Train running state estimation method and system fused with remainder extended Kalman filter

Abstract

The invention provides a train operation state estimation method and system fused with a remainder extended Kalman filter, and belongs to the technical field of rail transit train operation management based on deep learning. Predicting based on the nonlinear state space model of the train to obtain an intermediate state estimation result of the train; a deep neural network module based on an LSTM structure takes the intermediate state estimation result, the error covariance, the Kalman gain and the system residual error as input features, and outputs a group of optimized state estimation results through nonlinear combined learning model error distribution; and carrying out weighted fusion on the intermediate state estimation result and the optimized state estimation result to obtain a final state estimation result. According to the method, the precision of system state estimation is improved, the nonlinear modeling capability of the system is enhanced, the complex nonlinear relationship in the system can be adaptively captured and learned, and the defects of a traditional filter in processing the nonlinear system are overcome.

Description

Technical Field

[0001] The present invention relates to the technical field of rail transit train operation management based on deep learning, and particularly relates to a train operation state estimation method and system integrating a residual extended Kalman filter. Background Art

[0002] In a train operation control system, train positioning technology is crucial, and its accuracy and reliability are important factors affecting the train's safety protection distance. The dynamic characteristics of the train are complex, and the operating environment is changeable. The air resistance suffered by a high-speed train is proportional to the square of the speed. Therefore, the dynamic behavior of a high-speed train exhibits strong non-linear characteristics and includes rapidly changing parameters, which makes it difficult to establish an accurate mathematical model. The actual train operation involves real-time switching between different operation modes, each mode corresponding to a model and often presenting as a mixture of multiple modes. At the same time, uncertainties in the sensor network, such as wind pressure, vibration, and temperature, will generate noise in the process, measurement, and communication. All these factors pose a huge challenge to the accurate speed measurement of high-speed trains. Generally, a state estimation method based on the Kalman filtering theory is adopted to provide more reliable and accurate train speed and position data.

[0003] Kalman filtering (KF) is a time-domain filtering method that uses the state space method and the recursive form of the minimum mean square error to describe the target system. However, it is only applicable to linear Gaussian noise systems and cannot handle the state estimation problem of non-linear models.

[0004] In 1969, Bucy proposed an extended Kalman filter (EKF) based on Taylor expansion to solve the state estimation problem of non-linear systems. However, due to the truncation of the higher-order terms in the Taylor series, EKF can only achieve first-order approximation accuracy. As the non-linearity increases, its filtering performance will deteriorate and even diverge. In addition to EKF, other commonly used Kalman filters also include the unscented Kalman filter (UKF) and the cubature Kalman filter (CKF). Both UKF and CKF use sigma-point interpolation to design a Kalman filter-like form to improve the influence of truncation error, but their maximum approximation accuracy can only approach the second order

[24] . It can be found that in all the above filters, only the statistical information of the system state noise is used to calculate the Kalman gain, and the obtained state estimation value is only in the form of a linear optimal combination of the state prediction value, the Kalman gain, and the innovation. How to obtain its non-linear optimal combination form, and then obtain a larger optimization space to design a Kalman filter applicable to strongly non-linear systems has become a direction worth exploring.

[0005] In recent years, the research on target state estimation by combining deep learning and Kalman filtering has become an important research direction. Especially in the context of data fitting and prediction, data-driven methods combined with Kalman filtering have been used to model time series data for long-term data prediction. Existing research has proposed combining an encoder with a Kalman filter to identify the latent representation of a first-order dynamic model while promoting the estimation of missing data. In addition, some research has proposed the Deep Variational Bayesian Filter (DVBF), which can learn from raw non-Markov sequential data, infer the state space model of the system, and the generated model performs stably in long-term prediction. These methods effectively emphasize the rationality of combining data-driven methods with Kalman filtering. However, it is worth noting that the aforementioned methods all regard Kalman filtering as an auxiliary tool in the data-driven process, mainly solving prediction and estimation problems related to unmodeled data.

[0006] Currently, the research on using neural networks to assist Kalman filtering in solving modeled data problems is still relatively limited. Recently, Kyeongjun proposed a Kalman filtering solution based on a deep neural network, which combines the Kalman filtering solution process with a deep neural network. Compared with the Extended Kalman Filter (EKF), it achieves better estimation accuracy in nonlinear model state estimation. However, this method only predicts the state estimation value and still uses the EKF method to solve the state estimation error covariance. Moreover, in the iterative solution process, due to the fact that the fully connected neural network cannot well model time series data, the stability of the prediction process decreases, and the estimation error increases over time. Therefore, compared with fully connected neural networks and convolutional neural networks, the Recurrent Neural Network (RNN) shows strong advantages in processing time series data (such as target tracking and trajectory prediction) and has become a common choice when dealing with time-related data. However, the Deep Neural Network (DNN) does not incorporate the domain knowledge of structured models in a prescribed manner. Instead, it relies on a large number of trainable parameters and large datasets and lacks the interpretability of structured methods such as Kalman filtering. These constraints limit the application of deep neural networks in real-time state prediction in some scenarios (such as the lack of good state information input labels).

