Satellite navigation application terminal integrity evaluation method considering non-Gaussian error

Abstract

The invention relates to a satellite navigation application terminal integrity evaluation method considering a non-Gaussian error. The method comprises the following steps: 1) determining an error source of a satellite navigation application terminal needing to be considered in a test environment and constructing an error model; 2) establishing a basic test scene of distance measurement error non-Gaussian distribution; 3) determining a fault mode occurrence probability and a fault mode which needs to be excited for integrity evaluation; 4) obtaining the corresponding fault mode occurrence probability of the integrity test sample under each risk source; 5) determining the worst fault and amplitude under the non-Gaussian distribution condition; (6) constructing an I / II type error probability evaluation model, and determining the minimum number of test samples needing to be collected and an evaluation test threshold; 7) randomly selecting a plurality of test sites, determining the number of test samples used by each test site, and injecting the worst fault and amplitude into the test samples; and 8) collecting a test sample generated by the satellite navigation application terminal, and evaluating whether the integrity risk of the test sample meets the expectation or not.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation, and particularly relates to a method for integrity evaluation of a satellite navigation application terminal considering non-Gaussian errors. Background Art

[0002] The Global Navigation Satellite System (GNSS) can provide seamless and accurate services all-weather and all-airspace by virtue of its integrated functions of navigation, positioning, and timing. At present, GNSS technology has been deeply integrated into dual-use fields such as carrier aircraft automatic landing guidance, intelligent vehicle autonomous driving, and agricultural machinery cluster collaboration in land, sea, air, and civilian applications. These practices have verified the important position of GNSS in critical fields related to life safety such as air transportation and autonomous driving. In this context, the GNSS service is being comprehensively upgraded from simply pursuing measurement accuracy to ensuring system reliability, making the integrity index, which characterizes the credibility of the navigation system, gradually become the core evaluation standard for life safety navigation applications.

[0003] During the precision approach and landing phase of an aircraft, the Real Time Kinematic (RTK) technology, as the core positioning means, realizes centimeter-level relative positioning by solving the double-difference carrier phase observations between the reference station and the mobile station. To meet the navigation performance requirements for precision landing such as RNP0.1 (Required Navigation Performance, RNP) and above, it is necessary to conduct multi-dimensional statistical analysis of the operating characteristics of the satellite navigation application terminal, establish an evaluation method for integrity risk indicators based on key parameters such as error source distribution and failure modes, and form an iterative basis for the integrity enhancement scheme for the precision approach and automatic landing scenario.

[0004] The existing evaluation methods have the following defects: The satellite navigation application terminal needs to face challenges from multiple non-ideal Gaussian distribution error sources such as the satellite segment, the space atmosphere segment, and the satellite navigation application receiver terminal. The traditional simulation test scenario construction is too idealized, which leads to distortion of the test environment; it is difficult to obtain the worst failure amplitude of the risk source caused by non-ideal Gaussian distribution error sources; the number of test samples required by the traditional method is too large, resulting in high costs for integrity risk assessment. In the short-term integrity evaluation scenario, the number of test samples is small, resulting in inaccurate confidence in integrity evaluation. Summary of the Invention

[0005] Aiming at the problems in scenarios such as the traditional simulation test scenario being too ideal, the difficulty in obtaining the worst failure amplitude under non-Gaussian conditions, and the inaccurate confidence in short-term integrity evaluation, the present invention proposes a method for integrity evaluation of a satellite navigation application terminal considering non-Gaussian errors, including:

[0006] Step S1) Determine the error sources of the satellite navigation application terminal to be considered in the test environment and construct the corresponding error model;

[0007] Step S2) Based on the error model, establish a basic test scenario with a non-Gaussian distribution of ranging errors, so as to perform subsequent steps in this basic test scenario;

[0008] Step S3) Determine the occurrence probability of the failure mode, and then determine the failure modes that need to be stimulated for the integrity evaluation of the satellite navigation application terminal;

[0009] Step S4) Convert the integrity risk index into an equivalent missed detection rate index, and obtain the occurrence probability of the corresponding failure modes of the integrity test samples under each risk source;

[0010] Step S5) Determine the worst failure and its amplitude under non-Gaussian distribution conditions based on the worst failure criterion;

[0011] Step S6) According to the equivalent missed detection rate index converted from the integrity risk index, construct an I / II type error probability evaluation model, and determine the minimum number of test samples to be collected and the evaluation test threshold;

[0012] Step S7) Randomly select multiple test sites globally, determine the number of test samples at each test site, and inject the worst failure and its amplitude into the test samples used at each test site;

[0013] Step S8) Collect the test samples generated by the satellite navigation application terminal, and evaluate whether the integrity risk of the satellite navigation application terminal meets the expectations.

[0014] Advantages of the present invention:

[0015] A method for integrity assessment of satellite navigation application terminals considering non-Gaussian errors provided by the present invention can simulate the non-ideal Gaussian error environment in which the satellite navigation application terminals are located. Starting from the key points of test evaluation such as typical non-Gaussian error sources, fault amplitude excitation, and limited test sample size, by simulating the non-ideal Gaussian environment of the error sources of the satellite navigation application terminals, the method of injecting the worst faults in the non-Gaussian environment and using the worst fault amplitudes solves the problems in traditional test methods that the simulation of the test environment is too ideal and the maximum integrity risk is inaccurate due to the calculation method of the worst fault amplitudes of traditional multi-satellites. By constructing an I / II type error probability evaluation model, the sample number required for the test can be determined, solving the problem of the imbalance of integrity evaluation confidence caused by the small number of test samples in traditional test methods in the non-Gaussian test environment. It can complete high-confidence and high-efficiency testing and assessment of the integrity risk of satellite navigation application terminals, providing a reliable guarantee for the satellite-guided landing of satellite navigation application terminals in the precision approach stage, and having important significance in the application of navigation and positioning in fields related to life safety. Description of the Drawings

[0016] Figure 1 It is a flowchart of a method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors provided by the present invention;

[0017] Figure 2 It is a schematic diagram of the processing flow after the integrity assessment method provided by the present invention is applied to the simulator and the test evaluation platform. Detailed Embodiments

[0018] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.

[0019] The method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors proposed by the present invention implements multiple fault excitations, and can effectively cope with the scenario constraints of concurrent multiple risk sources and difficult fault amplitude excitation, and evaluate the integrity risk of satellite navigation application terminals with high efficiency and high confidence.

[0020] Next, the technical solutions of the present invention will be further specifically described in conjunction with the drawings.

[0021] As Figure 1 shown, the present invention provides a method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors, including the following steps:

[0022] Step S1) Determine the error sources of the satellite navigation application terminal that need to be considered in the test environment, and construct corresponding error models.

