Train positioning method and system based on dynamic kernel width robust extended kalman filter

Abstract

The application provides a train positioning method and system based on dynamic kernel width robust extended Kalman filtering, belongs to the technical field of train positioning, establishes a system measurement model and a state model, performs train prior state prediction, and initializes a prior error covariance matrix and a measurement noise covariance matrix; a maximum entropy criterion is introduced to replace a minimum mean square error criterion as a loss function in filtering estimation; an improved lion swarm optimization algorithm is used to dynamically estimate the kernel width of each satellite observation information, so that an optimal kernel width parameter combination under visible satellites is obtained; based on the optimal kernel width parameter set, the measurement noise covariance matrix and the filtering gain matrix are updated, and the train state robust estimation is realized by combining the train prior state prediction result and the observation data. The application combines the maximum entropy principle and the intelligent optimization algorithm, realizes adaptive adjustment of the kernel width parameter, effectively suppresses the influence of the faulty observation quantity on the positioning performance, and thus provides a basis for reliable estimation of the train state in a time-varying disturbance environment.

Description

Technical Field

[0001] This invention relates to the field of train positioning technology, specifically to a train positioning method and system based on dynamic kernel width robust extended Kalman filtering. Background Technology

[0002] The CTCS-2 and CTCS-3 train control systems primarily rely on trackside infrastructure (such as ground transponders, track circuits, and axle counting devices) and wheel speed sensors on the train to collaboratively perceive operational status. However, these systems suffer from significant drawbacks, including large equipment deployment requirements, high construction and maintenance costs, and limited operational efficiency. They are particularly ill-suited to the railway construction and operation needs of harsh natural conditions in western and southwestern regions such as plateaus, mountains, and deserts. Against the backdrop of intelligent railway development, satellite navigation technology, as a representative emerging method, provides crucial technical support for overcoming these limitations. Satellite navigation systems offer advantages such as all-weather, all-time coverage, and high coverage, providing high-precision position awareness services for trains. They support functions such as train positioning, track occupancy detection, and train integrity checks, thereby significantly reducing reliance on trackside equipment and enhancing the autonomy and intelligence of train operation. Therefore, accelerating the deep integration of satellite navigation and train control systems is of significant practical importance for promoting the intelligent upgrading of train control systems.

[0003] However, the railway operating environment is complex and ever-changing. Trains frequently traverse tunnels, mountains, station buildings, and urban complexes, all of which significantly interfere with the propagation and reception of satellite signals. Factors such as the characteristics of electronic equipment, spatial electromagnetic interference, and localized obstructions can cause measurement signal malfunctions, leading to decreased observation quality and significantly increased positioning errors. When these errors exceed the system tolerance, they pose a major threat to train operation safety. Therefore, designing a highly robust and accurate train positioning method is a critical issue that urgently needs to be addressed in the application of satellite navigation in train control systems.

[0004] Extended Kalman filtering (EKB), a typical solution method for train positioning, achieves optimal estimation based on the minimum mean square error criterion and the ideal assumption that the observation noise follows a Gaussian distribution. However, when measurement faults occur in the observation data, the filtering accuracy will drop significantly. Introducing a fault detection and elimination mechanism is an effective way to improve positioning robustness. Its core lies in identifying and eliminating abnormal measurement values ​​that interfere with positioning performance. When there are a large number of available satellites, this method can ensure the continuity and reliability of the filtering process; however, in environments with limited satellite visibility or insufficient observation conditions, blindly eliminating outliers may lead to geometric deterioration, resulting in more severe positioning errors. Summary of the Invention

[0005] The purpose of this invention is to provide a train positioning method and system based on dynamic kernel width robust extended Kalman filtering, so as to solve at least one of the technical problems existing in the background art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a train positioning method based on dynamic kernel width robust extended Kalman filtering, comprising:

[0008] The system uses a satellite receiver to collect raw observation pseudorange and ephemeris data, establishes a system measurement model and state model, predicts the train's prior state based on the train's state variables at the previous moment, and initializes the prior error covariance matrix and measurement noise covariance matrix.

[0009] The maximum entropy criterion is introduced to replace the minimum mean square error criterion as the loss function in the filtering estimation, and the measurement noise covariance matrix is ​​reconstructed by the weight matrix constructed by the Gaussian kernel function.

[0010] Considering the influence of kernel width in Gaussian kernel function on the weights of observation information and prior prediction information in filter gain matrix, an improved lion swarm optimization algorithm is used to dynamically estimate the kernel width of observation information for each satellite, and obtain the optimal kernel width parameter combination for visible satellites.

[0011] Based on the optimal kernel width parameter set, the measurement noise covariance matrix and filter gain matrix are updated, and the train state robust estimation is achieved by combining the train prior state prediction results and observation data.

[0012] As a further limitation of the first aspect of the present invention, the method of using a satellite receiver to collect raw observation pseudorange and ephemeris data, establishing a system measurement model and state model, predicting the train's prior state based on the train's state variables at the previous moment, and initializing the prior error covariance matrix and measurement noise covariance matrix includes: acquiring raw observation data, extracting pseudorange and ephemeris data required for train positioning, and discretizing the state equation and measurement equation of the positioning system according to the basic theory of Kalman filtering; wherein, the state variables in the state equation have a total of 11 dimensions, including position, velocity, receiver clock error distance error, and equivalent clock drift error; considering the train's operating characteristics, a uniform acceleration motion model is selected to determine the train state transition matrix; in the measurement equation, satellite observation pseudorange is selected as the measurement; and the train's prior prediction is calculated based on the state equation.

[0013] As a further limitation of the first aspect of the present invention, the introduction of the maximum entropy criterion instead of the minimum mean square error criterion as the loss function in the filtering estimation, and the reconstruction of the measurement noise covariance matrix through the weight matrix composed of Gaussian kernel functions, includes: combining the state equation and the measurement equation to obtain a linear regression model, combining Kolesky decomposition to define a new error covariance matrix, introducing the maximum entropy criterion as the loss function of the filtering estimation, and based on the principle of the maximum entropy criterion, obtaining the solution of the state estimation by maximizing the optimization criterion, estimating the state at time k based on the fixed-point iterative algorithm, and re-representing the prior error covariance and the measurement noise covariance matrix.

[0014] As a further limitation of the first aspect of the present invention, the consideration of the influence of the kernel width in the Gaussian kernel function on the weights of the observed information and prior prediction information in the filter gain matrix, and the use of an improved lion flock optimization algorithm to dynamically estimate the kernel width of the observed information of each satellite to obtain the optimal combination of kernel width parameters for visible satellites, includes:

[0015] The improved lion pride optimization algorithm includes population initialization, fitness evaluation, pride position update, and boundary checking. Population initialization determines the total number of individuals in the pride, the distribution of different lion types, and their initial positions. The lion position represents a feasible solution to the unsolved variable, i.e., the specific value of the kernel width of each satellite at time k, whose dimension D is determined by the number of observed satellites. The level of uncertainty in the state estimate is selected as the fitness function. The fitness is obtained for each position update based on the position of each lion. After a finite number of population iterations, the historical best position of the pride is the solution set corresponding to the minimum fitness. Boundary constraints limit the range of values ​​for each optimization variable to prevent variables from going out of bounds during the optimization process. This range is usually defined by setting upper and lower boundaries. The positions of the lion king, lionesses, and cubs are updated cyclically through a finite number of iterations. The corresponding fitness values ​​are calculated, sorted, and the solution set corresponding to the minimum fitness is output, which is the optimal combination of kernel width parameters.