[0007] Since the EKF ignores the high-order terms of the Taylor series during linearization, it can only provide first-order approximation accuracy. When the nonlinearity of the system increases, the performance of the EKF will significantly degrade and even diverge. Existing Kalman filters (such as EKF, UKF, CKF, etc.) can only use the statistical information of the system state noise to calculate the Kalman gain, and the state estimate is only a linear optimal combination of the state prediction value, the Kalman gain, and the innovation. This method cannot fully optimize the estimation in a strongly nonlinear system, limiting the estimation accuracy. Although some studies have attempted to combine deep neural networks with Kalman filtering, these methods still use the EKF to solve the problem of the state estimation error covariance, and there are stability problems in time series data modeling. Summary of the Invention

[0008] The purpose of the present invention is to provide a train operation state estimation method and system based on a deep neural network fused with a remainder extended Kalman filter to solve at least one of the technical problems existing in the above background technology.

[0009] To achieve the above purpose, the present invention adopts the following technical solutions:

[0010] In the first aspect, the present invention provides a train operation state estimation method fused with a remainder extended Kalman filter, including:

[0011] Obtain train state information, including spatial coordinates, speed information, and heading angle; and obtain real-time state command information output by the train ATP / ATO control system, and sample and organize all observed data into a sequence input at a fixed time interval;

[0012] Based on the obtained train state information, predict the train intermediate state estimation result based on the nonlinear state space model of the train; among them, the state transition function in the model is x k+1 = f(x k , u k ) + w k , the observation model is y k = h(x k ) + v k , the model retains the high-order remainder ignored in the Taylor expansion, and corrects the error covariance matrix P k of the state estimation based on its statistical characteristics, so as to optimize the Kalman gain K k ;

[0013] Based on the deep neural network module with an LSTM structure, using the intermediate state estimation result, error covariance, Kalman gain, and system residual as input features, learn the model error distribution through nonlinear combination, and output a set of optimized state estimation results;

[0014] The intermediate state estimation result and the optimized state estimation result are weighted and fused to obtain the final state estimation result.

[0015] As a further limitation of the first aspect of the present invention, in the nonlinear state space model, an extended Kalman filter REKF designed to consider the remainder term is used. In order to make greater use of the information of the system's nonlinear state model and nonlinear observation model, REKF takes into account the Taylor high-order remainder terms discarded in the linearization process during the state estimation process; first, the high-order residual terms of the state and measurement equations are estimated; after obtaining the estimated value of u k+1 and the estimated error covariance, through the projection algorithm, the estimated value of the original estimated variable state and the estimated error covariance are given; first, using the unilateral projection operator, the estimated value of the first-order Taylor expansion remainder term of the state equation is obtained and the estimated value of the first-order Taylor expansion remainder term ξ of the observation equation k+1|k+1 ; then, using the double unilateral projection operator, the estimated error covariance matrices of the original system state variables ζ k and ξ k+1 are obtained and The estimation of the first-order Taylor expansion remainder terms of the nonlinear state equation and the nonlinear measurement observation is completed.

[0016] As a further limitation of the first aspect of the present invention, the implementation steps of the filter include: obtaining the initial values of the system and Calculating the estimated values and covariances of the high-order neglected terms in the nonlinear state equation, denoted as and as well as the estimated values and covariances of the high-order neglected terms in the nonlinear measurement equation, denoted as and Calculating the system state prediction and its error covariance matrix Obtaining the system measurement prediction value and the measurement error Combining the Kalman gain to obtain the filter estimated value and the estimated error covariance and using them as the initial values for the filter estimation at the next moment.

[0017] As a further limitation of the first aspect of the present invention, the results of the REKF process are used as the input of the deep learning network model, and its most suitable nonlinear combination is iteratively trained to formulate the formula of the deep Kalman filter; it includes two neural network models, one for predicting the system state estimated value and the other for predicting the estimated error covariance.

[0018] As a further limitation of the first aspect of the present invention, a label sample data set for deep learning training is constructed using the results of the REKF, and the state prediction error containing system model information is introduced. and the state interval error As a result of including system model information; therefore, according to the state update process of the Kalman filter, As the four input information of the first neural network model, As the output information, it will be used to predict the system state estimate; according to the Kalman filter state estimation error covariance update process, As the two input information of the second neural network model, Is the output information, which is used to predict the system estimation error covariance matrix; where, Indicates that The elements of are expanded into column vectors in sequence by column, and P k+1|k+1 Represents the true estimation error covariance.