[0023] The satellite navigation application terminal can suppress the correlation error with spatial effect by using RTK positioning technology. However, there are still first-order and above ionospheric errors and tropospheric errors remaining in the spatial decorrelation operation. In addition, the receiver, its environment, and external interference need to be considered. In this application solution, the interference error caused by continuous wave interference (CWI) is used as the error source. Therefore, the error sources mentioned in the present invention include ionospheric error, tropospheric error, continuous wave interference (CWI) error, multipath error, etc. The corresponding ranging error probability density functions caused by each error source are given one by one below, which are the corresponding error models.

[0024] (1) Obtain the ionospheric error through simulation under the nominal non-ionospheric active period conditions.

[0025] Taking the vertical ionospheric delay error as an example, the vertical ionospheric gradient is expressed as:

[0026]

[0027] where g represents the vertical ionospheric gradient, d(IPP b , IPP r ) represents the great circle distance between the ionosphere piercing points IPP b and IPP r (Ionosphere Piercing Point) of the reference station and the rover station, VTEC b represents the calibrated vertical total electron content at the system end, VTEC r represents the calibrated vertical total electron content of the satellite navigation application terminal. The VTEC b and VTEC r can be calculated using the global ionosphere map (GIM) data file of the analysis center according to the IONEX 1.0 standard document.

[0028] By statistically analyzing the dataset within the specified spacing between the ionosphere piercing point IPP b of the system end and the ionosphere piercing point IPP r of the satellite navigation application terminal during the integrity test, the fitted vertical ionospheric gradient can be expressed by an exponential distribution as:

[0029]

[0030] where p g (z) represents the probability density distribution function of the vertical ionospheric gradient z, z is the vertical ionospheric gradient, a gIndicates the exponential distribution parameter obtained by data fitting, and the ionospheric gradient unit is ppm or mm / km.

[0031] Convert Equation (2) into an absolute ionospheric gradient error model:

[0032]

[0033] Where p iono (ε iono ) represents the probability density function of the ionospheric delay error ε iono , ε iono represents the ionospheric delay error, d represents the horizontal distance between piercing points, and p g () represents the probability density function of the vertical ionospheric gradient. The ionospheric gradient error model p iono (ε iono ) can be specifically:

[0034]

[0035] Where for the sake of computational simplicity, the exponential distribution correlation coefficient a g is uniformly simplified to the parameter a, and a represents the coefficient of the probability density function of the ionospheric delay error.

[0036] (2) The tropospheric delay error follows the classical tropospheric delay residual error model recommended by the Radio Technical Commission for Aeronautics (RTCA), that is, it follows a Gaussian distribution with zero mean, and the probability density function of the tropospheric delay error can be obtained, that is, the tropospheric error model:

[0037]

[0038] Where

[0039] Where p tropo (ε tropo ) represents the probability density function of the tropospheric delay error ε tropo , ε tropo represents the tropospheric delay error, σ tropo (θ,Δh) represents the standard deviation of the tropospheric delay error, and σ N is the uncertainty of the tropospheric refractive index transmitted by the reference station, h0 is the height of the tropospheric scale, θ represents the satellite elevation angle, and Δh is the altitude difference between the reference station and the rover station.

[0040] (3) The satellite navigation user terminal is subject to CWI type interference. The interference signal behaves like white noise at the output of the pseudo-random noise (PRN) code correlator in the code and carrier tracking loops of the GNSS receiver. The statistical characteristics of the pseudorange and carrier phase tracking errors conform to a Gaussian distribution with zero mean. Then, the probability density function of the CWI type interference error (i.e., the continuous wave suppression interference error model) is:

[0041]

[0042] where p CWI (ε CWI ) represents the probability density function of the CWI type interference error ε CWI , ε CWI represents the CWI type interference error, and σ CWI represents the standard deviation of the receiver's observable tracking error.

[0043] (4) The multipath error model of the satellite navigation user terminal is realized by using the aliased Gaussian distribution envelope empirical multipath distribution model and introducing the elevation mapping function. The probability density function of the multipath error (multipath error model) is:

[0044]

[0045] where

[0046] where p mp (ε mp ) represents the probability density function of the multipath error ε mp , ε mp represents the multipath error, α i represents the component coefficient of the Gaussian distribution function, μ mp,i represents the mean of the i-th (i =

[0047] 1, 2, 3,..., n) Gaussian distribution components related to the satellite elevation angle θ, σ mp,i represents the standard deviation of the i-th (i = 1, 2, 3,..., n) Gaussian distribution component related to the satellite elevation angle θ, represents μ mp,i after being transformed by the elevation mapping function sinθ (θ is the satellite elevation angle), represents σ mp,i after being transformed by the elevation mapping function sinθ (θ is the satellite elevation angle). This is to remove the satellite elevation angle parameter and simplify the model.

[0048] Step S2) Based on the error model, establish a basic test scenario with a non-Gaussian distribution of ranging errors for subsequent steps in this basic test scenario.

[0049] The basic test scenario refers to setting the error sources mentioned in step S1) to the nominal state in the test environment of the simulator, that is, not applying faults to turn the error sources into risk sources.

[0050] The method for establishing a non-Gaussian distribution of ranging errors based on an error model for the basic test scenario is as follows:

[0051] In the test environment of the simulator, set the error sources mentioned in step S1) to the nominal state, and calculate the ranging errors of the observables under non-Gaussian distribution according to the error model constructed in step S1), including: pseudorange ranging error and carrier phase ranging error.

[0052] The pseudorange ranging error can be expressed as:

[0053] ε ρ =εi ono +ε tropo +ε CWI +ε mp (8)

[0054] where ε ρ represents the pseudorange ranging error, ε iono represents the ionospheric delay error, ε tropo represents the tropospheric delay error, ε CWI represents the CWI type interference error, ε mp represents the multipath error.

[0055] According to the multivariate probability density convolution formula in probability theory, the probability density of the pseudorange ranging error can be obtained, and its expression is:

[0056]

[0057] where

[0058] In equation (9), p ερ (ε ρ ) represents the probability density of the pseudorange ranging error ε ρ , ε ρ represents the pseudorange ranging error, a is the coefficient of the probability density function of the ionospheric delay error, α i represents the component coefficient of the Gaussian distribution function, μ mp,i represents the mean of the i-th (i = 1, 2, 3,..., n) Gaussian distribution component related to the satellite elevation angle θ, represents the mean after being transformed by the μ mp,i elevation mapping function sinθ (θ is the satellite elevation angle), σ mp,i represents the standard deviation of the i-th (i = 1, 2, 3,..., n) Gaussian distribution component related to the satellite elevation angle θ, represents σmp,i The standard deviation, σ, after being transformed by the elevation mapping function sinθ (where θ is the satellite elevation angle). tropo Denotes the standard deviation of the tropospheric delay error, σ CWI Denotes the standard deviation of the ranging error caused by CWI type interference. x is the intermediate variable in the integration process of the normal function.

