A method for evaluating the error envelope performance of take-off and landing guidance systems in aviation navigation networks

Abstract

The present invention discloses an error envelope performance evaluation method for an aviation navigation network take-off and landing guidance system, which relates to the field of satellite navigation technology, including a single-frequency pseudorange domain error envelope model evaluation method, a dual-frequency pseudorange domain error envelope model evaluation method, and a dual-frequency positioning domain error envelope model evaluation method. The above evaluation methods all include the following steps: Step S1, screening observation data, performing carrier phase smoothing filtering processing and extracting pseudorange single difference residuals; Step S2, constructing an error envelope model; Step S3, performing error envelope confidence evaluation and error envelope tightness evaluation. The present invention adopts the above-mentioned error envelope performance evaluation method for an aviation navigation network take-off and landing guidance system, which is conducive to the selection of a specific error envelope model in integrity evaluation, and can help the satellite-based precision take-off and landing guidance system integrity monitoring system to relatively easily obtain a lower protection level, thereby improving the availability of the system.

Description

Technical Field

[0001] The invention relates to the field of satellite navigation technology, and in particular to an error envelope performance evaluation method for a take-off and landing guidance system of an aviation navigation network. Background Art

[0002] The aviation navigation network is a comprehensive network composed of multiple aviation navigation facilities, equipment, systems and services, which aims to support safe, efficient, continuous and accurate navigation of aircraft in the air and on the ground. The aviation navigation network consists of the space segment Global Navigation Satellite System (GNSS) satellite constellation, airborne navigation equipment, ground segment infrastructure and information processing platform, covering the entire flight phase. The space segment GNSS satellite provides satellite-based navigation sources for airborne navigation equipment; the ground segment infrastructure such as distance measure equipment (DME) and instrument landing system (ILS) provides traditional land-based navigation signals and improves service coverage by co-location with mobile communication base stations; the ground segment L-band Digital Aeronautical Communications System (LDACS) ground equipment provides a new type of aviation communication and navigation integrated signal, while providing navigation sources for airborne navigation equipment, establishing air-to-ground broadband communication links, realizing the sharing of air-to-ground propagation environment monitoring and electromagnetic interference monitoring information, and building an aviation navigation network. The onboard navigation equipment integrates multiple navigation sources such as satellite-based and land-based, and combines the integrity monitoring enhancement and electromagnetic interference monitoring information generated by the ground information processing platform to achieve flexible fusion and integrity enhancement of pan-source navigation information throughout the flight phase, providing highly reliable aviation navigation services.

[0003] At present, the accuracy of aviation navigation systems can basically meet the requirements of aviation applications, but its integrity is still insufficient. Integrity, as a key performance indicator in the aviation navigation network, is a measure of the correctness of the information provided by the satellite navigation system. It indicates the ability of the system to promptly alert users when the navigation system fails or the error exceeds the limit. It is usually described by three indicators: Alert Limit (AL), Alert Time and Integrity Risk. Among them, integrity risk refers to the probability that the system fails and cannot be used normally and cannot alert users within the specified alert time. By using the air-ground data link in the aviation navigation network, air-ground collaborative integrity monitoring can be achieved, and a typical application is the satellite-based precision take-off and landing guidance system.

[0004] According to different approach performance requirements, satellite-based precision takeoff and landing guidance systems are also divided according to different approach service levels. The service levels currently in operation are mainly GAST-C and GAST-D. Both are suitable for single-frequency single-constellation systems. Among them, GAST-C provides CAT I approach services. After nearly 20 years of research and development, the technology has matured, and the corresponding minimum operating performance standards have been formed in DO-253C submitted by the Aeronautical Radio Technical Commission in 2008. GAST-D introduces multiple ionospheric anomaly monitors on the basis of GAST-C, which can meet the requirements of CAT II / III precision approaches. In recent years, satellite-based precision takeoff and landing guidance systems have gradually transitioned from traditional single-frequency single-constellation to dual-frequency multi-constellation (Dual-Frequency Multi-Constellation, DFMC), and mainly developed two service levels supporting the DFMC system, GAST-E and GAST-F. Both of them greatly reduce the impact of ionospheric anomalies on the navigation system through dual-frequency smoothing filtering technology, and also have the potential to meet the higher integrity requirements of CAT III precision approaches.