[0019] As a further limitation of the first aspect of the present invention, for the two input information of the second neural network model, two neural network models for predicting the system state estimate and the estimation error covariance are respectively established; the neural network model includes three parts of structure: the first part uses a fully connected layer to linearly map the input features to a higher dimension, the middle layer uses an LSTM network, which is the core part of the whole model, to realize the non-linear combination of the input features to the target output, and the third part uses a fully connected layer to linearly map its feature dimension to one dimension; the prediction value of the network is output through the non-linear regression layer.

[0020] In the second aspect, the present invention provides a train operation state estimation system integrating a residual extended Kalman filter, including:

[0021] An acquisition module, configured to acquire train state information, including spatial coordinates, speed information, and heading angle; and acquire real-time state command information output by the train ATP / ATO control system, and sample and organize all observation data into a sequence input at a fixed time interval;

[0022] An estimation module, configured to predict the train intermediate state estimation result based on the acquired train state information and based on the non-linear state space model of the train; where the state transition function in the model is x k+1 =f(x k , u k ) + w k , the observation model is y k =h(x k ) + v k , the model retains the high-order remainder ignored in the Taylor expansion, and based on its statistical characteristics, the error covariance matrix P of the state estimationk Make corrections to optimize the Kalman gain K k ;

[0023] An optimization module for a deep neural network module based on the LSTM structure, which takes the intermediate state estimation result, error covariance, Kalman gain, and system residual as input features, learns the model error distribution through non-linear combination, and outputs a set of optimized state estimation results;

[0024] A fusion module for weighted fusion of the intermediate state estimation result and the optimized state estimation result to obtain the final state estimation result.

[0025] In a third aspect, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which when executed by a processor, implement the train operation state estimation method of the fusion residual extended Kalman filter as described in the first aspect.

[0026] In a fourth aspect, the present invention 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, and the processor calls the program instructions to execute the train operation state estimation method of the fusion residual extended Kalman filter as described in the first aspect.

[0027] In a fifth aspect, the present invention 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 runs, the processor executes the computer program stored in the memory so that the electronic device executes instructions for implementing the train operation state estimation method of the fusion residual extended Kalman filter as described in the first aspect.

[0028] Advantages of the present invention: First, by introducing the Residual-based Extended Kalman Filter (REKF) and the Deep Residual Extended Kalman Filter (DREKF), the high-order residuals that are ignored in the traditional EKF can be fully utilized, thus greatly improving the accuracy of system state estimation. The traditional EKF only uses first-order linearization approximation and cannot effectively handle high-order non-linear terms, while these residuals are crucial for improving the state estimation accuracy. Second, the present invention enhances the non-linear modeling ability of the system by combining the Deep Neural Network (DNN) technology. The DREKF can adaptively capture and learn the complex non-linear relationships in the system through deep learning, making up for the deficiencies of traditional filters in dealing with non-linear systems. Therefore, the DREKF performs significantly better than traditional methods in non-linear systems and can provide higher accuracy and greater flexibility. Finally, the present invention forms the Fusion Deep Residual Extended Kalman Filter (FDREKF) by fusing the results of the DREKF and the REKF. This fusion method combines the advantages of both, enhancing the robustness and stability of the filter. In the face of complex dynamic systems, the FDREKF can maintain higher accuracy and stronger adaptability, especially in the case of large system uncertainties or high noise, showing better performance. This makes the present invention have a wider applicability and stronger practical value in practical applications. Brief Description of the Drawings

[0029] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0030] Figure 1This is the structural framework diagram of the fusion residual extended Kalman filter described in the embodiments of the present invention. It includes three parts: REKF (Residual-based Extended Kalman Filter), DREKF (Deep Residual EKF), and FDREKF (Fusion Deep Residual EKF). First, the REKF module performs filtering calculations based on the state space model and outputs intermediate features such as state prediction values, covariance matrices, Kalman gains, and high-order residual residuals. Subsequently, these features are input into the LSTM neural network and processed through a fully connected input layer, an LSTM unit structure (including forget gates, input gates, and output gates), and an output layer to generate a deeply optimized state estimation result and error covariance, which constitute the output of the DREKF module. Finally, in the FDREKF module, the estimation results of REKF and DREKF are fused through covariance weighting to obtain the final state estimation value and error covariance, thereby achieving high-precision and high-robustness joint estimation of the nonlinear operating state of the train. Detailed implementation manners

[0031] The following details the implementation manners of the present invention. The examples of the implementation manners are shown in the drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions throughout. The implementation manners described through the drawings are exemplary and are only used to explain the present invention and should not be construed as a limitation to the present invention.

[0032] Those skilled in the art of the present technology can understand that, unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as the general understanding of those of ordinary skill in the art to which the present invention belongs.

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

[0034] Those skilled in the art of the present technology can understand that, unless specifically stated, the singular forms "a", "an", "the", and "said" used herein may also include the plural forms. It should be further understood that the term "including" used in the specification of the present invention means the presence of the described 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 their groups.

