Beidou-based train positioning risk source detection method, system and equipment

Abstract

The invention provides a Beidou-based train positioning risk source detection method, system and device, and belongs to the technical field of train positioning. An innovation test statistic sequence is constructed, the sequence is decomposed and reconstructed through wavelet transform, and detail components and approximate components are obtained; performing nonparametric fitting on the wavelet component, and determining an initial detection threshold under the condition of a given false alarm rate; calculating detection thresholds of the detail component and the approximate component, judging whether a step fault and a slope fault exist or not, if so, decomposing the normalized information of the current epoch, eliminating a GNSS pseudo-range / pseudo-range rate observation value corresponding to the maximum component, and performing fault detection again; and updating filtering state estimation and an error covariance matrix according to the new observation matrix and the covariance matrix, and recalculating the position, the speed and the attitude of the train. According to the method, signal abrupt change caused by a step fault can be detected, feature analysis monitoring is performed on an approximate component, a slope fault changing along with time is identified, and the Beidou train positioning precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of train positioning, and in particular to a Beidou-based train positioning risk source detection method, system and device based on wavelet analysis and non-parameter fitting. Background Art

[0002] The train positioning system operates in a complex environment along the railway. Positioning sensors such as satellite navigation and inertial devices are affected by random noise, adverse interference and other factors during the measurement process, resulting in a decrease in positioning accuracy and increasing the risk of train positioning. In this regard, it is necessary to formulate an effective risk mitigation strategy to detect risk sources and isolate faulty satellites in the train positioning system to maintain the accuracy of the train positioning system. However, when the number of visible satellites in the system is not enough to support risk source detection, the algorithm may not be able to maintain the accuracy required by the system. Therefore, it is necessary to study how to reduce or eliminate the impact of fault signals on positioning accuracy in this case, and maintain sufficient observations to maintain the stability of the system and the accuracy of the positioning system. Summary of the invention

[0003] The purpose of the present invention is to provide a Beidou-based train positioning risk source detection method, system and equipment based on wavelet analysis and non-parametric fitting, construct an information test statistic sequence without relying on statistical distribution assumptions, and use wavelet analysis to perform Beidou positioning risk source detection to solve at least one technical problem existing in the above-mentioned background technology.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] In a first aspect, the present invention provides a Beidou-based train positioning risk source detection method, comprising:

[0006] Construct an information test statistic sequence, decompose and reconstruct the sequence through wavelet transform, and obtain detail components and approximate components;

[0007] The kernel density estimation method is used to perform non-parametric fitting on the wavelet components, and the initial detection threshold is determined according to the cumulative probability density function under the condition of a given false alarm rate; the Bootstrap method is introduced to calculate the detection threshold of the detail component and the detection threshold of the approximate component respectively;

[0008] Based on the detection threshold of the detail component and the detection threshold of the approximate component, determine whether there is a step fault and a ramp fault of the faulty satellite. If the above fault exists, decompose the normalized information of the current epoch using Cholesky decomposition, exclude the satellite navigation system (Global Navigation Satellite System, GNSS) pseudorange / pseudorange rate observation value corresponding to the maximum component, and then re-perform fault detection;

[0009] The filter state estimation and error covariance matrix are updated according to the new observation matrix and covariance matrix, and the position, speed and attitude of the train are recalculated.

[0010] Furthermore, the filtering information γ at time k k is the current GNSS pseudorange / pseudorange rate z k Pseudorange / pseudorange rate observations based on inertial navigation calculation The difference is γ k The detection statistic NIS is constructed as:

[0011] A step fault manifests itself as a local anomaly or mutation of the signal, which belongs to the high-frequency information of the signal and corresponds to the detail coefficient obtained by discrete wavelet transform. A ramp fault manifests itself as an abnormal part of the signal that changes over time and belongs to the low-frequency information of the signal and corresponds to the approximate coefficient obtained by discrete wavelet transform.

[0012] Furthermore, the Mallat algorithm is a fast algorithm for discrete wavelet transform. Assuming h(t) and g(t) are high-pass and low-pass filters of the wavelet function, the decomposition formula of the Mallat algorithm is:

[0013]

[0014] Where t=1, 2, ..., N is the sequence number of the discrete signal; A j is the approximate coefficient, which contains the overall trend information of the signal and corresponds to the low-frequency part of the signal; D j It is the detail coefficient, which contains the local information of the signal and corresponds to the high-frequency part of the signal.