[0005] The integrity of satellite-based precision take-off and landing guidance systems can be divided into non-protection-level integrity and protection-level integrity. Non-protection-level integrity generally detects and eliminates abnormal observations in real time through specific fault monitoring algorithms. Protection-level integrity generally assumes that pseudorange errors obey Gaussian distribution, but in fact, the distribution of these errors and test statistics is usually non-Gaussian. Therefore, these errors need to be conservatively processed so that the error distribution is no longer limited to Gaussian distribution. This conservative processing process is called "envelope".

[0006] Traditional error envelope methods include cumulative distribution function (CDF) envelope and paired overbounding. With the deepening of research in recent years, the academic community has proposed a variety of statistical uncertainty error envelope models, including extreme value theory model (EVT), Gaussian kernel-Pareto tail model (GPD), stable distribution model and mixed Gaussian distribution model (GMM). These error envelope models lack a unified model performance evaluation method and can only judge the performance of the model by calculating the protection level. However, models such as GPD that do not have convolution additivity involve complex convolution operations in the process of calculating the protection level, which greatly increases the computational load.

[0007] In addition to the above classification according to the specific envelope model, the error envelope is generally divided into two categories according to the domain where the error is distributed: pseudorange domain error envelope (envelope of pseudorange domain error) and positioning domain error envelope (envelope of positioning domain error). The positioning domain error is linearly transformed from the pseudorange domain error to the positioning domain, and there is no convolution operation problem of positioning domain projection.

[0008] In view of the lack of unified evaluation standards for error envelope models, the present invention proposes a method for evaluating the error envelope performance of an aviation navigation network take-off and landing guidance system in combination with existing methods and ideas. For the error envelope method in the pseudorange domain, in order to avoid the complex convolution operation when the pseudorange domain is projected into the positioning domain, the performance of the error envelope model is directly evaluated in the pseudorange domain, thereby reducing the computational load. For the error envelope method in the positioning domain, the performance evaluation method of the error envelope model of the satellite-based precision take-off and landing guidance system is also applicable. Summary of the invention

[0009] The purpose of the present invention is to provide an error envelope performance evaluation method for a take-off and landing guidance system of an aviation navigation network, which solves the problems raised in the above-mentioned background technology, can evaluate the error envelope model performance in the pseudorange domain and the positioning domain, and is adaptable to single-frequency single-constellation and dual-frequency multi-constellation systems, thereby providing a quantitative standard for the selection of the error envelope model during integrity monitoring.

[0010] To achieve the above object, the present invention provides an error envelope performance evaluation method for an aviation navigation network take-off and landing guidance system, including a single-frequency pseudorange domain error envelope model evaluation method, a dual-frequency pseudorange domain error envelope model evaluation method, and a dual-frequency positioning domain error envelope model evaluation method. The above evaluation methods all include the following steps:

[0011] Step S1, filter the observation data, perform carrier phase smoothing filtering and extract pseudorange single difference residual;

[0012] Step S2, constructing an error envelope model;

[0013] Step S3: perform error envelope confidence evaluation and error envelope tightness evaluation.

[0014] Preferably, the specific steps of step S1 are as follows:

[0015] Step S11, screening of observation data: considering the characteristics of the satellite-based precision take-off and landing guidance system and smoothing filtering processing, data screening is performed to screen out the continuous time data of the constellation, satellite and frequency point;

[0016] Step S12, performing carrier phase smoothing pseudorange processing: using the Hatch filtering method to perform single-frequency smoothing filtering on the pseudorange observation amount to reduce the noise level in the observation amount;

[0017] Step S13, extracting pseudo-range single difference residuals: according to the differential principle of the satellite-based precision take-off and landing guidance system, extracting spare pseudo-range single difference residuals to eliminate satellite clock error and atmospheric delay error.

[0018] Preferably, step S2 of the single-frequency pseudorange domain error envelope model evaluation method specifically includes: constructing a single-frequency pseudorange domain error envelope model by using a CDF envelope algorithm.

[0019] Preferably, step S2 of the dual-frequency pseudorange domain error envelope model evaluation method specifically includes:

[0020] The single-frequency pseudorange residuals of the two frequency points are fitted respectively by a fitting algorithm to generate a corresponding pseudorange residual fitting model;

[0021] The single-frequency pseudorange error envelope model is generated from the pseudorange residual fitting model by using uncertainty analysis method;

[0022] Perform dual-frequency combination to form a dual-frequency pseudorange error envelope model.