[0035] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" etc. mean that the specific features, structures, materials, or characteristics described in connection 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 a suitable manner in any one or more embodiments or examples. Without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0036] For the convenience of understanding the present invention, the following further explains the present invention with specific embodiments in conjunction with the accompanying drawings, and the specific embodiments do not constitute a limitation to the embodiments of the present invention.

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

[0038] The present invention designs an extended Kalman filter considering the remainder (REKF). In the traditional extended Kalman filter (EKF), higher-order terms are ignored through Taylor expansion during the linearization process, which leads to low estimation accuracy for strongly nonlinear systems. By considering these ignored higher-order remainders, the invention compensates for them during the system state estimation process, thus significantly improving the estimation accuracy. By estimating the mean and covariance of the higher-order remainders, REKF can better capture the nonlinear characteristics of the system. Especially in the case of strong nonlinearity, compared with the traditional EKF, REKF shows higher estimation accuracy and stability. A high-precision nonlinear filter (DREKF) is developed in combination with a deep neural network. Based on the estimation results of REKF, a deep neural network Kalman filter (DREKF) is designed, and the results of the prediction step and update step of REKF are used as the input features of the neural network. In this way, DREKF can train a more accurate nonlinear combination model, thereby further optimizing the state estimation. To overcome the limitations of the deep neural network in traditional Kalman filtering (such as the lack of good label input), this method uses the output results of REKF as the training samples of the neural network, solves the problem of insufficient labels, and at the same time maintains the structural advantages of Kalman filtering. A fusion filter (FDREKF) is proposed. On the basis of REKF and DREKF, a fusion filter (FDREKF) is further proposed. By combining the estimation results of these two filters, a more accurate and stable state estimation method is obtained. The best balance between estimation accuracy and computational complexity is achieved. FDREKF can significantly improve the estimation accuracy in strongly nonlinear Gaussian systems and improve the estimation stability of the system through a more efficient fusion process. Simulation experiments show that FDREKF shows better estimation results than REKF and DREKF in a strongly nonlinear environment and has better stability and accuracy.

[0039] Embodiment 1

[0040] In this Embodiment 1, first, a train operation state estimation system integrating a remainder extended Kalman filter is provided, including: an acquisition module for acquiring train state information, including spatial coordinates, speed information, and heading angle; and acquiring real-time state command information output by the train ATP / ATO control system, and sampling and organizing all observation data into a sequence at a fixed time interval for input. An estimation module for predicting the train intermediate state estimation result based on the acquired train state information and the nonlinear state space model of the train; wherein, the state transition function in the model is x k+1 = f(x k , u k ) + w k , and the observation model is y k = h(x k)+v k , the model retains the high-order remainder terms ignored in the Taylor expansion and corrects the error covariance matrix P of the state estimation based on its statistical characteristics k to optimize the Kalman gain K k . The optimization module is a deep neural network module based on the LSTM structure. Using the intermediate state estimation result, error covariance, Kalman gain, and system residual as input features, it learns the model error distribution through non-linear combination and outputs a set of optimized state estimation results. The fusion module is used to perform weighted fusion on the intermediate state estimation result and the optimized state estimation result to obtain the final state estimation result

[0041] As Figure 1 shown, the structural framework of the fusion remainder extended Kalman filter includes three parts: REKF (Residual-based Extended Kalman Filter), DREKF (Deep Residual EKF), and FDREKF (Fusion Deep Residual EKF). First, the REKF module performs filtering calculations based on the state space model and outputs intermediate features such as state prediction values, covariance matrices, Kalman gains, and high-order remainder residuals. Subsequently, these features are input into the LSTM neural network and processed through a fully connected input layer, LSTM cell structure (including forget gate, input gate, output gate), and output layer to generate a deeply optimized state estimation result and error covariance, which constitute the output of the DREKF module. Finally, in the FDREKF module, the estimation results of REKF and DREKF are fused through covariance weighting to obtain the final state estimation value and error covariance, thereby achieving high-precision and high-robustness joint estimation of the non-linear operating state of the train

[0042] In this embodiment, based on the above system, a high-precision operating state estimation method for a non-linear train system is implemented. By fusing a deep neural network and a remainder extended Kalman filter (REKF), while maintaining the interpretability of the filtering theory, the non-linear fitting ability of the neural network is introduced to improve the estimation accuracy. The complete process is as follows

[0043] Data acquisition stage: The train operating state estimation system first obtains necessary observation data through a multi-source sensor network. The positioning data mainly comes from the AOA (Angle of Arrival) and AOD (Angle of Departure) positioning technologies based on the 5G communication network, and high-precision positioning is achieved by combining the ground RRH (Remote Radio Head) layout to obtain the spatial coordinates (s k ,q k ,p k ) of the train on the track. The speed information is measured by an on-vehicle Doppler radar, and the heading angle (θk ) is obtained by supplementing the track direction with an inertial navigation system or an encoder. In addition, the system synchronously accesses the real-time status instruction information output by the train ATP / ATO control system, and samples and organizes all the observed data into a sequence input at a fixed time interval (Δt). Among them, x k = [s k , q k , p k , θ k T