[0015] Furthermore, the kernel density estimation method is used to perform non-parametric fitting on the probability densities of detail components and approximate components, and the corresponding detection threshold is determined from the corresponding cumulative distribution function according to the given false alarm rate. The Bootstrap method is used to sample the test statistic to generate multiple sample sets, and the process is repeated for each sample set. The detection threshold is averaged and used as the final detection threshold.

[0016] Furthermore, when the positioning system has no faults, the filtered information obeys a zero-mean normal distribution; if there is a fault, Cholesky decomposition is used to remove the correlation of the information covariance; the lower triangular matrix is ​​used to normalize the actual estimated information; by comparing the normalized information one by one, the satellite observation corresponding to the largest element is marked, and it is isolated and the test statistic is reconstructed to perform fault detection again.

[0017] Furthermore, after isolating the corresponding observations of the faulty satellite, the new observation matrix and the measurement error covariance are calculated, and the Kalman gain matrix is ​​further calculated. Finally, the predicted state is corrected and the state estimation error covariance matrix is ​​updated to obtain the train position, speed, and attitude.

[0018] In a second aspect, the present invention provides a train positioning system, comprising:

[0019] Construct a transformation module to construct an information test statistic sequence, decompose and reconstruct the sequence through wavelet transform, and obtain detail components and approximate components;

[0020] The fitting module is used to perform non-parametric fitting of the wavelet components using the kernel density estimation method, and determine the initial detection threshold according to the cumulative probability density function under the condition of a given false alarm rate; the Bootstrap method is introduced to calculate the detection threshold of the detail component and the detection threshold of the approximate component respectively;

[0021] A judgment module is used to judge whether there is a step fault or a slope fault based on the detection threshold of the detail component and the detection threshold of the approximate component. If there is a fault, the normalized information of the current epoch is decomposed by using Cholesky decomposition, the GNSS pseudorange / pseudorange rate observation value corresponding to the maximum component is excluded, and the fault detection is performed again;

[0022] The update calculation module is used to update the filter state estimation and error covariance matrix according to the new observation matrix and covariance matrix, and recalculate the position, speed and posture of the train.

[0023] In a third aspect, the present invention provides a non-transitory computer-readable storage medium, which is used to store computer instructions. When the computer instructions are executed by a processor, the Beidou-based Beidou train positioning risk source detection method based on wavelet analysis and non-parametric fitting as described in the first aspect is implemented.

[0024] In a fourth aspect, the present invention provides a computer device comprising a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the Beidou-based Beidou train positioning risk source detection method based on wavelet analysis and non-parametric fitting as described in the first aspect.

[0025] In the fifth aspect, the present invention provides an electronic device, comprising: a processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes instructions for implementing the Beidou-based Beidou train positioning risk source detection method based on wavelet analysis and non-parametric fitting as described in the first aspect.

[0026] The beneficial effects of the present invention are as follows: based on wavelet analysis and non-parametric fitting, the signal is decomposed into high-frequency detail components and low-frequency approximate components. By performing feature analysis on the detail components, signal mutations caused by step faults can be detected, and feature analysis on the approximate components can be performed to monitor and identify slope faults that change over time, thereby improving the Beidou train positioning accuracy.

[0027] Additional advantages of the present invention will be more clearly given in the following description or learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0029] Figure 1 This is a flow chart of the Beidou-based train positioning risk source detection method described in an embodiment of the present invention.

[0030] Figure 2 This is a detailed flow chart of the Beidou-based train positioning risk source detection method based on wavelet analysis and non-parametric fitting described in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below by the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0032] It should be understood by those skilled in the art that unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art to which this invention belongs.

[0033] It should also be understood that terms, such as those defined in commonly used dictionaries, should be understood to have a meaning consistent with that in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless as defined herein.

[0034] Those skilled in the art will appreciate that, unless otherwise stated, the singular forms "a", "an", "said" and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements and / or groups thereof.

[0035] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. Different embodiments or examples described in this specification and features of different embodiments or examples may be combined and combined by those skilled in the art without contradiction.

[0036] To facilitate understanding of the present invention, the present invention is further explained below with reference to specific embodiments in conjunction with the accompanying drawings, and the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0037] Those skilled in the art should understand that the drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily necessary for implementing the present invention.