[0023] Preferably, step S2 of the dual-frequency positioning domain error envelope model evaluation method specifically includes:

[0024] Perform positioning domain projection and linearly transform the pseudorange single difference residual to the positioning domain;

[0025] Through the positioning domain error fitting model, the single-frequency positioning domain normalized errors of two frequency points are fitted respectively by a fitting algorithm to generate a corresponding positioning domain error fitting model;

[0026] Perform dual-frequency combination to form a dual-frequency pseudorange error envelope model.

[0027] Preferably, step S3 of the single-frequency pseudorange domain error envelope model evaluation method specifically includes:

[0028] Evaluate the confidence of the single-frequency pseudorange domain error envelope model to ensure that the confidence requirements are met;

[0029] Calculate the difference between the single frequency difference pseudorange residual and the single frequency pseudorange domain error envelope model KL Divergence,quantitatively characterizes the performance of the error envelope model.

[0030] Preferably, step S3 of the dual-frequency pseudorange domain error envelope model evaluation method specifically includes:

[0031] Evaluate the confidence of the dual-frequency error envelope model to ensure that the confidence requirements are met;

[0032] Calculate the difference between the dual-frequency differential pseudorange residual and the dual-frequency pseudorange domain error envelope model KL Divergence,quantitatively characterizes the performance of the error envelope model.

[0033] Preferably, step S3 of the dual-frequency positioning domain error envelope model evaluation method specifically includes:

[0034] Evaluate the confidence of the dual-frequency positioning domain error envelope model to ensure that the confidence requirements are met;

[0035] Calculate the difference between the dual-frequency positioning domain error and the dual-frequency positioning domain error envelope model KLDivergence,quantitatively characterizes the performance of the error envelope model.

[0036] Preferably, KL Divergence quantifies the level of difference between two distributions and is given by the following formula:

[0037] ;

[0038] in, Q(X) is the distribution of the fitted model, P(X) is the distribution of the real samples, when P(x) = Q(x) hour, KL The divergence calculation result is 0.

[0039] Therefore, the present invention adopts the above-mentioned aviation navigation network take-off and landing guidance system error envelope performance evaluation method, which has the following beneficial effects:

[0040] (1) The present invention provides a method for evaluating the performance of an error envelope model in the pseudorange domain for the pseudorange error envelope method, thereby avoiding the complex convolution operation when projecting from the pseudorange domain to the positioning domain. The appropriate error envelope model can be selected without specifically calculating the protection level.

[0041] (2) The present invention provides a method for quantifying the performance of the error envelope model for the positioning domain error envelope algorithm, thereby avoiding the complex operation of obtaining the inverse function for the final calculation of the protection level.

[0042] (3) The error envelope model performance evaluation method for the satellite-based precision take-off and landing guidance system proposed in the present invention can quantitatively evaluate a variety of error envelope models in single and dual frequencies as well as in the pseudorange domain and positioning domain, providing a universal quantitative tool for horizontal comparison between error envelope models.

[0043] (4) The present invention is conducive to the selection of a specific error envelope model in integrity assessment, and can help the integrity monitoring system of the satellite-based precision take-off and landing guidance system to obtain a lower protection level relatively easily, thereby improving the availability of the system.

[0044] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a structural schematic diagram of an embodiment of an error envelope performance evaluation method for an aviation navigation network take-off and landing guidance system of the present invention;

[0046] Figure 2 The present invention provides a flow chart of carrier phase smoothed pseudorange of an error envelope performance evaluation method for an aviation navigation network take-off and landing guidance system. DETAILED DESCRIPTION

[0047] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0048] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0049] Example

[0050] See also Figure 1-2 The present invention provides an error envelope performance evaluation method for an aviation navigation network take-off and landing guidance system, including a single-frequency pseudorange domain error envelope model evaluation method, a dual-frequency pseudorange domain error envelope model evaluation method, and a dual-frequency positioning domain error envelope model evaluation method. The above evaluation methods all include the following steps:

[0051] Step S1, filter the observation data, perform carrier phase smoothing filtering and extract pseudorange single difference residual;

[0052] Step S2, constructing an error envelope model;

[0053] Step S3: perform error envelope confidence evaluation and error envelope tightness evaluation.