[0016] As a further limitation of the first aspect of the present invention, after updating the position of each individual in the pride, the position variables of each lion in each dimension need to be checked for boundaries: if the value of a certain dimension exceeds the preset upper limit, it is adjusted to the upper boundary value; if it is lower than the lower limit, it is set to the lower boundary value; if the variable is between the upper and lower boundaries, it means that the current value is valid and acceptable.

[0017] As a further limitation of the first aspect of the present invention, the method of updating the measurement noise covariance matrix and the filter gain matrix based on the optimal kernel width parameter set, and realizing robust estimation of train state by combining the train prior state prediction results and observation data, includes: updating the matrix and measurement noise matrix according to the obtained optimal kernel width parameter combination, calculating the gain matrix, updating the train state at time k in combination with the observation measurements, and updating the error covariance matrix at time k using the train prior error covariance matrix.

[0018] Secondly, the present invention provides a train positioning system based on dynamic kernel width robust extended Kalman filter, comprising:

[0019] The initialization module is used to collect raw observation pseudorange and ephemeris data using a satellite receiver, establish a system measurement model and state model, predict the train's prior state based on the train's state variables at the previous moment, and initialize the prior error covariance matrix and measurement noise covariance matrix.

[0020] The reconstruction module is used to introduce the maximum entropy criterion instead of the minimum mean square error criterion as the loss function in the filtering estimation, and reconstruct the measurement noise covariance matrix through the weight matrix composed of Gaussian kernel functions.

[0021] The estimation module is used to consider the influence of the kernel width in the Gaussian kernel function on the weights of the observation information and prior prediction information in the filter gain matrix. An improved lion flock optimization algorithm is used to dynamically estimate the kernel width of the observation information of each satellite and obtain the optimal combination of kernel width parameters for visible satellites.

[0022] The update module is used to update the measurement noise covariance matrix and the filter gain matrix based on the optimal kernel width parameter set, and to achieve robust estimation of the train state by combining the train prior state prediction results and observation data.

[0023] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the train positioning method based on dynamic kernel width robust extended Kalman filtering as described in the first aspect.

[0024] Fourthly, the present invention provides a computer device including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor invokes the program instructions to execute the train positioning method based on dynamic kernel width robust extended Kalman filter as described in the first aspect.

[0025] Fifthly, 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 to cause the electronic device to execute instructions for implementing the train positioning method based on dynamic kernel width robust extended Kalman filtering as described in the first aspect.

[0026] The beneficial effects of this invention are: by introducing the maximum entropy criterion to reconstruct the extended Kalman filter and combining it with an intelligent optimization algorithm to achieve adaptive estimation of the Gaussian kernel width under different observations, it can fundamentally solve the problem of positioning performance degradation caused by fault measurement and improve the accuracy and robustness of train position estimation.

[0027] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0028] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a schematic diagram illustrating the implementation principle of the train positioning method based on dynamic kernel width robust extended Kalman filter as described in an embodiment of the present invention. Detailed Implementation

[0030] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0031] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0032] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0033] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated 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.

[0034] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0035] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0036] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0037] To address the issue of decreased accuracy in extended Kalman filter estimation due to measurement failures caused by external uncertainties in satellite measurements, a novel robust train positioning method is proposed. This method introduces the maximum entropy criterion to reconstruct the extended Kalman filter and combines it with an intelligent optimization algorithm to achieve adaptive estimation of the Gaussian kernel width under different observations. This fundamentally solves the problem of decreased positioning performance caused by faulty measurements and improves the accuracy and robustness of train position estimation. This invention discloses a train positioning method based on dynamic kernel width robust extended Kalman filtering, comprising: acquiring raw observation pseudorange and ephemeris data using a satellite receiver; establishing a system measurement model and state model; predicting the train's prior state based on the train's state variables at the previous moment; and initializing the prior error covariance matrix and the measurement noise covariance matrix; introducing the maximum entropy criterion instead of the minimum mean square error criterion as the loss function in the filtering estimation; reconstructing the measurement noise covariance matrix using a weight matrix constructed from Gaussian kernel functions; considering the influence of the kernel width in the Gaussian kernel function on the weights of observation information and prior prediction information in the filtering gain matrix; dynamically estimating the kernel width of the observation information of each satellite using an improved lion swarm optimization algorithm to obtain the optimal kernel width parameter combination under visible satellites; updating the measurement noise covariance matrix and the filtering gain matrix based on the optimal kernel width parameter set; and achieving robust estimation of the train state by combining the train's prior state prediction results and observation data. This invention combines the maximum entropy principle and intelligent optimization algorithms to achieve adaptive adjustment of the kernel width parameter, effectively suppressing the impact of fault observations on positioning performance, thereby providing a basis for reliable estimation of train state under time-varying disturbance environments.

[0038] Example 1

[0039] In this embodiment 1, a train positioning system based on dynamic kernel width robust extended Kalman filter is first provided, including: an initialization module, used to collect raw observation pseudorange and ephemeris data using a satellite receiver, establish a system measurement model and state model, predict the train's prior state based on the train state variables of the previous moment, and initialize the prior error covariance matrix and the measurement noise covariance matrix; a reconstruction module, used to introduce the maximum entropy criterion instead of the minimum mean square error criterion as the loss function in the filter estimation, and reconstruct the measurement noise covariance matrix through a weight matrix composed of Gaussian kernel functions; an estimation module, used to consider the influence of the kernel width in the Gaussian kernel function on the weights of observation information and prior prediction information in the filter gain matrix, and use an improved lion swarm optimization algorithm to dynamically estimate the kernel width of the observation information of each satellite to obtain the optimal kernel width parameter combination under visible satellites; and an update module, used to update the measurement noise covariance matrix and the filter gain matrix based on the optimal kernel width parameter set, and combine the train prior state prediction results and observation data to achieve robust estimation of the train state.

[0040] In this embodiment, the above-described system is used to implement a train positioning method based on dynamic kernel width robust extended Kalman filtering, including: collecting raw observation pseudorange and ephemeris data using a satellite receiver, establishing a system measurement model and state model, predicting the train's prior state based on the train state variables of the previous moment, and initializing the prior error covariance matrix and the measurement noise covariance matrix; introducing the maximum entropy criterion instead of the minimum mean square error criterion as the loss function in the filtering estimation, and reconstructing the measurement noise covariance matrix using a weight matrix composed of Gaussian kernel functions; considering the influence of the kernel width in the Gaussian kernel function on the weights of observation information and prior prediction information in the filtering gain matrix, using an improved lion swarm optimization algorithm to dynamically estimate the kernel width of the observation information of each satellite, and obtaining the optimal kernel width parameter combination under visible satellites; updating the measurement noise covariance matrix and the filtering gain matrix based on the optimal kernel width parameter set, and combining the train prior state prediction results and observation data to achieve robust estimation of the train state.