[0038] Example 1

[0039] In this embodiment 1, a train positioning system is first provided, including: a transformation module for constructing an information test statistic sequence, decomposing and reconstructing the sequence through wavelet transform, and obtaining detail components and approximate components. A fitting module for performing non-parametric fitting of wavelet components using a kernel density estimation method, and determining the initial detection threshold according to the cumulative probability density function under a given false alarm rate; introducing a Bootstrap method to calculate the detection threshold of the detail component and the detection threshold of the approximate component respectively. A judgment module for judging whether there is a step fault and a slope fault based on the detection threshold of the detail component and the detection threshold of the approximate component. If there is a fault, the normalized information of the current epoch is decomposed using Cholesky decomposition, the GNSS pseudorange / pseudorange rate observation corresponding to the maximum component is excluded, and then the fault detection is performed again. An update calculation module is used to update the filter state estimation and the error covariance matrix according to the new observation matrix and covariance matrix, and recalculate the position, speed and attitude of the train.

[0040] In this embodiment, the above-mentioned positioning system is used to implement a Beidou-based train positioning risk source detection method, which includes: step S1: constructing an information test statistic sequence, decomposing and reconstructing the sequence through wavelet transform, and obtaining detail components and approximate components; step S2: using the kernel density estimation method to perform non-parametric fitting on the wavelet component, and determining the initial detection threshold according to the cumulative probability density function under the condition of a given false alarm rate; introducing the Bootstrap method to calculate the detection threshold of the detail component and the detection threshold of the approximate component respectively; step S3: based on the detection threshold of the detail component and the detection threshold of the approximate component, determine whether there is a step fault and a slope fault. If a fault exists, use Cholesky decomposition to decompose the normalized information of the current epoch, exclude the GNSS pseudorange / pseudorange rate observation value corresponding to the maximum component, and then re-perform fault detection; step S4: update the filter state estimation and error covariance matrix according to the new observation matrix and covariance matrix, and recalculate the position, speed and attitude of the train.

[0041] Among them, in step S1, the filtering information γ at time k k is the current GNSS pseudorange / pseudorange rate z k Pseudorange / pseudorange rate observations based on inertial navigation calculation Difference:

[0042] Using γ k Construct the detection statistic NIS (Normalized Innovation Squared):

[0043] Wavelet transform is divided into discrete wavelet transform (DWT) and continuous wavelet transform (CWT). The continuous wavelet function is obtained by scaling and translating the basic wavelet. Its mathematical expression is:

[0044]

[0045] In the formula, ψ a,b (t) is a continuous wavelet function; ψ(t) is the basic wavelet; a is the scale factor, which controls the degree of expansion and contraction of the time axis and determines the frequency domain resolution of the wavelet transform; b is the translation factor, which controls the translation position of the wavelet on the time axis and captures the local characteristics of the signal in time; a, b∈R and a>0.

[0046] CWT represents any signal f(t)∈L 2 The convolution of (R) and the basic wavelet is:

[0047]

[0048] Where W f (a, b) are continuous wavelet transform coefficients, ψ * (t) is the conjugate function of ψ(t), is a,b The conjugate function of (t).

[0049] The discrete wavelet function is the a,b The scale factor and translation factor in (t) are discretized and can be expressed as:

[0050]

[0051] Where j is the number of decomposable layers, k∈Z, a0 and b0 are discrete initial values ​​respectively.

[0052] Mallat algorithm is a fast algorithm for discrete wavelet transform. Assuming h(t) and g(t) are high-pass and low-pass filters of the wavelet function, the decomposition formula of Mallat algorithm can be expressed as:

[0053]

[0054] Where t=1,2,…,N is the sequence number of the discrete signal; A j is the approximate coefficient, which contains the overall trend information of the signal and corresponds to the low-frequency part of the signal; D j is the detail coefficient, which contains the local information of the signal and corresponds to the high-frequency part of the signal.

[0055] A step fault is manifested as a local anomaly or mutation of the signal, which belongs to the high-frequency information of the signal and corresponds to the detail coefficient obtained by DWT. A ramp fault is manifested as the abnormal part of the signal that changes over time, which belongs to the low-frequency information of the signal and corresponds to the approximate coefficient obtained by DWT.

[0056] In step S2, the probability density of the detail component and the approximate component is non-parametrically fitted using the kernel density estimation method, and the corresponding detection threshold is determined from the corresponding cumulative distribution function according to the given false alarm rate. The Bootstrap method is further used to sample the test statistic to generate multiple sample sets. The process is repeated for each sample set, and the detection threshold is averaged and used as the final detection threshold.