[0044] Filtering Prediction and Update Phase: In the core calculation process of state estimation, a nonlinear state space model of the train is constructed, where the state transition function is x k+1 = f(x k , u k ) + w k , and the observation model is y k = h(x k ) + v k . Different from the traditional EKF method, REKF retains the high-order remainders (ζ k and ξ k ) that are ignored in the Taylor expansion, and corrects the error covariance matrix P k of the state estimation based on their statistical characteristics, so as to optimize the Kalman gain K k , and improve the estimation accuracy and stability in the filtering process. The output of this phase is a set of high-precision intermediate state estimation results.

[0045] Deep Fusion Phase (DREKF): To further enhance the fitting ability for nonlinear complex dynamics, the system introduces a deep neural network module based on the LSTM structure. This network takes the intermediate state estimation values, error covariance, Kalman gain, system residuals, etc. output by REKF as input features, and outputs a set of optimized final state estimation results by learning the error distribution through a nonlinear combination. The LSTM model is trained with offline historical data and loaded during system deployment, and has strong robustness and generalization performance, especially suitable for the train operation scenario with frequent environmental changes.

[0046] Fusion Filtering Phase (FDREKF): In some system scenarios, to achieve a better balance between estimation accuracy and algorithm stability, the fusion filtering module FDREKF can be enabled to perform weighted fusion on the estimation results of REKF and DREKF. The specific form is: where the weights satisfy W r + W d = I, and minimize the trace of the estimation covariance Tr(W r P r + W d P​d ) is the goal. This module improves the overall performance of the system in complex scenarios with strong non - linearity and severe operating condition fluctuations.

[0047] Application feedback stage: The final estimated result is transmitted to the train's automatic control system (ATP / ATO) in real - time as a reference state value for train control and speed regulation. At the same time, the estimated data is recorded in the system's background database for subsequent model re - training, operation safety assessment, and trajectory playback analysis. In addition, the estimated result also provides interfaces to systems such as the dispatching center and intelligent maintenance platform to support the realization of train operation state prediction and fault warning functions.

[0048] In this embodiment, in order to estimate the train operation state quickly and accurately, it is first necessary to establish a train operation model. The proposed state transition model takes into account the position, speed, and heading angle of the train. Therefore, the state vector x of the system at a certain moment k is expressed as:

[0049] x k = [s k , q k , p k , θ k T (1)

[0050] where the variables s k , q k , p k and θ k represent the x - coordinate, y - coordinate, speed, and heading angle of the train respectively. Considering that the change of the train position between two consecutive time points depends on the heading angle and speed of the train, the considered state model can be expressed in a general form:

[0051] x k+1 = f(x k ) + w k (2)

[0052] where f(·) is a non - linear state transition model, expressed as:

[0053]

[0054] where Δt is the sampling interval between consecutive time points, w k ~N(0, Q k ) represents the zero - mean Gaussian process noise in the state model, and Q k is the covariance matrix of the state noise. In addition, Ψ(p k ) represents a non - linear function describing the conversion of the train running speed.

[0055] In this embodiment, the operation of the train under non-uniform speed conditions is considered, and models of different train operation speed modes are established. Based on the traction requirements of the train under different operation modes, traction, cruise, and coasting are regarded as one train operation mode in this paper, while braking is identified as another operation mode.

[0056] (1) The train braking model is

[0057]

[0058] where p k and p k+1 represent the train speeds at times k and k + 1 respectively. A(μ) and Br are the adhesion force and the air braking force. C p (p k ) is the running resistance, M A is the mass of the train, and w P is the random perturbation of the external factors on the train speed.

[0059] In Equation (4), the running resistance C p (p k ) consists of the basic resistance C1(p k ) and the additional resistance C2(s k ), that is:

[0060] C p (p k , s k ) = C1(p k ) + C2(s k ) (5)

[0061] The basic resistance C1(p k ) is positively correlated with the running speed p k of the train and is usually expressed as:

[0062]

[0063] where C0 represents the rolling resistance coefficient, C1 represents other mechanical resistance coefficients proportional to the train speed, and C2 represents the air resistance coefficient proportional to the square of the train speed. Usually, these coefficients are set according to heuristic methods. C2(s k ) represents the combined resistance from slopes, curves, and tunnel effects.