[0041] In this embodiment, the process of using a satellite receiver to collect raw observation pseudorange and ephemeris data, establishing a system measurement model and state model, predicting the train's prior state based on the train's state variables at the previous moment, and initializing the prior error covariance matrix and measurement noise covariance matrix includes: acquiring raw observation data, extracting pseudorange and ephemeris data required for train positioning, and discretizing the state equation and measurement equation of the positioning system based on the fundamental theory of Kalman filtering; wherein, the state variables in the state equation have 11 dimensions, including position, velocity, receiver clock error distance error, and equivalent clock drift error; considering the train's operating characteristics, a uniform acceleration motion model is selected to determine the train state transition matrix; in the measurement equation, satellite observation pseudorange is selected as the measurement; and the train's prior prediction and prior error covariance matrix are calculated based on the state equation and measurement equation.

[0042] Specifically, raw observation data is acquired from satellite receivers installed on the train, and pseudorange and ephemeris data required for train positioning are extracted. This sensing data will be used to achieve train position estimation. Since train positioning systems are inherently nonlinear systems, the extended Kalman filter, due to its low complexity and good real-time performance, can efficiently handle nonlinear characteristics and is currently the main method for processing train positioning data. According to the basic theory of Kalman filtering, the discretized state equation and measurement equation of the positioning system can be expressed as: In this formula, x k-1 Let z be the state vector at time k-1. k w is the measurement vector at time k. k-1 It is process noise that follows a zero-mean Gaussian distribution, and its corresponding covariance matrix is ​​denoted as Q. k-1 v k It is measurement noise that follows a zero-mean Gaussian distribution, and its corresponding covariance matrix is ​​denoted as R. k Fk-1 H is the state transition matrix. k It is the Hessian matrix of the measurement equation.

[0043] The state equation has 11 dimensions, including position, velocity, receiver clock error, distance error, and equivalent clock drift error, expressed as: x k =[p x v x a x p y v y a y p z v z a z δt dδt], where, (p x ,p y ,p z ), (v x ,v y ,v z ) and (a x ,a y ,a z Let represent the position, velocity, and acceleration in three directions in the geocentric Earth-fixed coordinate system, δt be the receiver clock bias, and dδt be the equivalent clock drift error. Considering the train's operating characteristics, a uniformly accelerated motion model is chosen to determine the train's state transition matrix, expressed as:

[0044]

[0045] Where, τ s It is the time interval for information processing.

[0046] In the measurement equation, satellite observation pseudorange is chosen as the measurement. If N satellites are observed at time k, the true position of the receiver is denoted as (O... x O y O z ), speed is (Ov x ,Ov y ,Ov z The position of the j-th satellite in the Earth-centered Earth-fixed coordinate system is... The pseudorange between the receiver and the j-th satellite can be expressed as:

[0047] ρ GNSS,j =ρ T,j +T+δt+ε

[0048]

[0049] In the formula, ρ T,jδt is the geometric distance from the receiver to the satellite, T is the sum of satellite clock bias, ionospheric error and tropospheric error, δt is the distance error caused by receiver clock bias and clock drift, and ε is the error caused by multipath effect or receiver noise.

[0050] Based on the model established above, the train prior prediction and prior error covariance matrix are calculated as follows:

[0051] Predict the prior state based on the train state transition matrix:

[0052] Initialize the prior error covariance matrix:

[0053] In this embodiment, the maximum entropy criterion is introduced to replace the minimum mean square error criterion as the loss function in the filtering estimation. The measurement noise covariance matrix is ​​reconstructed through the weight matrix constructed by the Gaussian kernel function. This includes: combining the state equation and the measurement equation to obtain a linear regression model; combining Kolesky decomposition to define a new error covariance matrix; introducing the maximum entropy criterion as the loss function for filtering estimation; based on the principle of the maximum entropy criterion, the solution for state estimation can be obtained by maximizing the optimization criterion; based on the fixed-point iterative algorithm, the state at time k is estimated; and the prior error covariance and measurement noise covariance matrix are re-represented.

[0054] Specifically, by combining the state equation and the measurement equation, the following linear regression model can be obtained.

[0055]

[0056] In the formula, I represents the identity matrix, and α k =[-w k v k ] T .

[0057] Define a new error covariance matrix Δ k for

[0058]

[0059] Among them, S k It can be obtained through Kolesky decomposition. (By left multiplication) The linear regression model can be rewritten as:

[0060] L k =Γ k x k +δ k

[0061] In the formula, L k ,Γ k , and δ k Defined respectively

[0062]

[0063] The maximum entropy criterion is introduced as the loss function for filtering estimation.

[0064]

[0065] In the formula G σ Let be the Gaussian kernel function, and σ represent the kernel width. Based on the maximum entropy criterion, the solution for the state estimate can be obtained by maximizing the above optimization criterion.

[0066]

[0067] In the formula, L = m + n, where m and n are the dimensions of the state vector and the measurement vector, respectively, and δ k (i) represents the residual (L) k -Γ k x k The i-th term of )

[0068]

[0069] Define C k (i)=G σ (δ k (i)) can be obtained

[0070]

[0071] C P,k =diag(G σ (δ k (i)),...,G σ (δ k (m)))

[0072] C R,k =diag(G σ (δ k (i)),...,G σ (δ k (n)))

[0073] diag (·) denotes the operation of building a diagonal matrix. Based on the fixed-point iterative algorithm, the state at time k can be estimated.

[0074]

[0075] Vector C k The error covariance matrix was reweighted and the measurement noise matrix was reconstructed. The new error covariance matrix is ​​expressed as:

[0076]

[0077] In practice, since the actual state is unknown, we assume that the estimate is unbiased, that is... Then C P,k It can be considered as an identity matrix. The prior error covariance and measurement noise covariance matrices are re-expressed as:

[0078]

[0079] In this embodiment, considering the influence of the kernel width in the Gaussian kernel function on the weights of observed information and prior prediction information in the filter gain matrix, the improved lion flock optimization algorithm is used to dynamically estimate the kernel width of the observed information of each satellite to obtain the optimal combination of kernel width parameters for visible satellites, including:

[0080] The improved lion pride optimization algorithm includes population initialization, fitness evaluation, pride position update, and boundary checking. Population initialization determines the total number of individuals in the pride, the distribution of different lion types, and their initial positions. The lion position represents a feasible solution to the unsolved variable, i.e., the specific value of the kernel width of each satellite at time k, whose dimension D is determined by the number of observed satellites. The level of uncertainty in the state estimate is selected as the fitness function. The fitness is obtained for each position update based on the position of each lion. After a finite number of population iterations, the historical best position of the pride is the solution set corresponding to the minimum fitness. Boundary constraints limit the range of values ​​for each optimization variable to prevent variables from going out of bounds during the optimization process. This range is usually defined by setting upper and lower boundaries. The positions of the lion king, lionesses, and cubs are updated cyclically through a finite number of iterations. The corresponding fitness values ​​are calculated, sorted, and the solution set corresponding to the minimum fitness is output, which is the optimal combination of kernel width parameters.