[0057] The kernel density estimation method constructs a continuous probability density function through the linear addition of discrete sample points. Taking one-dimensional data as an example, the formula is as follows:

[0058]

[0059] Where f represents the probability density function of the population, h is called the bandwidth, which is a hyperparameter, N represents the total number of samples, and K represents the kernel function.

[0060] The trapezoidal rule is used to approximate the integral, and the areas of the trapezoidal regions formed between adjacent points are accumulated to calculate the cumulative probability density function. The corresponding threshold is obtained according to the given false alarm rate. The detection threshold T can be obtained by the following formula:

[0061] The Bootstrap method is a method of estimating statistics by sampling with replacement and simulating the sampling distribution of data. It combines the kernel density estimation method to perform multiple sampling of wavelet components and estimate the detection threshold to improve the robustness of the threshold estimation.

[0062] Based on the above technical solution, in step S3, when the positioning system has no fault, γ k Normal distribution with zero mean:

[0063] E(γ k )=0

[0064]

[0065] Where V k is the theoretical information covariance, P k,k-1 is the Kalman filter one-step prediction state covariance matrix, R k is the observation noise covariance matrix.

[0066] If there is a fault, Cholesky decomposition is used to remove the correlation of the information covariance:

[0067] Use the lower triangular matrix to normalize the actual estimated information: k =Mγ k .

[0068] Through the k Compare one by one, mark r k The satellite observation corresponding to the largest element in is isolated and the test statistic is reconstructed to perform fault detection again.

[0069] In step S4, after isolating the corresponding observations of the faulty satellite, a new observation matrix and measurement error covariance are calculated, and the Kalman gain matrix is ​​further calculated. Finally, the predicted state is corrected and the state estimation error covariance matrix is ​​updated to obtain the train position, speed and attitude.

[0070] Example 2

[0071] like Figure 1 , Figure 2As shown, this embodiment provides a Beidou-based train positioning risk source detection method based on wavelet analysis and non-parametric fitting. In this method, the signal is decomposed into high-frequency detail components A w and the low-frequency approximate component D w , by the detail component A w Characteristic analysis can detect the signal mutation caused by step fault and the approximate component D w Signature analysis can monitor and identify slope faults that change over time, thereby improving the positioning accuracy of Beidou trains.

[0072] The specific technical solution adopted by the method described in this embodiment includes the following steps:

[0073] S1. Constructing the innovation test statistic sequence NIS k (n), n represents the total number of epochs. The sequence is decomposed and reconstructed through wavelet transform to obtain the detail component A w and approximate component D w .

[0074] S2. Use the kernel density estimation method to perform non-parametric fitting on the wavelet component, and determine the initial detection threshold based on the cumulative probability density function under the condition of a given false alarm rate. Introduce the Bootstrap method to calculate the detection threshold of the detail component separately The detection threshold of the approximate component

[0075] S3. Determine whether there is a step fault or a ramp fault. If the current epoch detail component or the approximate component of the current epoch It is determined that the satellite in the current epoch is faulty. The normalized innovation of the current epoch is decomposed using Cholesky decomposition, the GNSS pseudorange / pseudorange rate observation corresponding to the largest component is excluded, and fault detection is performed again until the combined positioning system is fault-free or the available observation value is 1.

[0076] S4. Update the filter state estimation and error covariance matrix according to the new observation matrix and covariance matrix, recalculate the position, speed and attitude of the train, and improve the Beidou train positioning accuracy.

[0077] Based on the above technical solution, in step S1, the filtering new information γ at time k k is the current GNSS pseudorange / pseudorange rate z k Pseudorange / pseudorange rate observations based on inertial navigation calculation Difference:

[0078] Using γ kConstruct the detection statistic NIS (Normalized Innovation Squared):

[0079] Wavelet transform is divided into discrete wavelet transform (DWT) and continuous wavelet transform (CWT). The continuous wavelet function is obtained by scaling and translating the basic wavelet. Its mathematical expression is:

[0080]

[0081] In the formula, ψ a,b (t) is a continuous wavelet function; ψ(t) is the basic wavelet; a is the scale factor, which controls the degree of expansion and contraction of the time axis and determines the frequency domain resolution of the wavelet transform; b is the translation factor, which controls the translation position of the wavelet on the time axis and captures the local characteristics of the signal in time; a, b∈R and a>0.