[0054] Example 1: Single-frequency pseudorange domain error envelope model evaluation method

[0055] Observational data screening

[0056] Taking the dual-frequency multi-constellation system composed of GPS and BDS as an example, the observations of GPS L1 and L5 bands and BDS B1C and B2a bands are selected, and the satellite data with elevation angles lower than 5° are screened and deleted. The time period when the number of available satellites in each constellation is greater than 6 is screened out, and the data with multiple breakpoints in a short period of time is deleted (to facilitate carrier phase smoothing). Finally, the dual-frequency pseudorange and carrier phase observation data of GPS and BDS in the same period are selected, which are complete and received by both the airborne terminal and the ground station.

[0057] Carrier phase smoothed pseudorange

[0058] First, the selected pseudo-range observations need to be smoothed and filtered to reduce the impact of noise. Hatch filtering is usually used. The carrier smoothing filtering process is as follows: Figure 1 As shown, P represents the pseudorange observation, Φ represents the carrier phase observation; F It is a low-pass filter with a filtering time constant of τ , τ Take 30s or 100s; X represents the Code-Minus-Carrier (CMC) observation, Y represents the smoothed code pseudorange. F This is usually achieved in the following way:

[0059] (1)

[0060] in, represents the epoch number of the observation data, , T is the sampling interval; is the smoothed CMC of the previous epoch.

[0061] Therefore, the smoothed code pseudorange is:

[0062] (2)

[0063] Among them, the smoothing initial epoch equal .

[0064] Pseudorange single difference residual extraction

[0065] The pseudo-range observations after smoothing filtering need to be processed by differential processing to eliminate errors such as satellite clock error and atmospheric delay (including ionospheric and tropospheric delay).

[0066] (3)

[0067] in, g Indicates the ground side. r Indicates the airborne end.

[0068] It is the pseudo-range observation quantity of the ground station of the satellite-based precision take-off and landing guidance system:

[0069] (4)

[0070] in, Indicates the actual distance from the observation satellite to the receiver. represents the satellite clock error, represents the ground receiver clock error, represents the ionospheric delay error, represents the tropospheric delay error, Represents multipath and thermal noise.

[0071] is the pseudorange observation of the airborne receiver:

[0072] (5)

[0073] in, Indicates the actual distance from the observation satellite to the airborne receiver. represents the satellite clock error, represents the ionospheric delay error, represents the tropospheric delay error, Represents multipath and thermal noise at the airborne end.

[0074] It is the pseudorange single difference residual, which eliminates the errors such as satellite clock error, ionospheric and tropospheric delay, and only includes the residuals of the above error terms as well as multipath and thermal noise.

[0075] Pseudorange domain error envelope

[0076] The Gaussian Core Exponential Tail (GCET) model divides the error distribution function into two parts: the distribution core and the distribution tail. The distribution core refers to the part of the distribution function near the mean; the distribution tail refers to the part on the left and right sides of the distribution function. These two parts are separated by a given critical point (the errors usually discussed are axisymmetric, so only one critical point needs to be defined for the left and right tails). The probability density function of the tail is:

[0077] (6)

[0078] in, E L is the critical point of the nuclear tail mentioned above, generally 1.96 to 2.58 times the standard deviation of the error sample, yes E exist E L The probability density at P tail for E > E L probability.

[0079] The GCET method uses hypothesis testing to verify E L The probability density function (PDF) at and the tail probability of exceeding EL conform to the Gaussian distribution. This requires checking Nindependent error samples and determine how many of them exceed E L If the samples are independent and each trial exceeds EL The probability of p 0 , then in N In the experiment, there were R Samples exceed E L The probability of follows a binomial distribution.

[0080] Model parameters P EL and P tail It can be obtained by using the error actual sample through hypothesis testing method, here is P tail Let the error sample exceed E L The probability of p 0 ,but N There are R More than E L The probability of follows a binomial distribution:

[0081] (7)

[0082] and N No more than S Samples larger than E L The probability is:

[0083] (8)

[0084] therefore, N More than 100 samples S Samples larger than E L The probability is 1- P cbinom The null hypothesis of the hypothesis test is P tail = p 0 , the samples that are greater than E L Number of N g With threshold T Compare, if more than T Then the null hypothesis is rejected.