[0059] Since the exact analytical solution cannot be obtained when calculating the quantile points from the probability density expression of the pseudorange ranging error, the integral value can be obtained by using the tabular calculation method.

[0060] For the carrier phase ranging error, since the carrier phase accuracy is higher than the pseudorange accuracy and the troposphere changes very little with time, the influence on the carrier phase ranging error can be approximately eliminated. The ionospheric delay error can also be approximated as a Gaussian distribution. Therefore, the carrier phase ranging error and its probability density are respectively expressed as:

[0061]

[0062] In the formula, p φ (ε φ ) represents the probability density distribution function of the carrier phase ranging error ε φ of, ε φ is the carrier phase ranging error, σ φ is the standard deviation of ε φ , σ iono,φ denotes the standard deviation of the ionospheric delay error under the carrier phase, σ mp,φ denotes the standard deviation of the multipath delay error related to the satellite elevation angle under the carrier phase, σ CWI denotes the standard deviation of the ranging error caused by CWI type interference. θ represents the satellite elevation angle.

[0063] The subsequent steps S3 - S8 are all carried out in the above - mentioned basic test scenario.

[0064] Step S3) Determine the occurrence probability of the failure mode, and then determine the failure modes that need to be stimulated for the integrity assessment of the satellite navigation application terminal.

[0065] Since the system side undertakes the monitoring work of abnormal risk sources highly relevant to the satellite navigation application terminal, such as satellite ephemeris anomalies and ionosphere / troposphere gradients, the satellite navigation application terminal only needs to consider non-related typical risk sources such as multipath anomalies and cycle slips. By comparing the prior faults of typical risk sources released by RTCA with the integrity risk indicators of the satellite navigation application terminal, the fault modes that need to be stimulated can be determined. A fault mode refers to the abnormal situation of single-star or multi-star satellite observables caused by risk sources such as multipath anomalies and cycle slips that need to be monitored by the satellite navigation application terminal, resulting in abnormal positioning of the satellite navigation application terminal. The occurrence probability of a single-star fault is calibrated according to the prior fault probability of the risk source, and the occurrence probability of a multi-star fault is the binomial cumulative sum of the occurrence probabilities of single-star faults. The occurrence probability of the fault mode is specifically expressed as:

[0066]

[0067] where

[0068] In the formula, P(H k ) represents the occurrence probability of the fault mode H k , H k (k = 1, 2, 3, 4, …) represents the fault mode containing m f faulty satellites; n s represents the number of satellites participating in positioning, (! is the factorial operator) represents the combination number, which indicates here that the fault mode is the permutation and combination of faulty satellites and non-faulty satellites among the satellites participating in positioning, and the occurrence fault probability of each satellite is the same; P f represents the total prior fault probability obtained by adding the prior fault probability P f，mp of multipath anomalies and the prior fault probability P f,cs of cycle slips, P f，mp represents the prior fault probability of multipath anomalies, P f,cs represents the prior fault probability of cycle slips; N sat,max represents the maximum number of faulty satellites, N total represents the number of fault modes that need to be stimulated. Obviously, after the maximum number of faulty satellites is determined, the fault modes that need to be stimulated can be confirmed.

[0069] The maximum number of faulty satellites can be determined by the integrity risk not included in the monitoring (the integrity risk not included in the monitoring is generally 1% of the index), and its constraint condition is expressed as:

[0070]

[0071] In the formula, N sat,max represents the maximum number of faulty satellites, n s represents the number of satellites participating in positioning, N satis the number of faulty satellites traversing the value range from 1 to n s IR req represents the integrity risk index represents the combination number represents P f to the power of k, and the meanings of other parameters are the same as those in the above formula (12).

[0072] Step S4) Convert the integrity risk index into an equivalent missed detection rate index, and obtain the occurrence probability of the corresponding fault mode of the integrity test sample under each risk source.

[0073] The purpose of converting the integrity risk index into an equivalent missed detection rate index is to amplify the test index, which can greatly reduce the required number of samples. Considering that the integrity risk failure event is mainly caused by the fault mode, the integrity risk test model can be expressed as:

[0074]

[0075] In the formula, IR req represents the integrity risk index, which is the integrity risk index of the satellite navigation application terminal in this embodiment, N total is the total number of fault modes that need to be excited, which includes single-satellite fault modes and multi-satellite fault modes, P(H k ) represents the occurrence probability of the fault mode, H k (k = 1, 2, 3, 4,...) represents the fault mode, PE is the positioning error of the satellite navigation application terminal, AL is the warning limit in the precision approach stage, t is the test statistic used for the integrity monitoring of the satellite navigation application terminal, and T is the test threshold.

[0076] Using the total prior fault probability of the fault modes that need to be excited, convert the integrity risk index into an equivalent missed detection rate index. The conversion method and the occurrence probability of the fault mode under each risk source are as follows:

[0077]

[0078] In the formula represents the equivalent missed detection rate index obtained by converting the integrity risk index using the total occurrence probability of the fault mode, IR req represents the integrity risk index, N total is the total number of fault modes that need to be excited, which includes single-satellite fault modes and multi-satellite fault modes, P(H k ) represents the occurrence probability of the fault mode, H k (k = 1, 2, 3, 4,...) represents the fault mode.

[0079] The integrity risk index is converted into an equivalent missed detection rate index, which can greatly reduce the order of magnitude of the samples to be collected and significantly reduce the difficulty of index testing.

[0080] For the purpose of ensuring the probability equivalence of the integrity risk index, a fault event needs to be forcibly triggered in each precision approach test process. Therefore, a single precision approach process is defined as an integrity test sample. The method is to select a single precision approach process as an integrity test sample, and based on the completeness condition of the occurrence probability of the fault mode and the mutual exclusion characteristics between the fault modes, a probability mapping relationship between the integrity test sample and the fault mode is established through Bayes' theorem. The specific implementation method is as follows: By calculating the conditional probability of each fault mode in the test sample space, the posterior probability distribution of its being the only fault cause is determined. The single occurrence probability of the fault mode corresponding to any integrity test sample can be obtained in the following way:

[0081]

[0082] In the formula is the occurrence probability of the corresponding fault mode H of the integrity test sample under the risk source, P(H k k ) represents the occurrence probability of the fault mode, H k (k = 1, 2, 3, 4,...) represents the fault mode, N total is the total number of fault modes that need to be excited, which includes single-star fault modes and multi-star fault modes, P f represents the total prior fault probability obtained by adding the prior fault probability of multipath anomaly and the prior fault probability of cycle slip, P x represents the prior fault probability of multipath anomaly or the prior fault probability of cycle slip, and x represents multipath anomaly or cycle slip.

[0083] Step S5) Determine the worst fault and its amplitude under non-Gaussian distribution conditions based on the worst fault criterion.