[0082] CWT represents any signal f(t)∈L 2 The convolution of (R) and the basic wavelet is:

[0083]

[0084] Where W f (a, b) are continuous wavelet transform coefficients, ψ * (t) is the conjugate function of ψ(t), is a,b The conjugate function of (t).

[0085] The discrete wavelet function is the a,b The scale factor and translation factor in (t) are discretized and can be expressed as:

[0086]

[0087] Where j is the number of decomposable layers, k∈Z, a0 and b0 are discrete initial values ​​respectively.

[0088] Mallat algorithm is a fast algorithm for discrete wavelet transform. Assuming h(t) and g(t) are high-pass and low-pass filters of the wavelet function, the decomposition formula of Mallat algorithm can be expressed as:

[0089]

[0090] Where t = 1, 2, ..., N is the sequence number of the discrete signal; A jis the approximate coefficient, which contains the overall trend information of the signal and corresponds to the low-frequency part of the signal; D j It is the detail coefficient, which contains the local information of the signal and corresponds to the high-frequency part of the signal.

[0091] A step fault is manifested as a local anomaly or mutation of the signal, which belongs to the high-frequency information of the signal and corresponds to the detail coefficient obtained by DWT. A ramp fault is manifested as the abnormal part of the signal that changes over time, which belongs to the low-frequency information of the signal and corresponds to the approximate coefficient obtained by DWT.

[0092] On the basis of the above technical solution, in step S2, the probability density of the detail component and the approximate component is non-parametrically fitted using the kernel density estimation method, and the corresponding detection threshold is determined from the corresponding cumulative distribution function according to the given false alarm rate. The Bootstrap method is further used to sample the test statistic to generate multiple sample sets. The process is repeated for each sample set, and the detection threshold is averaged and used as the final detection threshold.

[0093] The kernel density estimation method constructs a continuous probability density function through the linear addition of discrete sample points. Taking one-dimensional data as an example, the formula is as follows:

[0094]

[0095] Where f represents the probability density function of the population, h is called the bandwidth, which is a hyperparameter, N represents the total number of samples, and K represents the kernel function.

[0096] The trapezoidal rule is used to approximate the integral, and the areas of the trapezoidal regions formed between adjacent points are accumulated to calculate the cumulative probability density function. The corresponding threshold is obtained according to the given false alarm rate. The detection threshold T can be obtained by the following formula:

[0097] The Bootstrap method is a method of estimating statistics by sampling with replacement and simulating the sampling distribution of data. It combines the kernel density estimation method to perform multiple sampling of wavelet components and estimate the detection threshold to improve the robustness of the threshold estimation.

[0098] Based on the above technical solution, in step S3, when the positioning system has no fault, γ k Normal distribution with zero mean:

[0099] E(γ k )=0

[0100]

[0101] Where V k is the theoretical innovation covariance, Pk,k-1 is the Kalman filter one-step prediction state covariance matrix, R k is the observation noise covariance matrix.

[0102] If there is a fault, Cholesky decomposition is used to remove the correlation of the innovation covariance:

[0103] The actual estimated innovation is normalized using the lower triangular matrix: k =Mγ k .

[0104] Through the k Compare one by one, mark r k The satellite observation corresponding to the largest element in is isolated and the test statistic is reconstructed to perform fault detection again.

[0105] On the basis of the above technical solution, in step S4, after isolating the corresponding observations of the faulty satellite, a new observation matrix and measurement error covariance are calculated, and the Kalman gain matrix is ​​further calculated. Finally, the predicted state is corrected and the state estimation error covariance matrix is ​​updated to obtain the train position, speed and attitude.

[0106] Example 3

[0107] In this embodiment 3, a Beidou positioning risk source detection method based on wavelet analysis and non-parametric fitting is provided. Without relying on specific statistical distribution assumptions, an innovation test statistic sequence is constructed and the wavelet component is calculated using wavelet analysis. The detection threshold is obtained by combining kernel density estimation with Bootstrap. Finally, Cholesky decomposition is performed to eliminate faulty satellites to improve the Beidou train positioning accuracy.

[0108] The Beidou positioning risk source detection method based on wavelet analysis and non-parametric fitting includes the following steps:

[0109] S1. Construct the detection statistic NIS:

[0110] Where k represents the current moment, and the filtering new information Indicates the current GNSS pseudorange / pseudorange rate z k Pseudorange / pseudorange rate observations calculated by inertial navigation difference.