[0085] First, choose a suitable threshold T , to ensure that the probability of making the first type of error is 1-P cbinom ( N , T , p 0 ) is less than a given value (usually 0.05). Let the required envelope confidence be p ,treat T After confirming, find the right p 1 , to ensure that the probability of making a type II error = P cbinom ( N , T , p 1 ) not more than 1- p The obtained p 1 is P tail The confidence level is p Similarly, using E L The number of samples near can be obtained The upper confidence limit of .

[0086] Model Performance Evaluation

[0087] Since most of the pseudorange error samples are concentrated in the distribution core, directly analyzing the cumulative distribution function (CDF) tends to ignore the influence of the thick tail of the error distribution. The selection of the optimal envelope based on the parameters obtained by CDF quality assessment is prone to the situation where the core is over-envelope and the tail is not fully enveloping.

[0088] In order to ensure that the "weights" of the core and tail of the error envelope are the same when evaluating the envelope quality, the QQ plot (Quantile-Quantile Plot) is used to process the error distribution and envelope distribution. The QQ plot is a graphical tool used to compare the similarity between two probability distributions. It can be used to evaluate the degree of conformity between the error sample data and the error envelope distribution. It compares the quantiles of the two distributions to determine whether the shapes, positions, and scales of the two distributions are consistent.

[0089] In the QQ plot, the horizontal axis usually represents the quantile of the theoretical distribution, and the vertical axis represents the quantile of the sample data. By plotting a scatter plot of the sample distribution and the corresponding quantiles of the theoretical distribution, the relationship between the two distributions can be observed. If the two distributions are very similar, the points in the QQ plot will be close to a 45° straight line. If the points deviate significantly from this straight line, it indicates that there is a difference between the two distributions. Compared with CDF and PDF, the QQ plot amplifies the weight of the tail of the envelope distribution, which can more clearly reflect the tail difference between the error sample distribution and the error envelope distribution.

[0090] The model performance evaluation method includes two parts: error envelope confidence evaluation and envelope tightness evaluation. Error envelope confidence evaluation determines whether the envelope is successful by the numerical relationship between the error sample distribution and the error envelope. Envelope tightness evaluation determines whether the envelope distribution is too conservative by the similarity between the error sample distribution and the error envelope distribution.

[0091] a. Error envelope confidence assessment

[0092] In order to evaluate the confidence of the error envelope, we first draw a QQ graph with the horizontal axis as the quantile of the CDF of the absolute value of the error envelope and the vertical axis as the quantile of the CDF of the absolute value of the error sample. The CDF of the absolute value of the error envelope is calculated from the CDF of the error envelope. Assuming that the error envelope distribution is F(x) , then the distribution used for confidence assessment is 2 F(x) -1.

[0093] Take an average of 1000 sample points in the horizontal axis quantile interval [0,1], and their coordinates are ( x n , y n ), n is the sample point number. Statistics x n > y n Number of N , when the error envelope requires 95% confidence, it is required N >950. This indicates that the confidence level of the error envelope is greater than 95%, otherwise the envelope needs to be re-enveloped and more conservative processing needs to be performed.

[0094] b. Error envelope tightness evaluation

[0095] The error envelope tightness evaluation is also completed with the help of QQ plot. On the QQ plot, 1000 sample points are averaged in the interval [0,1] of the horizontal axis quantile and introduced KL Divergence (Kullback-Leibler Divergence) for this set of samples and y = x The similarity of the curves is quantified.

[0096] KL Divergence is a measure of the difference between two probability distributions, which can quantify the level of difference between the two distributions. Its formula is as follows:

[0097] (9)

[0098] in, Q(x) is the distribution of 1000 sample points,P(x) yes y = x The distribution of the sample points on the corresponding horizontal axis on the curve. P(x) = Q(x) hour, KL The result of the divergence calculation is 0. That is, when the sample points are closer y = x curve, KL The closer the divergence calculation result is to 0, the higher the tightness of the error envelope is, and the better the envelope performance is when the envelope confidence level is met.

[0099] Example 2: Performance evaluation method of dual-frequency pseudorange domain error envelope model

[0100] The dual-frequency pseudorange domain GPD envelope and the single-frequency pseudorange domain GCET envelope have the same process in data screening and pseudorange residual extraction. One of the main advantages of the dual-frequency system is that the dual-frequency smoothing filter greatly reduces the impact of ionospheric delay on aviation navigation. At the same time, the error after dual-frequency smoothing filtering is a linear combination of single-frequency errors, and its PDF is the convolution of two single-frequency error PDFs. The conservatism after convolution will also be amplified, which requires dual-frequency combination of the error envelope. The specific steps are as follows.