[0081] Specifically, in the improved lion pride optimization algorithm, individuals are divided into three categories: lion alphas, lionesses, and cubs. Based on their behavioral characteristics, these individuals are categorized into three types. When hungry, they will approach the lion alpha to obtain food, signifying a local search within the neighborhood of the optimal solution. After feeding, they will participate in hunting with the lionesses, equivalent to conducting deeper searches near the local optimum. Adult individuals will be driven to areas far from the lion alpha, gradually growing in a new environment, and potentially challenging the existing lion alpha to compete for leadership after discovering better resources. The core processes of the improved lion pride optimization algorithm include population initialization, fitness assessment, pride location updates, and boundary checks.

[0082] The main purpose of population initialization is to determine the total number of individuals in the pride, the distribution of different types of lions (alpha male, lionesses, cubs), and their initial positions. Since different roles within the pride fulfill different functions, the proportion of adult lions directly affects the algorithm's optimization ability, while a suitable number of cubs helps increase population diversity, thereby expanding the search space. Assuming the total number of individuals in the pride is N, and the number of adult lions is NAdult, the ratio between the two can be expressed as:

[0083] NAdult=βN

[0084] In the formula, β is the adult lion proportion factor, whose value determines the final search efficiency. To make the algorithm converge faster, it is usually set to 0.5. Accordingly, the number of cubs can be obtained as N-NAdult. Among the adult lions, there is only one alpha male, and the rest are female lions.

[0085] The lion's position represents a feasible solution to the unsolved variable, namely, the specific value of the kernel width of each satellite at time k, whose dimension D is determined by the number of observed satellites. The position of the i-th lion can be represented as:

[0086] p i =(p i1 ,p i2 ,...,p iD ), 1≤i≤N

[0087] After initialization, the locations of all lions in the population are recorded as follows:

[0088]

[0089] Before calculating the kernel width for different observations using the improved lion flock optimization algorithm, it is necessary to first define the optimization objective, i.e., set the fitness function. This paper selects the level uncertainty of the state estimation as the fitness function. The level uncertainty does not depend on the true position reference and can evaluate the train positioning performance in real time based on the observation data, expressed as:

[0090]

[0091] In the formula, σ i Slope is the standard deviation of the measurement error of the i-th satellite. i Let K(P) represent the characteristic slope of the i-th satellite, λ be the decentralization parameter of the chi-square distribution that satisfies the false negative probability requirement, and K(P) be the characteristic slope of the i-th satellite. md ) is the expansion factor d, which is based on the residual distribution and satisfies a certain false negative rate. H This represents the standard deviation in the horizontal direction of the state estimate. phais represents the new Mahalanobis distance. Based on the position p of each lion... i =(p i1 ,p i2 ,...,piD To obtain the fitness f(HUL) at each location update. i After a finite number of population iterations, the historical best position of the lion pride is the solution set corresponding to the minimum fitness.

[0092] During a lion pride's hunt, the search direction and size of each individual depend on their role within the group. The lion alpha, lionesses, and cubs work together, continuously adjusting their spatial positions to achieve the optimal hunting outcome.

[0093] The lion king represents the most fit individual in the population and is responsible for leading the migration, always remaining in the current optimal position. To maintain its dominance, the lion king only moves within a small area near the optimal position to explore whether a better solution exists in a local region. Assuming L iterations, the historical optimal position obtained by the i-th lion is p. i,L Then, in the (L+1)th iteration, the position of the Lion King is updated as follows:

[0094] pLeader i,L+1 =g L (1+γ||p i,L -g L ||), 0 < γ < 1

[0095] In the formula, g L γ represents the global optimal position of the population in the Lth iteration, i.e., the position of the lion king. γ is the scaling factor of the lion king's movement range, which is usually generated by a normal distribution.

[0096] Lionesses are primarily responsible for hunting within a pride. During the hunt, they share localized information with each other, enabling coordinated searching and capture of prey. The position update mechanism of a lionesse is influenced by the positions of other individual lionesses; the position of the (L+1)th generation lionesse can be represented as...

[0097]

[0098] In the formula, p c,L For the historical best position of another randomly selected lioness, α h This is a scaling factor that adjusts the lioness's movement range, controlling her step size and search speed. The factor is set according to a strategy of "large step size exploration and small step size search," which enhances the algorithm's global search capability while improving convergence efficiency in later stages, thus achieving a performance balance. As the number of iterations increases, the scaling factor gradually decreases, and the lioness's step size shortens accordingly, eventually approaching zero. The specific relationship between this factor, the step size, and the number of iterations can be expressed as:

[0099]

[0100] In the formula, L a This represents the total number of iterations, and `step` represents the step size of the lioness's movement, calculated from the average of the maximum values ​​of each dimension within her activity range. and minimum mean Obtained. ω represents the weighting factor, used to balance the effects of local and global optimization, preventing the lioness from getting trapped in local optima during the optimization process. Specifically, it is expressed as...

[0101] In the formula, w max It is the maximum inertia weight value, w min It is the minimum inertia weight value, L max It represents the maximum number of iterations.

[0102] As the weakest individuals in the pride, lion cubs' activities primarily revolve around the alpha male and lionesses, encompassing three behavioral patterns: communal feeding, imitative hunting, and elite-reverse learning. The search areas of lion cubs vary depending on their behavioral differences. This is illustrated by a random variable q that follows a uniform distribution on the interval [0,1]. f Lion cubs can be divided into three categories, with different values ​​corresponding to different behavioral patterns.

[0103] When q f When the value is less than 0.5λ, the cubs are hungry and will move closer to the lion king to share food, which corresponds to a local search near the current global optimal position.

[0104] When 0.5λ≤q f When the cubs are less than λ, they are learning hunting skills and participating in the mother lion's hunting process. At this time, they will approach the mother lion and search in the vicinity of the mother lion's area.

[0105] When λ≤q f When the value is less than 1, the cubs enter the elite reverse learning stage, are driven to an area far away from the lion king, and need to find food resources independently. In the solution space, this is manifested as exploring areas far away from the current optimal solution in order to discover potential better solutions.

[0106] The above strategy helps improve the diversity and randomness of the search direction, thereby reducing the risk of the algorithm getting trapped in local optima. Based on the above behavioral patterns, the position update rule for the cub in the (L+1)th iteration can be expressed as:

[0107]

[0108] In the formula, p m,L p represents the position of the m-th cub in the L-th iteration. j,L This represents the historically optimal position for the Lth generation of lion cubs following their mothers, where λ represents a moderating factor. The position where the m-th lion cub was driven away is denoted as . α fThis is a scaling factor that limits the cub's activity level, primarily used to adjust its search step size, and dynamically adjusted with the number of iterations. In the early stages of the algorithm, due to the cub's limited environmental awareness, a larger step size is typically used to enhance its global exploration ability in unknown areas; however, in the later stages, as the cub becomes more familiar with its surroundings and the target becomes apparent, the search step size gradually decreases, allowing it to focus more on in-depth exploration within specific areas.