[0111] The continuous wavelet function is obtained by scaling and translating the basic wavelet. The mathematical expression is:

[0112]

[0113] In the formula, ψ a,b(t) is a continuous wavelet function; ψ(t) is the basic wavelet; a is the scale factor, which controls the degree of expansion and contraction of the time axis and determines the frequency domain resolution of the wavelet transform; b is the translation factor, which controls the translation position of the wavelet on the time axis and captures the local characteristics of the signal in time; a, b∈R and a>0.

[0114] CWT represents any signal f(t)∈L 2 The convolution of (R) and the basic wavelet is:

[0115]

[0116] Where W f (a, b) are continuous wavelet transform coefficients, ψ * (t) is the conjugate function of ψ(t), is a,b The conjugate function of (t).

[0117] The discrete wavelet function is the a,b The scale factor and translation factor in (t) are discretized and can be expressed as:

[0118]

[0119] Where j is the number of decomposable layers, k∈Z, a0 and b0 are discrete initial values ​​respectively.

[0120] Mallat algorithm is a fast algorithm for discrete wavelet transform. Assuming h(t) and g(t) are high-pass and low-pass filters of the wavelet function, the decomposition formula of Mallat algorithm can be expressed as:

[0121]

[0122] Where t = 1, 2, ..., N is the sequence number of the discrete signal; A j is the approximate coefficient, which contains the overall trend information of the signal and corresponds to the low-frequency part of the signal; D j is the detail coefficient, which contains the local information of the signal and corresponds to the high-frequency part of the signal.

[0123] A step fault is manifested as a local anomaly or mutation of the signal, which belongs to the high-frequency information of the signal and corresponds to the detail coefficient obtained by DWT. A ramp fault is manifested as the abnormal part of the signal that changes over time, which belongs to the low-frequency information of the signal and corresponds to the approximate coefficient obtained by DWT.

[0124] S2. The probability density of detail components and approximate components is non-parametrically fitted using the kernel density estimation method. The corresponding detection threshold is determined from the corresponding cumulative distribution function according to the given false alarm rate. The Bootstrap method is further used to sample the test statistic to generate multiple sample sets. The process is repeated for each sample set. The detection threshold is averaged and used as the final detection threshold.

[0125] The kernel density estimation method constructs a continuous probability density function through the linear addition of discrete sample points. Taking one-dimensional data as an example, the formula is as follows:

[0126]

[0127] Where f represents the probability density function of the population, h is called the bandwidth, which is a hyperparameter, N represents the total number of samples, and K represents the kernel function.

[0128] The trapezoidal rule is used to approximate the integral, and the areas of the trapezoidal regions formed between adjacent points are accumulated to calculate the cumulative probability density function. The corresponding threshold is obtained according to the given false alarm rate. The detection threshold T can be obtained by the following formula:

[0129]

[0130] The Bootstrap method is a method of estimating statistics by sampling with replacement and simulating the sampling distribution of data. It combines the kernel density estimation method to perform multiple sampling of wavelet components and estimate the detection threshold to improve the robustness of the threshold estimation.

[0131] S3. Use Cholesky decomposition to remove the correlation of the innovation covariance:

[0132] The actual estimated innovation is normalized using the lower triangular matrix: k =Mγ k .

[0133] Through the k Compare one by one, mark r k The satellite observation corresponding to the largest element in is isolated and the test statistic is reconstructed to perform fault detection again.

[0134] S4. After isolating the corresponding observations of the faulty satellite, calculate the new observation matrix and measurement error covariance, further calculate the Kalman gain matrix, and finally correct the predicted state and update the state estimation error covariance matrix to obtain the train position, speed and attitude.

[0135] Example 4

[0136] This embodiment 4 provides a non-transitory computer-readable storage medium, which is used to store computer instructions. When the computer instructions are executed by a processor, the Beidou-based Beidou train positioning risk source detection method based on wavelet analysis and non-parametric fitting as described above is implemented. The method includes:

[0137] Construct an information test statistic sequence, decompose and reconstruct the sequence through wavelet transform, and obtain detail components and approximate components;

[0138] The kernel density estimation method is used to perform non-parametric fitting on the wavelet components, and the initial detection threshold is determined according to the cumulative probability density function under the condition of a given false alarm rate; the Bootstrap method is introduced to calculate the detection threshold of the detail component and the detection threshold of the approximate component respectively;

[0139] Based on the detection threshold of the detail component and the detection threshold of the approximate component, determine whether there is a step fault or a slope fault. If there is a fault, use Cholesky decomposition to decompose the normalized information of the current epoch, exclude the GNSS pseudorange / pseudorange rate observation value corresponding to the maximum component, and then re-perform fault detection;

[0140] The filter state estimation and error covariance matrix are updated according to the new observation matrix and covariance matrix, and the position, speed and attitude of the train are recalculated.