[0101] Dual frequency smoothing filter

[0102] In the dual-frequency multi-constellation satellite-based precision take-off and landing guidance system, the commonly used dual-frequency filtering methods are Dfree and Ifree. Since the single-frequency pseudo-range residual in Dfree filtering is independent of the pseudo-range residual of another frequency point, it does not involve the dual-frequency combination problem. Therefore, the present invention selects the dual-frequency combination of Ifree filtering as an example.

[0103] The Ifree filter has the same structure as the single-frequency Hatch filter, and the input quantity changes as follows:

[0104] (10)

[0105] in, represents the dual-frequency combination coefficient, , and They represent the center frequencies of the L1 (B1C, E1) and L5 (B2a, E5a) bands, namely 1575.42MHz and 1176.45MHz, respectively. represents the pseudorange observation value, Represents the carrier phase observation value.

[0106] Pseudorange domain error envelope

[0107] The pseudorange domain GPD envelope model mainly includes pseudorange error fitting and uncertainty envelope.

[0108] (11)

[0109] in, represents the pseudorange error, and are the left and right tails of the GPD distribution, is the Gaussian kernel of the distribution, and is the threshold between the core and the tail.

[0110] Next, the GPD model parameters are calculated by maximum likelihood estimation:

[0111] (12)

[0112] in, and is the parameter of the GPD distribution. After at least 2500 maximum likelihood estimates, the most conservative and as the GPD parameter.

[0113] After obtaining the GPD distribution parameters, in order to further make a conservative estimate, the uncertainty envelope of the obtained GPD distribution is performed. The specific operation is to convert the parameters and Change to and Based on experience, and The value of is:

[0114] (13)

[0115] in, and Represent the model parameters and The amount of change.

[0116] Dual-band combination

[0117] Since the error after Ifree filtering is a linear combination of single-frequency errors, the error probability density function after dual-frequency filtering is the convolution of two single-frequency error PDFs. The convolution of the dual-frequency pseudorange domain GPD envelope model is more complicated in numerical calculation. The specific expression of the PDF of the GPD distribution is as follows:

[0118] (14)

[0119] Calculate the L1 frequency band separately With L5 band , after convolution, the dual-frequency GPD error envelope is obtained:

[0120] (15)

[0121] in, represents the GPD envelope PDF of the L1 band, Represents the GPD envelope PDF of the L2 band.

[0122] Model Performance Evaluation

[0123] The dual-frequency positioning domain includes two parts: error envelope confidence evaluation and envelope tightness evaluation. The pseudorange single difference residual is used as the error sample, and the GPD uncertainty envelope is used as the error envelope distribution. Envelope confidence evaluation is used to ensure that the error envelope meets the confidence requirement (usually 95%). When the confidence requirement is met, envelope tightness evaluation is performed to quantify the error envelope quality, thereby achieving the effect of model performance evaluation.

[0124] Example 3: Performance evaluation method of dual-frequency positioning domain error envelope model

[0125] The positioning domain GMM error envelope method and the pseudorange domain error envelope method have some similar preprocessing steps, mainly including observation data screening, carrier phase smoothing pseudorange and pseudorange single difference residual extraction. It should be noted that the observations of the two frequency bands need to be processed by corresponding preprocessing steps. Similar preprocessing steps are not repeated in this embodiment, and only the processing flow unique to the dual-frequency positioning domain envelope is described.

[0126] Positioning domain projection

[0127] First, the pseudo-range residual is linearly transformed into the positioning domain to obtain the positioning domain error. The formula is as follows:

[0128] (16)

[0129] in, N is the number of visible satellites, E i It is i The pseudorange residuals of the satellites, E t yes t The positioning domain error after linear transformation at any moment, is the third column of the projection matrix i Elements correspond to the vertical projection coefficients. The projection matrix expression is as follows:

[0130] (17)

[0131] in, G is the orientation cosine matrix:

[0132] (18)

[0133] W is the weighting matrix:

[0134] (19)

[0135] : j = 1,…, N For satellite j The standard deviation of pseudorange difference error is:

[0136] (20)

[0137] Among them, σ pr-gnd is the standard deviation of the differential correction error calculated by the ground system, σ air is the standard deviation of the observation noise of the airborne receiver, σ iono is the standard deviation of the residual ionospheric error, σ tropo is the standard deviation of the residual tropospheric error.