[0084] Since the fault amplitude of the risk source has real number characteristics, and most faults may trigger integrity failure events, the ergodic analysis faces great challenges. Therefore, a conservative assessment of integrity risk based on the worst fault condition is proposed. The worst fault refers to the observable fault that can make the positioning error exceed the positioning warning limit and at the same time make the failure probability of the fault detector reach the maximum value. The worst fault can be divided into two categories: single-star worst fault and multi-star worst fault, and it is usually described by a vector for the satellites with faults and the fault amplitude. The worst fault analysis method can effectively avoid the ergodic calculation of the fault amplitudes of various risk sources, thus significantly improving the efficiency of integrity risk assessment.

[0085] ​Taking the least squares (LS) positioning estimator and the residual-based (RB) RB fault detector as examples, the calculation method of the worst fault and its amplitude under non-Gaussian distribution conditions is derived as follows:

[0086] First, determine the fault mode H k The worst fault vector model. The worst fault vector refers to the fault vector that causes the greatest integrity risk. The worst fault vector model is:

[0087]

[0088] where IR max is the maximum integrity risk, PE k is the positioning error of the satellite navigation application terminal under the fault mode H k , AL is the positioning error warning limit, P(H k ) represents the fault mode occurrence probability, H k (k = 1, 2, 3, 4,...) represents the fault mode, is the fault vector under the fault mode H k , ε represents the ranging error of the satellite navigation application terminal, σ ε represents the standard deviation of the ranging error ε of the satellite navigation application terminal, t k is the test statistic for the integrity of the satellite navigation application terminal under the fault mode H k , T is the test threshold, n s represents the number of satellites participating in the positioning; is the projection matrix from the measurement domain to the positioning domain, is an n s ×4 direction matrix, where the q column is 1 and the rest of the columns are 0, P = I n - H(H T H) -1 H T is the projection matrix from the measurement domain to the detection domain, I n is an n s ×n s identity matrix, H is the n s ×m dimensional double-difference observation matrix after removing the correlation of the measurement noise covariance matrix, m represents the number of user position parameters to be estimated, Q(*) is the right-tail function of the standard normal distribution, is the probability of the non-central chi-square distribution function with degrees of freedom n s - m and non-centrality parameter at T.

[0089] σ ε The value of can be obtained in the subsequent steps.

[0090] The right side of equation (17) represents the maximum probability that the positioning error of the satellite navigation application terminal exceeds the positioning warning limit and the fault detector fails to detect.

[0091] Secondly, obtain the worst fault unit vector and the worst fault vector.

[0092] Fault mode H k The worst fault vector under can be expressed as the product of the worst fault unit vector and the worst fault amplitude. Under non-Gaussian distribution conditions, the worst fault unit vector is the same as the worst fault unit vector under traditional Gaussian conditions. and can be expressed as:

[0093]

[0094] where e k represents an r×1 dimensional fault unit vector, characterizing the ratio between the measurement deviations of the faulty satellites, represents an r×1 dimensional worst fault unit vector, and r represents the number of faulty satellites under fault mode H k ; PE k is the positioning error of the satellite navigation application terminal under fault mode H k ; t k is the test statistic for the integrity of the satellite navigation application terminal under fault mode H k ; f k represents the unit fault amplitude, and f max,k represents the maximum eigenvector of the matrix ; represents the worst fault vector, represents the worst fault amplitude, is the projection matrix from the measurement domain to the positioning domain, s T is the transpose matrix of s, is an n s ×4 direction matrix, where the q-th column is 1 and the rest of the columns are 0, and n s represents the number of satellites participating in positioning, A k represents the n k ×r dimensional faulty satellite matrix under fault mode H s ; P = I n -H(H T H) -1 H T is the projection matrix from the measurement domain to the detection domain, and I n is the n s ×n s identity matrix, and H is the n s×m - dimensional double - difference observation matrix.

[0095] Next, obtain the worst - case fault amplitude.

[0096] The method adopted here is: under the condition that the ranging error conforms to the Gaussian distribution, the worst - case fault amplitude can be expressed by the worst - case fault vector as:

[0097]

[0098] In the formula denotes the worst - case fault amplitude, P(*) is the occurrence probability of event *, Q(*) is the right - tail function of the standard normal distribution, is the probability of the non - central chi - square distribution function with degrees of freedom n s - m and non - centrality parameter at T, and the meanings of other parameters with the same meaning are referred to in equations (17) and (18).

[0099] Furthermore, obtain the Gaussian envelope parameters for calculating the maximum integrity risk.

[0100] According to formula (19) for obtaining the worst - case fault amplitude, to obtain the maximum integrity risk, it is necessary to determine the parameter σ that conforms to the Gaussian distribution ε , but this is not suitable for the non - Gaussian distribution case of the ranging error ε. Therefore, it is necessary to use the Gaussian inflation method to envelope the non - Gaussian ranging error simulated by formula (9) to obtain the Gaussian envelope parameters of the satellite navigation application terminal.

[0101] Obtain the Gaussian envelope parameters of the satellite navigation application terminal. The specific implementation method is:

[0102] (1) According to the ranging error distribution model caused by each error source, obtain the covariance matrix composed of Gaussian error components and non - Gaussian error components between each satellite.

[0103] Since the observation error model in step S2 is non - Gaussian, and the ranging errors caused by multipath and CWI - type interference are related to altitude, a pseudo - random generator is used to generate a sufficient number (e.g., 10 8 pieces) of visible satellite pseudo - range ranging error samples with different satellite elevation angles through the Monte - Carlo method. The tropospheric error and the continuous - wave jamming error form a Gaussian error covariance matrix, and the ionospheric error and the multipath error form a non - Gaussian error covariance matrix. The covariance matrix composed of Gaussian error components and non - Gaussian error components can be expressed as:

[0104] Σ = Σ g + Σ ng ,

[0105] where

[0106] where Σ represents the ranging error covariance matrix, Σ g represents the Gaussian ranging error covariance matrix composed of the errors caused by tropospheric error sources and continuous wave suppression interference error sources, Σ ng represents the non-Gaussian ranging error covariance matrix composed of the errors caused by ionospheric error sources and multipath anomaly error sources, σ g,k represents the standard deviation of the ranging error composed of the Gaussian components of the k-th satellite, σ ng,k represents the standard deviation of the ranging error composed of the non-Gaussian components of the k-th satellite, σ ng,lm represents the ranging error covariance composed of the non-Gaussian components of the l-th satellite and the m-th satellite, k, l, m = 1, 2, …, n s and l ≠ m, n s represents the number of satellites participating in positioning.

[0107] (2) Using the Gaussian inflation method, calculate the standard deviation of the ranging error after inflation envelope.

[0108] Since Σ ng is a positive definite matrix, the standard deviation of the ranging error is inflated as follows:

[0109]

[0110] where σ ng represents the standard deviation of the ranging error composed of the non-Gaussian components after inflation envelope, σ g represents the standard deviation of the ranging error composed of the Gaussian components after inflation envelope, σ ε,Σ represents the standard deviation of the ranging error after inflation envelope, n s represents the number of satellites participating in positioning.