[0141] Example 5

[0142] This embodiment 5 provides a computer device, including a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, the processor calls the program instructions to execute the Beidou-based Beidou train positioning risk source detection method based on wavelet analysis and non-parametric fitting as described above, the method comprising:

[0143] Construct an information test statistic sequence, decompose and reconstruct the sequence through wavelet transform, and obtain detail components and approximate components;

[0144] The kernel density estimation method is used to perform non-parametric fitting on the wavelet components, and the initial detection threshold is determined according to the cumulative probability density function under the condition of a given false alarm rate; the Bootstrap method is introduced to calculate the detection threshold of the detail component and the detection threshold of the approximate component respectively;

[0145] Based on the detection threshold of the detail component and the detection threshold of the approximate component, determine whether there is a step fault or a slope fault. If there is a fault, use Cholesky decomposition to decompose the normalized information of the current epoch, exclude the GNSS pseudorange / pseudorange rate observation value corresponding to the maximum component, and then re-perform fault detection;

[0146] The filter state estimation and error covariance matrix are updated according to the new observation matrix and covariance matrix, and the position, speed and attitude of the train are recalculated.

[0147] Example 6

[0148] This embodiment 6 provides an electronic device, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes instructions for implementing the Beidou-based Beidou train positioning risk source detection method based on wavelet analysis and non-parametric fitting as described above, the method comprising:

[0149] Construct an information test statistic sequence, decompose and reconstruct the sequence through wavelet transform, and obtain detail components and approximate components;

[0150] The kernel density estimation method is used to perform non-parametric fitting on the wavelet components, and the initial detection threshold is determined according to the cumulative probability density function under the condition of a given false alarm rate; the Bootstrap method is introduced to calculate the detection threshold of the detail component and the detection threshold of the approximate component respectively;

[0151] Based on the detection threshold of the detail component and the detection threshold of the approximate component, determine whether there is a step fault or a slope fault. If there is a fault, use Cholesky decomposition to decompose the normalized information of the current epoch, exclude the GNSS pseudorange / pseudorange rate observation value corresponding to the maximum component, and then re-perform fault detection;

[0152] The filter state estimation and error covariance matrix are updated according to the new observation matrix and covariance matrix, and the position, speed and attitude of the train are recalculated.

[0153] In summary, the Beidou-based train positioning risk source detection method based on wavelet analysis and non-parametric fitting described in the embodiment of the present invention includes 1. Constructing an innovation test statistic sequence NIS k (n), decompose and reconstruct the sequence through wavelet transform to obtain the detail component A w and approximate component D w ; 2. Use the kernel density estimation method to perform non-parametric fitting on the wavelet component, and determine the initial detection threshold based on the cumulative probability density function under the condition of a given false alarm rate. Introduce the Bootstrap method to calculate the detection threshold of the detail component separately and the detection threshold of the approximate component; 3. Determine whether there is a step fault and a slope fault. If there is a fault, use Cholesky decomposition to decompose the normalized new information of the current epoch, exclude the GNSS pseudorange / pseudorange rate observation value corresponding to the largest component, and then re-detect the fault until the combined positioning system is fault-free or the available observation value is 1; 4. Update the filter state estimate and error covariance matrix according to the new observation matrix and covariance matrix, recalculate the position, speed and attitude of the train, and improve the Beidou train positioning accuracy.

[0154] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0155] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0156] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0157] These computer program instructions can also be loaded onto a computer or other programmable data processing device, and a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0158] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative work on the basis of the technical solution disclosed in the present invention should be included in the scope of protection of the present invention.