[0109] Boundary constraints limit the range of values ​​for each optimization variable, preventing them from exceeding limits during the optimization process. This range is typically defined by setting upper and lower boundaries. In practice, after updating the positions of each individual lion in the pride, boundary checks are performed on the position variables of each lion in each dimension: if the value of a certain dimension exceeds the preset upper limit, it is adjusted to the upper boundary value; if it is below the lower limit, it is set to the lower boundary value; if the variable is between the upper and lower boundaries, the current value is valid and acceptable. The mathematical expression of boundary constraints is as follows:

[0110]

[0111] In the formula, p id Let represent the d-th dimension variable of the i-th lion. uBound is the upper boundary value, and lBound is the lower boundary value; the specific boundary values ​​are related to the variable properties. An excessively large kernel width will decrease the algorithm's robustness, degrading the estimation performance to near that of the standard extended Kalman filter. In this paper, the upper boundary value is set to 10. Conversely, an excessively small kernel width will result in a singular or near-singular value in the algorithm matrix, leading to inaccurate estimation accuracy or solution anomalies. Therefore, the lower boundary value is set to 2.

[0112] The positions of the lion king, lionesses, and cubs are updated through a finite number of iterations. The corresponding fitness values ​​are calculated, sorted, and the solution set p corresponding to the minimum fitness is output. best =argminf N (HUL) is the optimal combination of kernel width parameters.

[0113] The method described above, which updates the measurement noise covariance matrix and the filter gain matrix based on the optimal kernel width parameter set and combines the train prior state prediction results and observation data to achieve robust estimation of the train state, includes: updating the matrix and measurement noise matrix according to the obtained optimal kernel width parameter combination, calculating the gain matrix, updating the train state at time k in combination with the observation measurements, and updating the error covariance matrix at time k using the train prior error covariance matrix.

[0114] Specifically, C is updated based on the obtained optimal combination of kernel width parameters. R,k :C R,k =diag(G σ (δ k (i)),...,G σ(δ k (n)))

[0115] Update the measurement noise matrix:

[0116] Calculate the gain matrix:

[0117] Combined with observation measurement z k Update the train status at time k:

[0118] Update the error covariance matrix at time k using the train prior error covariance matrix:

[0119] Example 2

[0120] This embodiment addresses the problem of decreased estimation accuracy of extended Kalman filter caused by satellite measurement failures. Based on the maximum entropy criterion and intelligent optimization algorithm, it proposes a train positioning method based on dynamic kernel width robust extended Kalman filter.

[0121] The implementation principle of the train positioning method based on dynamic kernel width robust extended Kalman filter provided in this embodiment is as follows: Figure 1 As shown, the processing steps include the following:

[0122] Step S1: Acquire raw observation data from the satellite receiver installed on the train, extracting the pseudorange and ephemeris data required for train positioning. This sensing data will be used to achieve train position estimation. Since the train positioning system is inherently a nonlinear system, the extended Kalman filter, due to its low complexity and good real-time performance, can efficiently handle nonlinear characteristics and is currently the main method for train positioning data processing. According to the basic theory of Kalman filtering, the discretized state equation and measurement equation of the positioning system can be expressed as:

[0123]

[0124] Where, x k-1 Let z be the state vector at time k-1. k w is the measurement vector at time k. k-1 It is process noise that follows a zero-mean Gaussian distribution, and its corresponding covariance matrix is ​​denoted as Q. k-1 v k It is measurement noise that follows a zero-mean Gaussian distribution, and its corresponding covariance matrix is ​​denoted as R. k F k-1 H is the state transition matrix. k It is the Hessian matrix of the measurement equation.

[0125] The state equations contain 11 dimensions of state variables, including position, velocity, receiver clock error, distance error, and equivalent clock drift error, expressed as:

[0126] x k =[p x v x a x p y v y a y p z v z a z δt dδt]

[0127] In the formula, (p x ,p y ,p z ), (v x ,v y ,v z ) and (a x ,a y ,a z Let represent the position, velocity, and acceleration in three directions in the geocentric Earth-fixed coordinate system, δt be the receiver clock bias, and dδt be the equivalent clock drift error. Considering the train's operating characteristics, a uniformly accelerated motion model is chosen to determine the train's state transition matrix, expressed as:

[0128]

[0129] Where, τ s It is the time interval during fusion estimation.

[0130] In the measurement equation, satellite observation pseudorange is chosen as the measurement. If N satellites are observed at time k, the true position of the receiver is denoted as (O... x O y O z ), speed is (Ov x ,Ov y ,Ov z The position of the j-th satellite in the Earth-centered Earth-fixed coordinate system is... The pseudorange between the receiver and the j-th satellite can be expressed as:

[0131] ρ GNSS,j =ρ T,j +T+δt+ε

[0132]

[0133] In the formula, ρ T,jδt is the geometric distance from the receiver to the satellite, T is the sum of satellite clock bias, ionospheric error and tropospheric error, δt is the distance error caused by receiver clock bias and clock drift, and ε is the error caused by multipath effect or receiver noise.

[0134] Based on the model established above, the train prior prediction and prior error covariance matrix are calculated as follows:

[0135] Predicting prior states based on the train state transition matrix

[0136]

[0137] Initialize the prior error covariance matrix

[0138]

[0139] Step S2: Introduce the maximum entropy criterion instead of the minimum mean square error criterion as the loss function in the filtering estimation. Reconstruct the measurement noise covariance matrix using the weight matrix constructed by the Gaussian kernel function, including:

[0140] By combining the state equation and the measurement equation, the following linear regression model can be obtained.

[0141]

[0142] In the formula, I represents the identity matrix, and α k =[-w k v k ] T .

[0143] Define a new error covariance matrix Δ k for

[0144]

[0145] Among them, S k It can be obtained through Kolesky decomposition. (By left multiplication) The linear regression model can be rewritten as: L k =Γ k x k +δ k In the formula, L k ,Γ k , and δ k They are defined as follows:

[0146]

[0147]

[0148] The maximum entropy criterion is introduced as the loss function for filtering estimation:

[0149]

[0150] In the formula G σ Let be the Gaussian kernel function, and σ represent the kernel width. Based on the maximum entropy criterion, the solution for the state estimate can be obtained by maximizing the above optimization criterion.

[0151]

[0152] In the formula, L = m + n, where m and n are the dimensions of the state vector and the measurement vector, respectively, and δ k (i) represents the residual (L) k -Γ k x k The i-th term of )

[0153]

[0154] Define C k (i)=G σ (δ k (i)) can be obtained

[0155]

[0156] C P,k =diag(G σ (δ k (i)),...,G σ (δ k (m)))

[0157] C R,k =diag(G σ (δ k (i)),...,G σ (δ k (n)))

[0158] `diag(·)` represents the operation of building a diagonal matrix. Based on the fixed-point iterative algorithm, the state at time k can be estimated.