[0111] (3) The satellite navigation application terminal will use the standard deviation of the ranging error σ ε,Σ after inflation envelope calculated by equation (21) to replace the original standard deviation of the ranging error σ ε in equation (19), and thus calculate and obtain the maximum integrity risk and the corresponding worst fault amplitude.

[0112] Furthermore, considering the influence of the standard deviation of the ranging error σ ε,Σ after inflation envelope on obtaining the maximum integrity risk and the worst fault amplitude, it is also necessary to use the error data fitting of Monte-Carlo simulation to obtain the parameters that conform to the Gaussian distribution to constrain the standard deviation of the ranging error σ ε,Σ .

[0113] The specific implementation method for obtaining the parameters that conform to the Gaussian distribution is as follows:

[0114] (1) Plot the Gaussian distribution Q-Q plot and calculate the quantiles of the sample data: Obtain the quantile points corresponding to the typical probabilities from the sample data and the standard Gaussian distribution respectively, such as probabilities of 0, ±0.025,

[0115] ±0.005, and the corresponding quantile points, where the quantile points of the sample data are obtained by sorting the data and finding the corresponding quantile positions, and the quantile points of the standard Gaussian distribution are calculated using the inverse cumulative distribution function.

[0116] (2) Use the least squares linear regression fitting to obtain the maximum best-fit slope: The linear function of the fitted Q-Q plot is

[0117] The method to obtain the parameter is as follows:

[0118]

[0119] where y i is the quantile point of the sample data, x i is the quantile point of the standard Gaussian distribution, 1 ≤ i ≤ n = 9 and (natural number set), μ is the mean of the Gaussian distribution fitted from the sample data, is the maximum best-fit slope fitted from the sample data, is the standard deviation of the ranging error of the fitted Gaussian distribution, and k is the inflation factor.

[0120] Generally speaking, the standard deviation of the ranging error σ ε,Σ after the inflation envelope is greater than the parameter It can be analyzed that both the maximum integrity risk and the worst fault calculated using Equation (19) will increase, so the parameter needs to be adjusted to ensure that the calculated value of the maximum integrity risk is within the allowable range. Based on Equation (22), by adjusting the inflation factor k (k > 1), ensure that the worst fault amplitude calculated from the ranging error standard deviation σ ε,Σ is within the allowable range of the maximum integrity risk calculated from the parameter Specifically, it is expressed as:

[0121]

[0122] where

[0123] where The lower limit of the range is the minimum assessable integrity risk K·IR that satisfies the characterization of the assessment ability req(The minimum evaluable factor K > 1 is determined according to the evaluation requirements), and the upper limit is the maximum integrity risk obtained by using the parameters and The maximum integrity risk calculated The value range of the inflation factor k is 1 to 1.2; is and The general expression of, that is, σ can be regarded as a variable, σ ε,Σ and Are the variable values respectively.

[0124] Finally, the standard deviation σ of the ranging error after determining the inflated envelope ε,Σ The worst fault amplitude is obtained by setting the upper and lower boundaries through Equation (19), and generally can be conservatively set to about 0 to 20 m, that is, the lower boundary is 0 and the upper boundary is 20 m.

[0125] Step S6) According to the equivalent missed detection rate index converted from the integrity risk index, construct a type I / II error probability evaluation model to determine the minimum number of test samples to be collected and the evaluation test threshold.

[0126] To avoid the inaccuracy of the sample distribution characteristics caused by using a small number of sample tests, resulting in the inaccuracy of the evaluation confidence level, the present invention uses a type I / II error probability evaluation model to quantify the evaluation confidence level, ensure the accuracy of the evaluation confidence level, and evaluate the integrity risk of the satellite navigation application terminal by comparing the missed detection samples with the evaluation test threshold.

[0127] A missed detection sample refers to a test sample in which the positioning error PE of the satellite navigation application terminal exceeds the warning limit AL in the precision approach stage and the test statistic t is lower than the test threshold T while the satellite navigation application terminal does not give an alarm. By judging whether the test sample is a missed detection sample, the number of missed detection samples in all test samples can be counted. Since the LS estimator and the RB fault detector are adopted, it can be considered that the test statistic of the satellite navigation application terminal is independent of the positioning error, so the test samples are independent of each other. During the evaluation, if the number of missed detection samples is less than or equal to the preset allowable number of missed detection samples, the test passes, which indicates that the integrity risk index of the satellite navigation application terminal is qualified; otherwise, the test fails, which indicates that the integrity risk index of the satellite navigation application terminal is unqualified. Specifically expressed as:

[0128] TP:N MD ≤N sel

[0129] TF:N MD >N sel (24)

[0130] In the formula, TP indicates that the test passes, TF indicates that the test fails, and N MDIndicates the number of missed detection samples, N sel Indicates the evaluation test threshold, that is, the preset allowable number of missed detection samples.

[0131] Considering that the missed detection rate of the Receiver Autonomous Integrity Monitoring (RAIM) algorithm for the navigation satellite user terminal is extremely low, usually at the level of -3 rank and the average number of missed detections is small A Poisson distribution can be used to establish an evaluation confidence model: that is, calculate the probability of type I / II errors. Among them, the probability of type I error refers to the probability that the actual missed detection rate of the satellite navigation application terminal does not exceed the preset missed detection rate but the test fails, indicating the evaluation false alarm risk; the probability of type II error refers to the probability that the actual missed detection rate of the satellite navigation application terminal exceeds the preset missed detection rate but the test passes, indicating the evaluation missed detection risk.

[0132] The type I / II error probability evaluation model is:

[0133]

[0134] In Equation (25), P typeI is the probability of type I error, P typeII is the probability of type II error, α is the requirement for the probability of type I error to be satisfied, β is the requirement for the probability of type II error to be satisfied, α and β are generally less than 5%, N sel indicates the evaluation test threshold, μ H0 is the product of NIS sel and under the null hypothesis of , that is, the average number of missed detections in the H0 scenario, μ H1 is the product of NIS sel and under the alternative hypothesis of , that is, the average number of missed detections in the H1 scenario. H0 and H1 are the null hypothesis and alternative hypothesis made to verify whether the missed detection rate of the RAIM algorithm meets the index requirements. Specifically, H0 is the hypothesis that the actual missed detection rate using the RAIM algorithm is not higher than the equivalent missed detection rate index, and H1 is the hypothesis that the actual missed detection rate using the RAIM algorithm is higher than the equivalent missed detection rate index, manifested as:

[0135]

[0136] In the formula, NIS sel indicates the minimum number of test samples, is the equivalent missed detection rate index converted from the integrity risk index, represents the actual missed detection rate of the satellite navigation application terminal to be tested. The actual missed detection rate is unknown in advance, and whether it meets the equivalent missed detection rate index is determined by Equation (24).