Claims

1. A Beidou-based train positioning risk source detection method, characterized in that: include: Construct an information test statistic sequence, decompose and reconstruct the sequence through wavelet transform, and obtain detail components and approximate components; The kernel density estimation method is used to perform non-parametric fitting on the wavelet components. Under the condition of a given false alarm rate, the initial detection threshold is determined according to the cumulative probability density function. The Bootstrap method is used to calculate the detection threshold of the detail component and the detection threshold of the approximate component respectively. Based on the detection threshold of the detail component and the detection threshold of the approximate component, determine whether there are risk sources such as step faults and slope faults. If there are risks, use Cholesky decomposition to decompose the normalized information of the current epoch, exclude the GNSS pseudorange / pseudorange rate observations corresponding to the maximum component, and then re-perform positioning risk source detection; After eliminating the observation risk sources, a new observation matrix and covariance matrix are constructed to update the filter state estimate and error covariance matrix, and the position, speed and attitude of the train are recalculated.

2. The Beidou-based train positioning risk source detection method according to claim 1 is characterized in that: Filter information γ at time k k is the current GNSS pseudorange / pseudorange rate z k Pseudorange / pseudorange rate observations based on inertial navigation calculation The difference is γ k The detection statistic NIS is constructed as: The corresponding risks include step faults and ramp faults of the observation satellite. Step faults are manifested as local abnormalities or mutations of the signal, which belong to the high-frequency information of the signal and correspond to the detail coefficients obtained by discrete wavelet transform; ramp faults are manifested as the abnormal part of the signal that changes over time, which belong to the low-frequency information of the signal and correspond to the approximate coefficients obtained by discrete wavelet transform.

3. The Beidou-based train positioning risk source detection method according to claim 2 is characterized in that: Mallat algorithm is a fast algorithm for discrete wavelet transform. Assume h(t) and g(t) are high-pass and low-pass filters of the wavelet function respectively. The decomposition formula of Mallat algorithm is: Where t=1, 2, ..., N is the sequence number of the discrete signal; A j is the approximate coefficient, which contains the overall trend information of the signal and corresponds to the low-frequency part of the signal; D j It is the detail coefficient, which contains the local information of the signal and corresponds to the high-frequency part of the signal.

4. The Beidou-based train positioning risk source detection method according to claim 1 is characterized in that: The kernel density estimation method is used to perform non-parametric fitting on the probability density of detail components and approximate components, and the corresponding detection threshold is determined from the corresponding cumulative distribution function according to the given false alarm rate. The Bootstrap method is used to sample the test statistic to generate multiple sample sets. The process is repeated for each sample set, and the average of the detection threshold is taken as the final detection threshold.

5. The Beidou-based train positioning risk source detection method according to claim 1 is characterized in that: When the positioning system is fault-free, the filtered information obeys the zero-mean normal distribution; if there is a fault, Cholesky decomposition is used to remove the correlation of the information covariance; the lower triangular matrix is ​​used to normalize the actual estimated information; by comparing the normalized information one by one, the satellite observation corresponding to the largest element is marked, isolated, and the test statistic is reconstructed to perform fault detection again.

6. The Beidou-based train positioning risk source detection method according to claim 1 is characterized in that: After isolating the corresponding observations of the faulty satellite, the new observation matrix and measurement error covariance are calculated, and the Kalman gain matrix is ​​further calculated. Finally, the predicted state is corrected and the state estimation error covariance matrix is ​​updated to obtain the train position, speed and attitude.

7. A Beidou-based train positioning risk source detection method, characterized in that: include: Construct a transformation module to construct an information test statistic sequence, decompose and reconstruct the sequence through wavelet transform, and obtain detail components and approximate components; The fitting module is used to perform non-parametric fitting of the wavelet components using the kernel density estimation method, and determine the initial detection threshold according to the cumulative probability density function under the condition of a given false alarm rate; the Bootstrap method is introduced to calculate the detection threshold of the detail component and the detection threshold of the approximate component respectively; A judgment module is used to judge whether there is a step fault or a slope fault based on the detection threshold of the detail component and the detection threshold of the approximate component. If there is a fault, the normalized information of the current epoch is decomposed by using Cholesky decomposition, the GNSS pseudorange / pseudorange rate observation value corresponding to the maximum component is excluded, and the fault detection is performed again; The update calculation module is used to update the filter state estimation and error covariance matrix according to the new observation matrix and covariance matrix, and recalculate the position, speed and posture of the train.

8. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, the Beidou-based train positioning risk source detection method as described in any one of claims 1-6 is implemented.

9. A computer device, characterized in that: It includes a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the Beidou-based train positioning risk source detection method as described in any one of claims 1-6.

10. An electronic device, characterized in that: include: A processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes instructions for implementing the Beidou-based train positioning risk source detection method as described in any one of claims 1-6.

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