; P is the weight matrix, The estimated and solved variance for the unknown parameters is: The corresponding residual vector and its covariance are solved as follows: v=(I-(A T PA) -1 A T Pl)l (6) Q v =P -1 -A(A T PA) -1 A T (7); In step S1, the global inspection is specifically as follows: The satellite system is tested for gross errors by using the residual as a hypothesis test statistic, and the variance factor for constructing the detection fault is determined as: in: is the posterior variance factor, t is the number of unknown parameters, When the satellite system has no faults, the function follows a centralized chi-square distribution: Where: nt is the degree of freedom, α is the significance level, If the variance factor ratio exceeds the given threshold, it is judged that a fault exists, otherwise, it is judged that no fault occurs; In step S1, the local inspection is specifically as follows: To test whether there are outliers in the measurements, the following hypotheses need to be tested: Assume that the fault occurs at the i-th observation value, h i is a vector whose i-th element is equal to 1 and other elements are equal to 0. Fault detection and identification can be derived from the mean shift model: Using the block matrix, the fault size can be obtained as: The variance of the estimated fault value can be expressed by the error propagation law: Therefore, the fault test statistic on the i-th observation can be expressed as: When there is no fault on the observed value, that is, Then i Should obey the standard normal distribution, then the null hypothesis H0 is established, on the contrary, when there is a fault, Then i The expectation is no longer zero, so the alternative hypothesis H1 is considered to be established. The expected occurrence size of the i-th fault value statistic is δ d Offset: Where: d =N 1-α / 2 (0,1)+N 1-β (0,1) is the non-centralization parameter, If the expected offset of the fault value statistic is δ d , then the MDB of the i-th observation is: The correlation coefficient between the i-th and k-th observations is: Where: |ρ ik |=|ρ ki |≤1; In step S2, When simulating through the Beidou satellite navigation system, 35 satellites and a simulated vehicle are set in the simulation process. The 35 satellites include 5 geostationary orbit satellites, 3 inclined geosynchronous orbit satellites and 27 medium earth orbit satellites, among which 01-27, 28-32 and 33-35 are the numbers of medium earth orbit satellites, geostationary orbit satellites and inclined geosynchronous orbit satellites respectively. The simulated vehicle running time is 4476s in total, and the simulated vehicle travels on north-south or east-west streets; At the four epochs of observation time 1000s, 1500s, 2000s, and 3000s, the number of visible satellites is 8, 7, 6, and 5, respectively; In step S21, when the number of observed satellites is equal to 5, fault detection can be performed, but fault identification cannot be performed. When the number of observed satellites is greater than 6, fault detection and identification can be performed. There are 8 satellites at 1000s. At this time, the correlation between satellites is weak. There are 6 satellites at 2000s. At this time, the correlation between satellites is strong. A fault value of 15m is added to the pseudoranges of satellite No. 20 at 1000s and satellite No. 19 at 2000s. When calculating, the false alarm rate is set to α as 1%, the missed detection rate is set to β as 20%, the threshold of the w statistic is 3.291, and the correlation coefficient threshold ρ is set to 0.9; When the pseudorange of satellite No. 20 at epoch 1000s contains a fault value of 15m, When the fault is not eliminated: the global test threshold is 3.715, and the measured statistic is 24.

537. After the fault is eliminated: the global test threshold is 4.279, and the measured statistic is 0.

180. When the pseudorange of satellite No. 19 in epoch 2000 contains a fault value of 15m, Before fault elimination: chi-square test threshold 5.298, measured statistic 27.234, after fault elimination: global test threshold 0.721, measured statistic 7.879; In step S22, a 15m fault value is continuously added to the pseudorange of a single satellite in the three time periods of 0-1300s, 1644-2372s, and 3589-3883s. There are 8 visible satellites in the time period of 0-1300s, and the satellite numbers are [01, 08, 14, 19, 20, 21, 29, 30] respectively. The time period of 0-1300s is the correlation between the 20th satellite and other satellites, and the correlation coefficients are all below 0.

6. Therefore, a 15m fault is continuously added to the pseudorange of the 20th satellite. There are 6 visible satellites in the time period of 1644-2372s, and the satellite numbers are [01, 08, 19, 20, 29 , 30], the 1644-2372s time period is the correlation between satellite No. 19 and other satellites. The correlation coefficients between two satellites and satellite No. 19 are greater than 0.

9. Therefore, a 15m fault value is continuously added to the pseudorange observation value of satellite No.

19. There are 6 visible satellites in the 3589-3883s time period, and the satellite numbers are [07, 08, 19, 20, 29, 30]. The 3589-3883s time period is the correlation between satellite No. 19 and other satellites. The correlation coefficients between satellite No. 19 and satellites No. 07 and 20 are as high as 0.

99. Therefore, a 15m fault value is continuously added to the pseudorange observation value of satellite No.

19. In the 0-1300s time period, all faults can be correctly identified; In the time periods of 1644-2372s and 3589-3883s, the actual fault was added to the 19th satellite, while the identified faults were in the three positions of the 07th, 20th and 30th satellites. A total of 729 fault values ​​were added to the 19th satellite in the time period of 1644-2372s, of which 596 faults were correctly identified and 133 fault values ​​were incorrectly located. A total of 295 fault values ​​were added to the 19th satellite in the time period 3589-3883s, of which 197 fault values ​​were correctly identified and 98 fault values ​​were incorrectly located; When there are more observable satellites, the correlation between satellites is weak; as the number of observable satellites decreases, the correlation between satellites becomes stronger; The chi-square global test and the w local test can effectively detect and identify faults; the correlation between satellites is weak, and the probability that the fault identification method can correctly identify the fault location is high; as the correlation between satellites becomes stronger, the probability of erroneously locating the fault location becomes higher; In a strong correlation environment, the fault detection and isolation method is prone to incorrectly locate the fault position, retaining the faulty observations and eliminating the correct observations, resulting in a sharp drop in positioning accuracy; the robust positioning method that takes into account satellite correlation uses a weight function processing strategy for adaptive robustness in a satellite strong correlation environment, effectively improving positioning accuracy.

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