[0064] The adhesion braking force A(μ) of the train is affected by the adhesion coefficient μ between the wheel and the track and the train weight M A and is expressed as:

[0065] A(μ) = μMg (7) A

[0066] ​Among them, g is the gravitational acceleration coefficient. In Equation (7), the adhesion coefficient between the wheel and the track decreases as the train speed decreases. Their mutual relationship is also affected by the track surface conditions. For example, when the train moves from a dry track to a slippery track, the adhesion coefficient will decrease significantly, and the train system is prone to locking and slipping, and it is difficult for the air braking force of the braking system to effectively stop the train. In this case, the system cannot accurately obtain the real-time state of the train, which increases the risk of train operation.

[0067] The air braking force Br is affected by multiple braking performance parameters and is expressed as:

[0068]

[0069] Among them, d is the diameter of the brake cylinder, r is the friction radius of the brake disc, R c is the diameter of the train wheel, N A is the total number of brake pads. These parameters can be directly measured by conventional methods and remain unchanged during the train operation. Therefore, in the calculation, these parameters are regarded as constants. The additional parameters η and γ B are the transmission efficiency and braking force ratio of the main braking device respectively, μ A is the friction coefficient of the train brake disc, which depends on the train operation state and the material of the brake disc, while P re is the air pressure in the brake cylinder. During the actual emergency braking process of the train, the entire air pressure will be released.

[0070] (2) The traction / cruise / glide model is as follows:

[0071]

[0072] In this model, represents the traction force, which can be adjusted in real time according to the actual operation state. The specific operation mode of the model is determined by the traction force, and its expression is:

[0073]

[0074] Next, the non-linear measurement modeling of train operation is carried out. The non-linear measurement model of train operation state variables can be expressed as:

[0075] y k+1 = h(x k+1 ) + v k+1 (11)

[0076] Among them, h(·) represents the non - linear measurement output function, mainly including train positioning and speed measurement. The measurement vector h(x) is used for train positioning. This method utilizes the precise positioning service based on 5G NR communication, and estimates the state value of the current train through the Angle of Arrival (AOA) and Angle of Departure (AOD) methods, thereby achieving a sufficiently high positioning accuracy. v k+1 ~N(0,R k+1 ) represents the zero - mean Gaussian process noise of the measurement model. Assume that there are N RRH Remote Radio Heads (RRHs) participating in the train positioning process. The measurement function of the i - th available RRH can be obtained as follows:

[0077]

[0078] Among them, L k+1 =[s k+1 ,q k+1 T and L(i)=[s(i),q(i)] T respectively represent the position of the i - th available RHH and the position of the train, while c represents the speed of light. By combining all available RHHs, the final non - linear function for train positioning can be obtained as follows:

[0079] h x (x k+1 )=[h0(x k+1 ),h1(x k+1 ),…,h NRRH (x k+1 )] T (13)

[0080] In addition, in this embodiment, a Doppler radar is selected to measure the speed of the train. The speed - measuring radar is installed at the bottom of the train, and calculates the relative speed between the train and the track through the frequency difference between the transmitted wave and the ground - reflected wave. The advantage of using a Doppler radar for speed measurement is that when abnormal conditions occur in the train wheels, the speed measurement of the radar is not affected. Assume that the number of radar pulses per kilometer is N dopp , if p dopp pulses are received within the time interval T dopp , then the train speed measured by Doppler is:

[0081]

[0082] The state - space model of speed measurement using a Doppler radar combined with the train braking model (Equation (4)) can be written as:

[0083]

[0084] Among them, e​k is the measurement error of the sensor.

[0085] Assume that the measurement equation for train speed measurement is h p (·), then the final measurement equation for the train running state is:

[0086]

[0087] For the convenience of subsequent derivation, in this embodiment, the state variables in (2) are represented as n-dimensional, and the measurement variables in (11) are represented as m-dimensional.

[0088] In this embodiment, the design concept of the Extended Kalman Filter (EKF) is to approximate the non-linear state and measurement models as linear forms by using Taylor series expansion and retaining the first-order linear terms. This approximation enables state estimation within the existing Kalman filtering framework.

[0089] The EKF mainly includes two steps: the prediction step and the update step, and the process is as follows:

[0090] Prediction stage:

[0091]

[0092] Update stage:

[0093]

[0094] Among them, and represent the Kalman filter state prediction value and the measurement prediction value. A k+1|k and H k+1 represent the Jacobian matrices of the system non-linear state model and the non-linear observation model respectively derived at and respectively. and are the system constant vectors after the Taylor expansion of the state equation and the measurement equation are combined respectively. and represent the predicted estimation error covariance and the estimation error covariance respectively. represents the innovation. K k+1 represents the Kalman gain, represents the final estimated value of the Kalman filter.