[0159]

[0160] Vector C k The error covariance matrix was reweighted and the measurement noise matrix was reconstructed. The new error covariance matrix is ​​expressed as follows:

[0161]

[0162] In practice, since the actual state is unknown, we assume that the estimate is unbiased, that is... Then C P,k This can be viewed as an identity matrix. The prior error covariance and measurement noise variance are simplified again as follows:

[0163]

[0164]

[0165] Step S3: Dynamically estimate the kernel width of each observed satellite using the improved lion swarm optimization algorithm to obtain the optimal kernel width parameter combination for visible satellites, including:

[0166] In the improved lion pride optimization algorithm, individuals are divided into three categories: alpha lions, lionesses, and cubs. Based on their behavioral characteristics, these individuals are categorized into three types. When hungry, they will approach the alpha lion to obtain food, signifying a local search within the neighborhood of the optimal solution. After feeding, they will participate in hunting with the lionesses, equivalent to conducting deeper searches near the local optimum. Adult individuals are driven to areas far from the alpha lion, gradually growing in a new environment, and potentially challenging the existing alpha lion for leadership after discovering better resources. The core processes of the improved lion pride optimization algorithm include population initialization, fitness assessment, pride location updates, and boundary checks.

[0167] Step 1: Population Initialization

[0168] The main purpose of population initialization is to determine the total number of individuals in the pride, the distribution of different types of lions (alpha male, lionesses, cubs), and their initial positions. Since different roles within the pride fulfill different functions, the proportion of adult lions directly affects the algorithm's optimization ability, while a suitable number of cubs helps increase population diversity, thereby expanding the search space. Assuming the total number of individuals in the pride is N, and the number of adult lions is NAdult, the ratio between the two can be expressed as:

[0169] NAdult=βN

[0170] In the formula, β is the adult lion proportion factor, whose value determines the final search efficiency. To make the algorithm converge faster, it is usually set to 0.5. Accordingly, the number of cubs can be obtained as N-NAdult. Among the adult lions, there is only one alpha male, and the rest are female lions.

[0171] The lion's position represents a feasible solution to the unsolved variable, namely, the specific value of the kernel width of each satellite at time k, whose dimension D is determined by the number of observed satellites. The position of the i-th lion can be represented as:

[0172] p i =(p i1 ,p i2 ,...,p iD ), 1≤i≤N

[0173] After initialization, the locations of all lions in the population are recorded as follows:

[0174]

[0175] Step 2: Determine the fitness function

[0176] Before calculating the kernel width for different observations using the improved lion flock optimization algorithm, it is necessary to first define the optimization objective, i.e., set the fitness function. This paper selects the level uncertainty of the state estimation as the fitness function. The level uncertainty does not depend on the true position reference and can evaluate the train positioning performance in real time based on the observation data, expressed as:

[0177]

[0178] In the formula σ i Slope is the standard deviation of the measurement error of the i-th satellite. i Let K(P) represent the characteristic slope of the i-th satellite, λ be the decentralization parameter of the chi-square distribution that satisfies the false negative probability requirement, and K(P) be the characteristic slope of the i-th satellite. md ) is the expansion factor d, which is based on the residual distribution and satisfies a certain false negative rate. H This represents the standard deviation in the horizontal direction of the state estimate. phais represents the new Mahalanobis distance. Based on the position p of each lion... i =(p i1 ,p i2 ,...,p iD To obtain the fitness f(HUL) at each location update. i After a finite number of population iterations, the historical best position of the lion pride is the solution set corresponding to the minimum fitness.

[0179] Step 3: Update the lion pride's location

[0180] During a lion pride's hunt, the search direction and size of each individual depend on their role within the group. The lion alpha, lionesses, and cubs work together, continuously adjusting their spatial positions to achieve the optimal hunting outcome.

[0181] The lion king represents the most fit individual in the population and is responsible for leading the migration, always remaining in the current optimal position. To maintain its dominance, the lion king only moves within a small area near the optimal position to explore whether a better solution exists in a local region. Assuming L iterations, the historical optimal position obtained by the i-th lion is p. i,L Then, in the (L+1)th iteration, the position of the Lion King is updated as follows:

[0182] pLeader i,L+1 =g L (1+γ||p i,L -g L ||), 0 < γ < 1

[0183] In the formula, g L γ represents the global optimal position of the population in the Lth iteration, i.e., the position of the lion king. γ is the scaling factor of the lion king's movement range, which is usually generated by a normal distribution.

[0184] Lionesses are primarily responsible for hunting within a pride. During the hunt, they share localized information with each other, enabling coordinated searching and capture of prey. The position update mechanism of a lionesse is influenced by the positions of other individual lionesses; the position of the (L+1)th generation lionesse can be represented as...

[0185]

[0186] In the formula, p c,L For the historical best position of another randomly selected lioness, α h This is a scaling factor that adjusts the lioness's movement range, controlling her step size and search speed. The factor is set according to a strategy of "large step size exploration and small step size search," which enhances the algorithm's global search capability while improving convergence efficiency in later stages, thus achieving a performance balance. As the number of iterations increases, the scaling factor gradually decreases, and the lioness's step size shortens accordingly, eventually approaching zero. The specific relationship between this factor, the step size, and the number of iterations can be expressed as:

[0187]

[0188] In the formula, L a This represents the total number of iterations, and `step` represents the step size of the lioness's movement, calculated from the average of the maximum values ​​of each dimension within her activity range. and minimum mean Obtained. ω represents the weighting factor, used to balance the effects of local and global optimization, preventing the lioness from getting trapped in local optima during the optimization process. Specifically, it is expressed as...

[0189]

[0190] In the formula, w max It is the maximum inertia weight value, w min It is the minimum inertia weight value, L max It represents the maximum number of iterations.

[0191] As the weakest individuals in the pride, lion cubs' activities primarily revolve around the alpha male and lionesses, encompassing three behavioral patterns: communal feeding, imitative hunting, and elite-reverse learning. The search areas of lion cubs vary depending on their behavioral differences. This is illustrated by a random variable q that follows a uniform distribution on the interval [0,1]. f Lion cubs can be divided into three categories, with different values ​​corresponding to different behavioral patterns.

[0192] When qf When the value is less than 0.5λ, the cubs are hungry and will move closer to the lion king to share food, which corresponds to a local search near the current global optimal position.

[0193] When 0.5λ≤q f When the cubs are less than λ, they are learning hunting skills and participating in the mother lion's hunting process. At this time, they will approach the mother lion and search in the vicinity of the mother lion's area.

[0194] When λ≤q f When the value is less than 1, the cubs enter the elite reverse learning stage, are driven to an area far away from the lion king, and need to find food resources independently. In the solution space, this is manifested as exploring areas far away from the current optimal solution in order to discover potential better solutions.

[0195] The above strategy helps improve the diversity and randomness of the search direction, thereby reducing the risk of the algorithm getting trapped in local optima. Based on the above behavioral patterns, the position update rule for the cub in the (L+1)th iteration can be expressed as:

[0196]

[0197] In the formula, p m,L p represents the position of the m-th cub in the L-th iteration. j,L This represents the historically optimal position for the Lth generation of lion cubs following their mothers, where λ represents a moderating factor. The position where the m-th lion cub was driven away is denoted as .