[0137] By using the confidence interval method to control the Type I error probability not higher than α and the Type II error probability not higher than β, the reliability of the integrity assessment can be ensured.

[0138] The method for determining the minimum number of test samples to be collected and the evaluation test threshold is as follows:

[0139] Calculate the minimum number of test samples NIS using the minimum assessable factor K mentioned in step S5 sel and the evaluation test threshold N sel :

[0140]

[0141] In the formula, NIS sel represents the minimum number of test samples, and N sel represents the evaluation test threshold, which is affected by the minimum assessable factor K and the minimum assessable dead zone λ at the evaluation test threshold min (N sel ) is constrained, []_ represents the floor function, χ 2 (n,p) represents the upper quantile of the chi-square distribution with degree of freedom n at probability p, and λ min (N sel ) represents the minimum assessable dead zone, which characterizes the missed detection rate boundary that meets or exceeds the required evaluation confidence level under the assumptions of H0 and H1, and is expressed as:

[0142]

[0143] where represents the maximum μ H0 , represents the minimum μ H1 , and χ 2 (n,p) represents the upper quantile of the chi-square distribution with degree of freedom n at probability p.

[0144] Note that in equations (27) and (28), n and p in χ 2 (n,p) are variable parameters.

[0145] Step S7) Randomly select multiple test sites globally, determine the number of test samples for each test site, and inject the worst fault and its amplitude into the test samples used at each test site.

[0146] Randomly select N station test sites globally (on the Earth). The selected test sites should be on each ocean and continent and be evenly distributed in the global latitude, longitude, and altitude. The number of test samples for each test site is weighted and divided according to the average vertical dilution of precision (AVDOP) that can be obtained from pre-operation:

[0147]

[0148] where n k represents the number of test samples required for test site k, []_ represents the floor function, and N station represents the number of test sites, NIS sel represents the minimum number of test samples, AVDOP k represents the average vertical dilution of precision factor of test site k, and the method for calculating AVDOP k is as follows:

[0149]

[0150] where H k,i is the element in the k-th row and i-th column of the double-differenced observation matrix after removing the correlation of the measurement noise covariance matrix.

[0151] To ensure that the number of test samples n k is an integer, the number of test samples for the first N station -1 test points is rounded down, and the number of test samples for the last test point is the difference between the total number of test samples and the sum of the number of test samples for the first N station -1 test points, that is

[0152]

[0153] Taking a single precision approach (for example, a single approach in civil aviation applications is 150 s) as a test sample, the corresponding worst-case faults are injected into each test sample according to the occurrence probability of each fault mode determined in step S2. The occurrence probability of the fault mode corresponding to the worst-case fault is determined according to the method provided in step S2. For example, the occurrence probability of the fault mode H k is Similarly, the worst-case faults are injected into the remaining test sites in the above manner in turn.

[0154] By injecting the worst-case faults into the test samples, including injecting the worst-case fault amplitude, the problems of difficult non-Gaussian fault excitation and low evaluation confidence are solved, and the difficulty of evaluating satellite navigation application terminals is greatly reduced.

[0155] Step S8) Collect the test samples generated by the satellite navigation application terminal and evaluate whether its integrity risk meets the expectation.

[0156] First, collect test samples. Based on the navigation scenario of a single precision approach, collect the time-series data of the positioning error output by the satellite navigation application terminal and the corresponding integrity warning flag sequence to form a standard test sample set. The scale of the standard test sample set is based on the required number of test samples calculated in step S6.

[0157] Secondly, count the total number of undetected samples in all the collected test samples. Based on the definition of undetected samples in step S6 as the judgment criterion, perform pairwise comparison and analysis on the collected test samples, identify and mark undetected events, and thus count the cumulative value of the number of undetected samples in all test samples to obtain the total number of undetected samples.

[0158] Finally, evaluate the integrity risk index. Compare the total number of undetected samples with the preset evaluation and inspection threshold N sel If the total number of undetected samples is less than or equal to the preset evaluation and inspection threshold N sel , the inspection passes, it is determined that the integrity risk of the satellite navigation application terminal meets the design index requirements, meets the expectations, and is qualified; otherwise, if the total number of undetected samples is greater than the preset evaluation and inspection threshold, the inspection fails, and it is determined that the integrity risk of the satellite navigation application terminal exceeds the acceptable range, does not meet the expectations, and is unqualified.

[0159] Appendix Figure 2 Schematically shows the processing flow of applying the integrity evaluation method provided by the present invention to a multi-system satellite navigation simulator and an integrity test and evaluation device.

[0160] The above content is a further detailed description of the present invention in combination with specific implementation manners. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, which should all be regarded as belonging to the protection scope determined by the claims submitted by the present invention.

Claims

1. A method for integrity assessment of satellite navigation application terminals considering non-Gaussian errors, including: Step S1) Determine the error sources of the satellite navigation application terminal to be considered in the test environment and construct corresponding error models; Step S2) Establish a basic test scenario with non-Gaussian distribution of ranging errors based on the error model for subsequent steps in this basic test scenario; Step S3) Determine the occurrence probability of failure modes, and then determine the failure modes to be excited for the integrity assessment of the satellite navigation application terminal; Step S4) Convert the integrity risk index into an equivalent missed detection rate index, and obtain the occurrence probability of corresponding failure modes of the integrity test samples under each risk source; Step S5) Determine the worst failure and its amplitude under non-Gaussian distribution conditions based on the worst failure criterion; Step S6) Construct an I / II type error probability assessment model according to the equivalent missed detection rate index converted from the integrity risk index, determine the minimum number of test samples to be collected and the evaluation test threshold; Step S7) Randomly select multiple test locations globally, determine the number of test samples at each test site, and inject the worst failure and its amplitude into the test samples used at each test location; Step S8) Collect the test samples generated by the satellite navigation application terminal and evaluate whether the integrity risk of the satellite navigation application terminal meets the expectations.

2. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors according to claim 1, wherein in step S1, the error sources include: Ionospheric error, tropospheric error, continuous wave jamming error, and multipath error. The error models include an ionospheric gradient error model, a tropospheric error model, a continuous wave jamming error model, and a multipath error model.

3. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors according to claim 2, wherein the ionospheric gradient error model is: where p iono (ε iono ) represents the probability density function of the ionospheric delay error ε iono , d represents the horizontal distance between the piercing points, p g () represents the probability density function of the vertical ionospheric gradient, which is expressed as: where p g (z) represents the probability density distribution function of the vertical ionospheric gradient z, and a g represents the exponential distribution parameter obtained by data fitting; After simplification, the ionospheric gradient error model is obtained as: Where a represents the probability density function coefficient of the ionospheric delay error; The tropospheric error model is: Among them where p tropo (ε tropo ) represents the probability density function of the tropospheric delay error ε tropo , σ tropo (θ, Δh) represents the standard deviation of the tropospheric delay error, σ N is the uncertainty of the tropospheric refractive index transmitted by the reference station, h0 is the height of the tropospheric scale, θ represents the satellite elevation angle, and Δh is the altitude difference between the reference station and the rover station; The continuous wave jamming error model is: where p CWI (ε CWI ) represents the probability density function of the continuous wave suppression interference error ε CWI , and σ CWI represents the standard deviation of the observation tracking error of the receiver; The multipath error model is: Among them where p mp (ε mp ) represents the probability density function of the multipath error ε mp , α i represents the component coefficient of the Gaussian distribution function, μ mp,i represents the mean of the i-th Gaussian distribution component related to the satellite elevation angle, σ mp,i represents the standard deviation of the i-th Gaussian distribution component related to the satellite elevation angle, represents μ mp,i after being transformed by the elevation mapping function sinθ, represents σ mp,i after being transformed by the elevation mapping function sinθ, where i = 1, 2, 3, …, n and θ represents the satellite elevation angle.

4. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors according to claim 3, wherein in step S2, the method for establishing a basic test scenario with non-Gaussian distribution of ranging errors based on the error model is: In the test environment of the simulator, set the error sources mentioned in step S1) to the nominal state, and calculate the pseudorange ranging error and carrier phase ranging error under non-Gaussian distribution according to the error model, where: The pseudorange ranging error is: ε ρ = ε iono + ε tropo + ε CWI + ε mp where ε ρ represents the pseudorange ranging error, ε iono represents the ionospheric delay error, ε tropo represents the tropospheric delay error, ε CWI represents the continuous wave jamming error, ε mp represents the multipath error; The probability density of the pseudorange ranging error is: Among them Among them represents the pseudorange ranging error ε ρ of the probability density, a is the coefficient of the probability density function of the ionospheric delay error, α i represents the component coefficient of the Gaussian distribution function, μ mp,i represents the mean of the i-th Gaussian distribution component related to the satellite elevation angle θ, represents the mean after being transformed by the elevation mapping function sinθ through μ mp，i elevation mapping function sinθ, σ mp,i represents the standard deviation of the i-th Gaussian distribution component related to the satellite elevation angle θ, represents σ mp,i the standard deviation after being transformed by the elevation mapping function sinθ, σ tropo represents the standard deviation of the tropospheric delay error, σ CWI represents the standard deviation of the ranging error caused by CWI type interference, x is the intermediate variable in the integration process of the normal function, where i = 1, 2, 3, …, n, and θ represents the satellite elevation angle; The carrier phase ranging error and its probability density are respectively: where p φ (ε φ ) represents the probability density distribution function of the carrier phase ranging error, ε φ is the carrier phase ranging error, σ φ is the standard deviation of ε φ , σ iono,φ represents the standard deviation of the ionospheric delay error under the carrier phase, σ mp,φ represents the standard deviation of the multipath delay error related to the satellite elevation angle under the carrier phase, σ CWI represents the standard deviation of the ranging error caused by continuous wave suppression interference, and θ represents the satellite elevation angle.

5. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors according to claim 1, wherein in step S3, the specific method for determining the occurrence probability of failure modes and then determining the failure modes to be excited for the integrity assessment of the satellite navigation application terminal is: Among them where P(H k ) represents the occurrence probability of the fault mode H k , H k represents the fault mode containing m f faulty satellites, k = 1, 2, 3, 4, …; n s represents the number of satellites participating in positioning, represents the combination number, P f represents the total prior fault probability obtained by adding the prior fault probability P f，mp of multipath anomaly and the prior fault probability P f,cs of cycle slip; N sat,max represents the maximum number of faulty satellites, N total represents the number of fault modes that need to be excited; After confirming the maximum number of failed satellites, the failure modes to be excited can be determined.

6. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors as described in claim 1, wherein in step S4, the method for converting the integrity risk index into an equivalent missed detection rate index is as follows: Among them represents the equivalent missed detection rate index IR converted from the integrity risk index using the sum of the occurrence probabilities of failure modes req represents the integrity risk index, N total The total number of failure modes that need to be excited, which includes single-star failure modes and multi-star failure modes, P(H k ) represents the occurrence probability of the failure mode, H k represents the failure mode; The method for obtaining the occurrence probability of the corresponding fault mode of the integrity test sample under each risk source is as follows: Select a single precision approach process as an integrity test sample, and determine the posterior probability distribution of it as the only fault cause by calculating the conditional probability of each fault mode in the test sample space. The single occurrence probability of the fault mode corresponding to any integrity test sample is obtained in the following way: Among them is the corresponding failure mode H of the integrity test sample under the risk source k is the occurrence probability, P(H k ) represents the occurrence probability of the failure mode, H k represents the failure mode, N total is the total number of failure modes that need to be excited, which includes single-star failure modes and multi-star failure modes, P f represents the total prior failure probability obtained by adding the prior failure probability of multipath anomaly and the prior failure probability of cycle slip, P x represents the prior failure probability of multipath anomaly or the prior failure probability of cycle slip, and x represents multipath anomaly or cycle slip.

7. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors as described in claim 1, wherein in step S5, the method for determining the worst fault and its amplitude under non-Gaussian distribution conditions based on the worst fault criterion includes: 1) Determine the worst fault vector model under the fault mode as: Among them, IR max is the maximum integrity risk, PE k is the positioning error of the satellite navigation application terminal in the fault mode, AL is the positioning error warning limit, P(H k ) represents the occurrence probability of the fault mode, H k represents the fault mode, is the fault vector in the fault mode, t k is the test statistic for the integrity of the satellite navigation application terminal in the fault mode, T is the test threshold, is the projection matrix from the measurement domain to the positioning domain, is an n s ×4 direction matrix, where the qth column is 1 and the rest of the columns are 0, n s represents the number of satellites participating in the positioning, ε represents the ranging error of the satellite navigation application terminal, σ ε represents the standard deviation of the ranging error ε of the satellite navigation application terminal, P = I n - H(H T H) -1 H T is the projection matrix from the measurement domain to the detection domain, I n is an n s ×n s identity matrix, H is the n s ×m - dimensional double - difference observation matrix after removing the correlation of the measurement noise covariance matrix, m represents the number of user position parameters to be estimated, Q(*) is the right - tail function of the standard normal distribution, is the probability at T of the non - central chi - square distribution function with degrees of freedom n s - m and non - centrality parameter ; 2) The worst fault vector under the fault mode is the product of the worst fault unit vector and the worst fault amplitude. The methods for obtaining the worst fault unit vector and the worst fault vector are as follows: where e k represents an r×1 dimensional fault unit vector, represents an r×1 dimensional worst fault unit vector, and r represents the number of faulty satellites in the fault mode H k ; PE k is the positioning error of the satellite navigation application terminal under the fault mode H k ; t k is the test statistic for the integrity of the satellite navigation application terminal under the fault mode H k ; f k represents the unit fault amplitude, and f max,k represents the maximum eigenvector of the matrix ; represents the worst fault vector, represents the worst fault amplitude; s T is the transpose matrix of s, is the projection matrix from the measurement domain to the positioning domain, is an n s ×4 direction matrix, where the q column is 1 and the rest of the columns are 0, and n s represents the number of satellites participating in positioning, and A k represents the n k ×r dimensional faulty satellite matrix under the fault mode H s , and P = I n - H(H T H) -1 H T is the projection matrix from the measurement domain to the detection domain, and I n is an n s ×n s identity matrix, and H is an n s ×m dimensional double-difference observation matrix after removing the correlation of the measurement noise covariance matrix; 3) Obtain the worst fault amplitude, and the specific method is as follows: where represents the worst failure amplitude, P(*) is the occurrence probability of event *, and Q(*) is the right-tail function of the standard normal distribution, represents the r×1 dimensional worst failure unit vector, is the probability at T of the non-central chi-square distribution function with degrees of freedom n s -m and non-centrality parameter and the meanings of other same parameters are the same as above.

8. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors as described in claim 7, wherein in the process of obtaining the worst fault amplitude, it further includes: a) According to the ranging error distribution model caused by each error source, obtain the covariance matrix composed of Gaussian error components and non-Gaussian error components between each satellite. The method is as follows: Σ = Σ g + Σ ng , Among them where Σ represents the ranging error covariance matrix, Σ g represents the Gaussian ranging error covariance matrix composed of the errors caused by the tropospheric error source and the continuous wave suppression interference error source, Σ ng represents the non-Gaussian ranging error covariance matrix composed of the errors caused by the ionospheric error source and the multipath anomaly error source, σ g,k represents the standard deviation of the ranging error composed of the Gaussian components of the k-th satellite, σ ng,k represents the standard deviation of the ranging error composed of the non-Gaussian components of the k-th satellite, σ ng,lm represents the ranging error covariance composed of the non-Gaussian components of the l-th satellite and the m-th satellite, k, l, m = 1, 2, …, n s and l ≠ m, n s represents the number of satellites participating in the positioning; b) Use the Gaussian inflation method to calculate the standard deviation of the ranging error after inflation envelope. The method is as follows: where σ ng represents the standard deviation of the ranging error composed of non-Gaussian components after the dilation envelope, and σ g represents the standard deviation of the ranging error composed of Gaussian components after the dilation envelope, and σ ε,Σ represents the standard deviation of the ranging error after the dilation envelope, and n s represents the number of satellites participating in the positioning; c) Use the obtained standard deviation of ranging error σ ε,Σ to replace the original standard deviation of ranging error σ ε to obtain the worst fault amplitude therefrom.

9. The integrity assessment method for a satellite navigation application terminal considering non-Gaussian errors according to claim 8 further includes: Fitting error data obtained using Monte-Carlo simulation to obtain parameters conforming to a Gaussian distribution to constrain the standard deviation σ of the ranging error after the inflation envelope ε,Σ , where the parameters are first adjusted to ensure that the calculated value of the maximum integrity risk is within the allowable range, and then the inflation factor k is adjusted to ensure that the worst fault amplitude calculated from the standard deviation σ of the ranging error ε,Σ is within the allowable range of the maximum integrity risk calculated from the parameters , specifically manifested as: Among them Among them The lower limit of the range is the minimum assessable integrity risk K·IR that satisfies the characterization of the assessment ability req , and the upper limit is the maximum integrity risk obtained by using the parameters and calculated. The value range of the inflation factor k is 1 to 1.2 10. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors according to claim 9, wherein the method for obtaining the parameter is as follows: where y i is the quantile point of the sample data, x i is the quantile point of the standard Gaussian distribution, 1 ≤ i ≤ n = 9 and i ∈ the set of natural numbers μ is the mean of the Gaussian distribution fitted from the sample data, is the maximum best-fit slope fitted from the sample data, is the standard deviation of the ranging error of the Gaussian distribution fitted, and k is the inflation factor.

11. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors as described in claim 1. In step S6), the I / II type error probability assessment model constructed is: Among which P typeI is the probability of type I error, P typeII is the probability of type II error, α is the requirement for the probability of type I error to be satisfied, β is the requirement for the probability of type II error to be satisfied, N sel represents the evaluation test threshold, μ H0 is the product of NIS sel and under the hypothesis of H0, μ H1 is the product of NIS sel and under the hypothesis of H1, H0 is the hypothesis that the actual missed detection rate using the RAIM algorithm is not higher than the equivalent missed detection rate index, H1 is the hypothesis that the actual missed detection rate using the RAIM algorithm is higher than the equivalent missed detection rate index, that is: Where NIS sel represents the minimum number of test samples, is the equivalent missed detection rate index converted from the integrity risk index, representing the actual missed detection rate of the satellite navigation application terminal to be inspected; Controlling the Type I error probability P by using the confidence interval method typeI not higher than α and the Type II error probability P typeII not higher than β.

12. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors as described in claim 11, wherein the method for determining the minimum number of test samples to be collected and the evaluation test threshold is: Use the minimum assessable factor to calculate the minimum number of test samples and the evaluation test threshold: Among them, NIS sel represents the minimum number of test samples, N sel represents the evaluation inspection threshold, []_ represents the floor symbol, K is the minimum evaluable factor, χ 2 (n, p) represents the upper quantile of the chi-square distribution with n degrees of freedom at probability p, λ min (N sel ) represents the minimum evaluable dead zone, which is specifically: where χ 2 (n, p) represents the upper quantile of the chi-square distribution with n degrees of freedom at probability p.

13. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors as described in claim 1, wherein in step S7), the number of test samples at each test site is weighted and divided according to the average vertical accuracy dilution factor: where n k represents the number of test samples required for test site k, []_ represents the floor symbol, and N station represents the number of test sites, and NIS sel represents the minimum number of test samples, and AVDOP k represents the average vertical dilution of precision factor for test site k, and the method for obtaining AVDOP k is as follows: where H k,i is the element in the k-th row and i-th column of the double-difference observation matrix after removing the correlation of the measurement noise covariance matrix.

14. A method for integrity assessment of a satellite navigation application terminal considering non-Gaussian errors according to claim 1, wherein the step S8) further includes: First, in the process of collecting test samples of the satellite navigation terminal, collect the positioning error time series data output by the satellite navigation application terminal and the corresponding integrity alarm flag sequence to form a standard test sample set; then, count the total number of missed detection samples in all the collected test samples; finally, compare the total number of missed detection samples with the preset evaluation test threshold. If the total number of missed detection samples is less than or equal to the preset evaluation test threshold, the test passes, and it is determined that the integrity risk of the satellite navigation application terminal meets the expectation; Otherwise, the test fails, and it is determined that the integrity risk of the satellite navigation application terminal does not meet the expectation.

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