[0138] Positioning domain error fitting model

[0139] After extracting the positioning domain error, it needs to be modeled. The positioning domain error can be used as a sample for GMM fitting. The GMM model can fit the error distribution by combining multiple Gaussian distributions, usually using the EM algorithm for fitting.

[0140] Suppose there is a GMM model ,in is the observation data, i.e., the positioning domain error; are the model parameters, including the mean of each Gaussian distribution , standard deviation and weight In order to obtain the likelihood function that maximizes the observed data, it is necessary to consider the latent variables contained in the model , that is, which Gaussian distribution each data point belongs to.

[0141] The basic idea of ​​the EM algorithm is to alternately perform two steps: the expectation step (E step) and the maximization step (M step) to find the maximum value of the log-likelihood function.

[0142] In step E, the posterior probability of each data point belonging to each Gaussian distribution is calculated. Indicates t The first iteration i The samples come from j The probability of a Gaussian component is:

[0143] (twenty one)

[0144] in, Indicates the value of a data point. Represents a Gaussian distribution.

[0145] In the M step, the expected function is differentiated and the parameters are updated. .

[0146] After multiple iterations (usually no more than 100 times), when the parameter difference between two iterations is less than the specified iteration threshold of 10 -5 When , the parameters of the GMM fitting model can be obtained.

[0147] Statistical uncertainty error envelope

[0148] Evaluating the uncertainty of parameter estimates mainly involves calculating the confidence interval of the parameter estimate. The Fisher information matrix is ​​calculated using the Louis algorithm to obtain the confidence interval of the parameter estimate.

[0149] Assume that the result estimated by the EM algorithm is , according to the Fisher criterion, the asymptotic variance can be expressed as the information matrix I 0 The inverse matrix is ​​used to solve:

[0150] (twenty two)

[0151] in, represents the partial derivative operation, represents the conditional probability distribution.

[0152] Since GMM fitting involves latent variables, the Fisher information matrix is ​​difficult to calculate directly. Louis handles the situation with latent variables by decomposing the Fisher information into the sum of "complete information" and "missing information". The complete information expression is as follows:

[0153] (twenty three)

[0154] in, represents the expectation operation, represents the maximum likelihood probability distribution.

[0155] The missing information expression is as follows:

[0156] (twenty four)

[0157] in, Var Represents the variance operation.

[0158] The Fisher information matrix is:

[0159] (25)

[0160] in, , , It is the default expression of conditional probability in probability statistics.

[0161] I 0 The diagonal elements of the inverse matrix of are the variances of the corresponding parameters. Therefore, the parameters The confidence interval for is:

[0162] (26)

[0163] in, Represents the parameters in the inverse matrix of I0 The corresponding diagonal matrix elements. Select the upper bound of the confidence interval As the error envelope parameter, the error envelope distribution is obtained.

[0164] Dual-band combination

[0165] The error distribution after dual-frequency combination is the convolution of the single-frequency error distribution of the two frequency bands. The same dual-frequency combination as that for dual-frequency positioning is selected, and the ionosphere-free (Ifree) combination is taken as an example. The input of the Ifree combination is:

[0166] (27)

[0167] in, is the dual-frequency combination coefficient, , and They are the center frequencies of the L1 (B1C) band and the L5 (B2a) band, namely 1575.42MHz and 1176.45MHz. Since each component of the GMM distribution is Gaussian and has convolution invariance, the error distribution dual-frequency combination is the linear addition of the single-frequency distribution. The two-component GMM dual-frequency combination is as follows:

[0168] (28)

[0169] in, Represents the positioning domain error.

[0170] This is the error envelope of the dual-frequency positioning domain.

[0171] Model Performance Evaluation

[0172] The dual-frequency positioning domain includes two parts: error envelope confidence evaluation and envelope tightness evaluation. The positioning domain error projected from the pseudorange error is used as the error sample, and the confidence upper limit of the GMM uncertainty envelope is used as the error envelope distribution parameter. First, the envelope confidence evaluation is performed to ensure that the error envelope meets the confidence requirement (usually 95%). When the confidence requirement is met, the envelope tightness evaluation is performed to quantify the error envelope quality, thereby achieving the effect of model performance evaluation.