[0198]

[0199] α f This is a scaling factor that limits the cub's activity level, primarily used to adjust its search step size, and dynamically adjusted with the number of iterations. In the early stages of the algorithm, due to the cub's limited environmental awareness, a larger step size is typically used to enhance its global exploration ability in unknown areas; however, in the later stages, as the cub becomes more familiar with its surroundings and the target becomes apparent, the search step size gradually decreases, allowing it to focus more on in-depth exploration within specific areas.

[0200] Step 4: Determine whether the solution set exceeds the boundary constraints.

[0201] Boundary constraints limit the range of values ​​for each optimization variable, preventing them from exceeding limits during the optimization process. This range is typically defined by setting upper and lower boundaries. In practice, after updating the positions of each individual lion in the pride, boundary checks are performed on the position variables of each lion in each dimension: if the value of a certain dimension exceeds the preset upper limit, it is adjusted to the upper boundary value; if it is below the lower limit, it is set to the lower boundary value; if the variable is between the upper and lower boundaries, the current value is valid and acceptable. The mathematical expression of boundary constraints is as follows:

[0202]

[0203] In the formula, p id Let represent the d-th dimension variable of the i-th lion. uBound is the upper boundary value, and lBound is the lower boundary value; the specific boundary values ​​are related to the variable properties. An excessively large kernel width will decrease the algorithm's robustness, degrading the estimation performance to near that of the standard extended Kalman filter. In this paper, the upper boundary value is set to 10. Conversely, an excessively small kernel width will result in a singular or near-singular value in the algorithm matrix, leading to inaccurate estimation accuracy or solution anomalies. Therefore, the lower boundary value is set to 2.

[0204] The positions of the lion king, lionesses, and cubs are updated iteratively, their fitness values ​​are calculated, and the results are sorted. The solution set p corresponding to the minimum fitness is then output. best =argminf N (HUL) is the optimal combination of kernel width parameters.

[0205] Step S4: Based on the optimal kernel width parameter set, update the measurement noise covariance matrix and filter gain matrix, and combine the train prior state prediction results and observation data to achieve robust train state estimation. This includes:

[0206] Update C based on the obtained optimal kernel width parameter combination. R,k :C R,k =diag(G σ (δ k (i)),...,G σ (δ k (n)))

[0207] Update the measurement noise matrix:

[0208] Calculate the gain matrix:

[0209] Combined with observation measurement z k Update the train status at time k:

[0210] Update the error covariance matrix at time k using the train prior error covariance matrix:

[0211] In summary, this embodiment first acquires the raw data required for positioning from the satellite receiver, including almanac and pseudorange observations. This information is used as input for train state estimation and to determine the measurement model of the positioning system. Then, 11 dimensions of information, including position, speed, receiver clock error, distance error, and equivalent clock drift error, are selected to form the state variables, and a train state model is established. Based on the train state variables of the previous moment, the train's prior state is predicted, and the prior error covariance matrix and measurement noise covariance matrix are initialized. The traditional extended Kalman filter (EPF) uses the minimum mean square error (MSE) criterion, which struggles to maintain adequate estimation performance under measurement fault conditions. The maximum entropy criterion, however, captures higher-order statistics and effectively suppresses measurement noise with non-zero mean, non-Gaussian, or large outliers. Therefore, the maximum entropy criterion is introduced as a new cost function in the filter estimation, replacing the MSE criterion. The measurement noise covariance matrix is ​​reconstructed using a weight matrix constructed from a Gaussian kernel function. Considering the impact of the kernel width on the weights of each measurement in the filter gain matrix, an improved lion swarm optimization algorithm is used to dynamically estimate the kernel width of each observation satellite, yielding the optimal combination of kernel width parameters. Based on this optimal kernel width parameter set, the measurement noise covariance matrix and the filter gain matrix are updated, ultimately achieving robust estimation of train position. This invention effectively suppresses the impact of faulty observations on positioning performance, providing a basis for reliable train status estimation.

[0212] Example 3

[0213] This embodiment 3 provides a non-transitory computer-readable storage medium for storing computer instructions. When executed by a processor, the computer instructions implement the train positioning method based on dynamic kernel width robust extended Kalman filtering as described above. The method includes:

[0214] The system uses a satellite receiver to collect raw observation pseudorange and ephemeris data, establishes a system measurement model and state model, predicts the train's prior state based on the train's state variables at the previous moment, and initializes the prior error covariance matrix and measurement noise covariance matrix.

[0215] The maximum entropy criterion is introduced to replace the minimum mean square error criterion as the loss function in the filtering estimation, and the measurement noise covariance matrix is ​​reconstructed by the weight matrix constructed by the Gaussian kernel function.

[0216] Considering the influence of kernel width in Gaussian kernel function on the weights of observation information and prior prediction information in filter gain matrix, an improved lion swarm optimization algorithm is used to dynamically estimate the kernel width of observation information for each satellite, and obtain the optimal kernel width parameter combination for visible satellites.

[0217] Based on the optimal kernel width parameter set, the measurement noise covariance matrix and filter gain matrix are updated, and the train state robust estimation is achieved by combining the train prior state prediction results and observation data.

[0218] Example 4

[0219] This embodiment 4 provides a computer device, including 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. The processor calls the program instructions to execute the train positioning method based on dynamic kernel width robust extended Kalman filter as described above. The method includes:

[0220] The system uses a satellite receiver to collect raw observation pseudorange and ephemeris data, establishes a system measurement model and state model, predicts the train's prior state based on the train's state variables at the previous moment, and initializes the prior error covariance matrix and measurement noise covariance matrix.

[0221] The maximum entropy criterion is introduced to replace the minimum mean square error criterion as the loss function in the filtering estimation, and the measurement noise covariance matrix is ​​reconstructed by the weight matrix constructed by the Gaussian kernel function.

[0222] Considering the influence of kernel width in Gaussian kernel function on the weights of observation information and prior prediction information in filter gain matrix, an improved lion swarm optimization algorithm is used to dynamically estimate the kernel width of observation information for each satellite, and obtain the optimal kernel width parameter combination for visible satellites.

[0223] Based on the optimal kernel width parameter set, the measurement noise covariance matrix and filter gain matrix are updated, and the train state robust estimation is achieved by combining the train prior state prediction results and observation data.

[0224] Example 5

[0225] This embodiment 5 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the train positioning method based on dynamic kernel width robust extended Kalman filtering as described above. The method includes:

[0226] The system uses a satellite receiver to collect raw observation pseudorange and ephemeris data, establishes a system measurement model and state model, predicts the train's prior state based on the train's state variables at the previous moment, and initializes the prior error covariance matrix and measurement noise covariance matrix.

[0227] The maximum entropy criterion is introduced to replace the minimum mean square error criterion as the loss function in the filtering estimation, and the measurement noise covariance matrix is ​​reconstructed by the weight matrix constructed by the Gaussian kernel function.

[0228] Considering the influence of kernel width in Gaussian kernel function on the weights of observation information and prior prediction information in filter gain matrix, an improved lion swarm optimization algorithm is used to dynamically estimate the kernel width of observation information for each satellite, and obtain the optimal kernel width parameter combination for visible satellites.