[0095] As can be seen from the above derivation, the EKF mainly faces the following two problems: First, in the linearization process of the non-linear state model and the non-linear observation equation, only the first-order linear term is retained, and the second-order and higher-order terms are discarded. For a strongly non-linear model, the discarded part has a greater impact on the filtering effect and may lead to poor estimation results. Second, in the derivation process of the Kalman filter, the statistical information of the system state noise is only used to calculate the Kalman gain. The estimation of the Kalman filter is a linear combination of the state prediction value, the Kalman gain, and the innovation, which limits the optimization space to only within the straight line range formed by these variables. Therefore, the optimization space is relatively small. However, if the non-linear combination of these variables can be obtained and the non-linearity can be enhanced, theoretically the state estimation equation can cover any point on the plane, thereby providing a larger optimization space.

[0096] Therefore, in order to better utilize the system model information and improve the estimation accuracy of the non-linear model, a deep neural network Kalman filter considering the residual term is designed in this embodiment.

[0097] In this embodiment, for the design of the extended Kalman filter with remainder consideration (REKF), in order to make greater use of the information of the system non-linear state model and the non-linear observation model, the REKF takes into account the Taylor high-order remainder terms discarded in the EKF linearization process during the state estimation process. Therefore, the REKF can obtain higher estimation accuracy. First, the high-order residual term estimation of the state and measurement equations is performed.

[0098] The state equation (2) is expanded in a first-order Taylor series at to obtain

[0099]

[0100] where ζ k represents the high-order discarded remainder term after the first-order Taylor expansion of f(x k ).

[0101] Similarly, the observation equation (11) is expanded in a first-order Taylor series at to obtain:

[0102]

[0103] where ξ k+1 represents the high-order discarded remainder term after the first-order Taylor expansion of h(x k+1 ).

[0104] To facilitate the comparison of the performance of the REKF and the EKF, we can express x k as:

[0105]

[0106] Therefore, combining (25) and substituting the x in formula (23) k+1 into (24), we can obtain:

[0107]

[0108] Simplifying and arranging formula (26), we can obtain:

[0109]

[0110] where

[0111]

[0112] u k+1 = [ζ k ξ k+1 (30)

[0113]

[0114] where follows a normal distribution with a mean of 0 and a variance of , that is It can be solved as follows:

[0115]

[0116] Considering that the dimension of u k+1 is higher than that of z k+1 . Therefore, assuming then formula (27) is re-described as follows:

[0117]

[0118] By transposing and arranging, we obtain the expression of

[0119]

[0120] Therefore, the expression of the original variable u k+1 is as follows:

[0121]

[0122] Finally, the estimated value k+1 of the original variable u is:

[0123]

[0124] Continuing the derivation, the estimation error of the original variable u k+1 is It can be obtained through the following formula:

[0125]

[0126] Finally, the estimated error covariance matrix P u (k + 1|k + 1) can be obtained through the following formula:

[0127]

[0128] After completing the solution of the estimated value of u k+1 and the estimated error covariance, through the projection algorithm, the estimated value of the original estimated variable state and the estimated error covariance are given. First, using the unilateral projection operator, the estimated value of the remainder term of the first-order Taylor expansion of the state equation is obtained and the estimated value of the remainder term of the first-order Taylor expansion of the observation equation ξ k+1|k+1 are as follows:

[0129]

[0130] Then, using the double unilateral projection operator, the estimated error covariance matrices of the original system state variable ζ k and ξ k+1 are obtained and are as follows:

[0131]

[0132] So far, the estimation of the remainder terms of the first-order Taylor expansion of the non-linear state equation and the non-linear measurement observation is completed.

[0133] In this embodiment, the derivation of the prediction and update steps of the REKF follows the steps (17) to (22) described in the EKF process.

[0134] Prediction step:

[0135] According to (23), the predicted value of the state is as follows:

[0136]

[0137] Furthermore, the state prediction error is solved as follows:

[0138]

[0139] where represents the estimated error of the remainder term of the system state equation.

[0140] According to the definition, the state prediction error covariance matrix is solved as the following formula:

[0141]

[0142] Based on Equation (24), the system observation prediction value is solved as:

[0143]

[0144] According to the definition, continue to solve the system observation prediction error as:

[0145]

[0146] where represents the estimated error of the remainder of the system measurement equation.

[0147] Update step:

[0148] Similar to EKF, design the estimated value of the REKF state variable as:

[0149]

[0150] Therefore, the estimation error can be obtained through the following formula:

[0151]

[0152] According to the Kalman gain can be derived through the following formula:

[0153]

[0154] Finally, the state estimation error covariance matrix can be obtained through the following formula:

[0155]

[0156] So far, the online execution of REKF is completed, and the implementation steps of the filter are as follows:

[0157] (1) Obtain the initial values of the system and

[0158] (2) Calculate the estimated values and covariances of the higher-order neglected terms in the nonlinear state equation, denoted as and and the estimated values and covariances of the higher-order neglected terms in the nonlinear measurement equation, denoted as and

[0159] (3) Calculate the system state prediction and its error covariance matrix According to formulas (43) to (45);

[0160] (4) Obtain the system measurement prediction value and the measurement error According to formulas (46) and (47);

[0161] (5) According to the expression of the Kalman gain can be obtained;

[0162] (6) Obtain the filter estimated value and the estimated error covariance According to formulas (48) and (51), and use them as the initial values for the filter estimation at the next moment.