[0173] Therefore, the present invention adopts the above-mentioned aviation navigation network take-off and landing guidance system error envelope performance evaluation method, which is conducive to the selection of a specific error envelope model in the integrity assessment, and can help the satellite-based precision take-off and landing guidance system integrity monitoring system to relatively easily obtain a lower protection level and improve the system availability.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for evaluating the error envelope performance of an aviation navigation network takeoff and landing guidance system, characterized in that: The present invention comprises a single-frequency pseudorange domain error envelope model evaluation method, a dual-frequency pseudorange domain error envelope model evaluation method and a dual-frequency positioning domain error envelope model evaluation method, and the above evaluation methods all comprise the following steps: Step S1, filter the observation data, perform carrier phase smoothing filtering and extract pseudorange single difference residual; Step S2, constructing an error envelope model; Step S3, performing error envelope confidence evaluation and error envelope tightness evaluation; Step S2 of the single-frequency pseudorange domain error envelope model evaluation method specifically includes: constructing a single-frequency pseudorange domain error envelope model by using a CDF envelope algorithm; Step S2 of the dual-frequency pseudorange domain error envelope model evaluation method specifically includes: The single-frequency pseudorange residuals of the two frequency points are fitted respectively by a fitting algorithm to generate a corresponding pseudorange residual fitting model; The single-frequency pseudorange error envelope model is generated from the pseudorange residual fitting model by using uncertainty analysis method; Perform dual-frequency combination to form a dual-frequency pseudo-range domain error envelope model; Step S2 of the dual-frequency positioning domain error envelope model evaluation method specifically includes: Perform positioning domain projection and linearly transform the pseudorange single difference residual to the positioning domain; Through the positioning domain error fitting model, the single-frequency positioning domain normalized errors of two frequency points are fitted respectively by a fitting algorithm to generate a corresponding positioning domain error fitting model; Perform dual-frequency combination to form a dual-frequency positioning domain error envelope model.

2. The error envelope performance evaluation method of an aviation navigation network take-off and landing guidance system according to claim 1 is characterized in that: The specific steps of step S1 are as follows: Step S11, screening of observation data: considering the characteristics of the satellite-based precision take-off and landing guidance system and smoothing filtering processing, data screening is performed to screen out the continuous time data of the constellation, satellite and frequency point; Step S12, performing carrier phase smoothing pseudorange processing: using the Hatch filtering method to perform single-frequency smoothing filtering on the pseudorange observation amount to reduce the noise level in the observation amount; Step S13, extracting pseudo-range single difference residuals: according to the differential principle of the satellite-based precision take-off and landing guidance system, extracting spare pseudo-range single difference residuals to eliminate satellite clock error and atmospheric delay error.

3. The error envelope performance evaluation method of an aviation navigation network take-off and landing guidance system according to claim 1 is characterized in that: Step S3 of the single-frequency pseudorange domain error envelope model evaluation method specifically includes: Evaluate the confidence of the single-frequency pseudorange domain error envelope model to ensure that the confidence requirements are met; Calculate the difference between the single frequency difference pseudorange residual and the single frequency pseudorange domain error envelope model KL Divergence,quantitatively characterizes the performance of the error envelope model.

4. The error envelope performance evaluation method for take-off and landing guidance system of an aviation navigation network according to claim 1, characterized in that: Step S3 of the dual-frequency pseudorange domain error envelope model evaluation method specifically includes: Evaluate the confidence of the dual-frequency error envelope model to ensure that the confidence requirements are met; Calculate the difference between the dual-frequency differential pseudorange residual and the dual-frequency pseudorange domain error envelope model KL Divergence,quantitatively characterizes the performance of the error envelope model.

5. The error envelope performance evaluation method for take-off and landing guidance system of an aviation navigation network according to claim 1, characterized in that: Step S3 of the dual-frequency positioning domain error envelope model evaluation method specifically includes: Evaluate the confidence of the dual-frequency positioning domain error envelope model to ensure that the confidence requirements are met; Calculate the difference between the dual-frequency positioning domain error and the dual-frequency positioning domain error envelope model KL Divergence,quantitatively characterizes the performance of the error envelope model.

6. The error envelope performance evaluation method of an aviation navigation network take-off and landing guidance system according to claim 5, characterized in that: KL Divergence quantifies the level of difference between two distributions and is given by the following formula: ； in, is the distribution of the fitted model, is the distribution of the real samples, when hour, KL The divergence calculation result is 0.

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