[0229] Based on the optimal kernel width parameter set, the measurement noise covariance matrix and filter gain matrix are updated, and the train state robust estimation is achieved by combining the train prior state prediction results and observation data.

[0230] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied 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.

[0231] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0232] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0233] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the function specified in one or more boxes.

[0234] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A train positioning method based on dynamic kernel width robust extended Kalman filter, characterized in that, include: Using a satellite receiver to collect raw observation pseudorange and ephemeris data, a system measurement model and state model are established. Based on the train's state variables from the previous moment, a priori state prediction of the train is performed, and the prior error covariance matrix and measurement noise covariance matrix are initialized. This process includes: acquiring raw observation data; extracting the pseudorange and ephemeris data required for train positioning; and, based on the fundamental theory of Kalman filtering, discretizing the state equation and measurement equation of the positioning system. The state equation contains 11 dimensions of state variables, including position, velocity, receiver clock error, distance error, and equivalent clock drift error. Considering the train's operating characteristics, a uniform acceleration motion model is selected to determine the train state transition matrix. In the measurement equation, satellite observation pseudorange is selected as the measurement. Based on the state equation and measurement equation, the train's prior prediction and prior error covariance matrix are calculated. The maximum entropy criterion is introduced instead of the minimum mean square error criterion as the loss function in the filtering estimation. The measurement noise covariance matrix is ​​reconstructed through the weight matrix constructed by the Gaussian kernel function, including the joint state equation and the measurement equation, to obtain a linear regression model. Combined with Koleski decomposition, a new error covariance matrix is ​​defined. The maximum entropy criterion is introduced as the loss function of the filtering estimation. Based on the principle of the maximum entropy criterion, the solution of the state estimation can be obtained by maximizing the optimization criterion. Based on the fixed-point iterative algorithm, the state at time k is estimated, and the prior error covariance and measurement noise covariance matrix are re-represented. Considering the influence of kernel width in Gaussian kernel function on the weights of observation information and prior prediction information in filter gain matrix, an improved lion swarm optimization algorithm is used to dynamically estimate the kernel width of observation information for each satellite, and obtain the optimal kernel width parameter combination for visible satellites. Based on the optimal kernel width parameter set, the measurement noise covariance matrix and filter gain matrix are updated, and the train state robust estimation is achieved by combining the train prior state prediction results and observation data.

2. The train positioning method based on dynamic kernel width robust extended Kalman filter according to claim 1, characterized in that, The aforementioned consideration of the influence of the kernel width in the Gaussian kernel function on the weights of observed information and prior prediction information in the filter gain matrix, employing an improved lion swarm optimization algorithm to dynamically estimate the kernel width of the observed information for each satellite, and obtaining the optimal combination of kernel width parameters for visible satellites, includes: The improved lion pride optimization algorithm includes population initialization, fitness evaluation, pride position update, and boundary checking. Population initialization determines the total number of individuals in the pride, the distribution of different lion types, and their initial positions. The lion position represents a feasible solution to the unsolved variable, i.e., the specific value of the kernel width of each satellite at time k, whose dimension D is determined by the number of observed satellites. The level of uncertainty in the state estimate is selected as the fitness function. The fitness is obtained for each position update based on the position of each lion. After a finite number of population iterations, the historical best position of the pride is the solution set corresponding to the minimum fitness. Boundary constraints limit the range of values ​​for each optimization variable to prevent variables from going out of bounds during the optimization process. This range is usually defined by setting upper and lower boundaries. The positions of the lion king, lionesses, and cubs are updated cyclically through a finite number of iterations. The corresponding fitness values ​​are calculated, sorted, and the solution set corresponding to the minimum fitness is output, which is the optimal combination of kernel width parameters.

3. The train positioning method based on dynamic kernel width robust extended Kalman filter according to claim 2, characterized in that, After updating the positions of each individual lion in the pride, boundary checks need to be performed on the position variables of each lion in each dimension: if the value of a certain dimension exceeds the preset upper limit, it is adjusted to the upper boundary value; if it is below the lower limit, it is set to the lower boundary value; if the variable is between the upper and lower limits, it means that the current value is valid and acceptable.

4. The train positioning method based on dynamic kernel width robust extended Kalman filter according to claim 1, characterized in that, The method described above, which updates the measurement noise covariance matrix and the filter gain matrix based on the optimal kernel width parameter set and combines the train prior state prediction results and observation data to achieve robust estimation of the train state, includes: updating the matrix and measurement noise matrix according to the obtained optimal kernel width parameter combination, calculating the gain matrix, updating the train state at time k in combination with the observation measurements, and updating the error covariance matrix at time k using the train prior error covariance matrix.

5. A train positioning system based on dynamic kernel width robust extended Kalman filter, characterized in that, include: The initialization module is used to acquire raw observation pseudorange and ephemeris data using a satellite receiver, establish the system measurement model and state model, predict the train's prior state based on the train's state variables from the previous moment, and initialize the prior error covariance matrix and measurement noise covariance matrix. This includes: acquiring raw observation data; extracting the pseudorange and ephemeris data required for train positioning; and, based on the fundamental theory of Kalman filtering, discretizing the state equation and measurement equation of the positioning system. The state equation contains 11 dimensions of state variables, including position, velocity, receiver clock error, distance error, and equivalent clock drift error. Considering the train's operating characteristics, a uniform acceleration motion model is selected to determine the train's state transition matrix. In the measurement equation, satellite observation pseudorange is selected as the measurement. Based on the state equation and measurement equation, the train's prior prediction and prior error covariance matrix are calculated. The reconstruction module is used to introduce the maximum entropy criterion instead of the minimum mean square error criterion as the loss function in the filtering estimation. It reconstructs the measurement noise covariance matrix through the weight matrix constructed by the Gaussian kernel function, including: joint state equation and measurement equation, to obtain a linear regression model. Combined with Kolesky decomposition, a new error covariance matrix is ​​defined. The maximum entropy criterion is introduced as the loss function of the filtering estimation. Based on the principle of the maximum entropy criterion, the solution of the state estimation can be obtained by maximizing the optimization criterion. Based on the fixed-point iterative algorithm, the state at time k is estimated, and the prior error covariance and measurement noise covariance matrix are re-represented. The estimation module is used to consider the influence of the kernel width in the Gaussian kernel function on the weights of the observation information and prior prediction information in the filter gain matrix. An improved lion flock optimization algorithm is used to dynamically estimate the kernel width of the observation information of each satellite and obtain the optimal combination of kernel width parameters for visible satellites. The update module is used to update the measurement noise covariance matrix and the filter gain matrix based on the optimal kernel width parameter set, and to achieve robust estimation of the train state by combining the train prior state prediction results and observation data.

6. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the train positioning method based on dynamic kernel width robust extended Kalman filter as described in any one of claims 1-4.

7. A computer device, characterized in that, The system includes a memory and a processor, which 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 train positioning method based on dynamic kernel width robust extended Kalman filter as described in any one of claims 1-4.

8. An electronic device, characterized in that, include: The electronic device includes 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 to cause the electronic device to execute instructions that implement the train positioning method based on dynamic kernel width robust extended Kalman filtering as described in any one of claims 1-4.

Images