[0163] In this embodiment, for the EKF derivation that retains the high-order residuals, in order to facilitate the comparative analysis of the REKF and EKF performances. Therefore, before analyzing the REKF performance, the prediction and update process expressions of the EKF will be derived based on the Taylor expansion model that retains the remainder terms, namely Eqs. (12) and (13).

[0164] Prediction step:

[0165] First, the system state prediction value and the system measurement prediction value are the same as the solution method of the previous EKF. To avoid repeating the formulas, the following mainly derives the changed expressions.

[0166] For convenience, ζ k and ξ k+1 can be re-expressed as follows:

[0167]

[0168] Based on Eqs. (17) and (23), solve the state prediction error as:

[0169]

[0170] Therefore, based on the above formula, the state estimation prediction error covariance can be solved as:

[0171]

[0172] Based on Eqs. (19) and (24), the system measurement prediction error is obtained as

[0173]

[0174] Update steps:

[0175] The designed system state estimate is

[0176]

[0177] where is the Kalman gain.

[0178] Therefore, the system estimation error can be obtained as

[0179]

[0180] Based on the Kalman gain can be obtained, and its expression is:

[0181]

[0182] According to the definition, the expression of the system estimation error covariance is:

[0183]

[0184] So far, the solution of the traditional EKF process considering the remainder term is completed. Next, a specific analysis of REKF will be carried out.

[0185] Performance comparison and analysis between REKF and EKF

[0186] (1) Performance analysis in the prediction stage

[0187] First of all, in terms of the predicted estimate, based on Equations (20) and (43), compared with the traditional EKF, in REKF, more information is utilized, that is, the remainder term information discarded in the Taylor expansion linearization process of EKF. Therefore, from the perspective of information utilization: if the filter design utilizes more information, it should have higher accuracy. Secondly, in terms of the predicted error covariance matrix representing the performance index of the filter prediction stage, based on Equations (45) and (55), it can be obtained that

[0188]

[0189] It can be observed that, similar to EKF, REKF utilizes more information in the prediction stage, reduces the predicted error covariance matrix, and enhances the reliability of model prediction. Therefore, in the prediction stage, the performance of REKF is better than that of the traditional EKF.

[0190] (2) Performance analysis in the update stage

[0191] From the perspective of the predicted measurement state, based on equations (19) and (46), compared with the traditional EKF, the REKF utilizes more information, namely the residual information that is ignored during the Taylor expansion of the EKF measurement equation. Therefore, a filter design that utilizes more information should have higher accuracy.

[0192] To facilitate the comparison of the sizes of the estimated error covariance matrices of the two filtering methods, first rearrange and transform equations (50) and (51) to obtain:

[0193]

[0194] Substitute equation (62) into equation (51) and simplify to obtain the following expression:

[0195]

[0196] Similarly, based on equations (59) and (60), the EKF-based estimated error covariance can be rearranged as follows:

[0197]

[0198] Therefore, according to equations (63) and (64), it can be found that the state estimation performance of the filter is mainly contributed by two aspects: one is the prediction error covariance, which contains prediction information, and the other is the measurement error, which contains measurement prediction information. Obviously:

[0199]

[0200] That is

[0201] This indicates that, compared with the EKF, the REKF utilizes more information in the update stage and can improve accuracy by obtaining more accurate state and measurement predictions. Therefore, the REKF is superior to the traditional EKF filter in terms of filtering performance.

[0202] Design of a high-precision deep neural network Kalman filter (DREKF) considering the residual term:

[0203] As can be seen from the above analysis, although REKF can achieve higher estimation accuracy compared to EKF, the statistical characteristics of the state noise in the Kalman filter system are usually only used to calculate the Kalman gain, and the estimation result is usually a linear combination of the system state prediction information and the observation information. This results in the optimization range of the filter estimation being restricted to the linear combination space of the state prediction estimate and the system measurement value. Therefore, the optimization space is relatively small. If the non-linear combination of these variables can be obtained and the non-linearity can be enhanced, then theoretically, the state estimation can be optimized in the state space and the measurement space, thus having a more significant optimization space.

[0204] To solve the above problems, better integrate deep learning into the structured model, and improve the utilization and interpretation ability of model information, this embodiment designs a high-precision non-linear Kalman filtering method combining Kalman filtering and deep neural networks. The result of the REKF process is used as the input of the deep learning network model, and its most suitable non-linear combination is iteratively trained to formulate the formula of the deep Kalman filter. This process includes two neural network models, one for predicting the system state estimate value and the other for predicting the estimation error covariance.

[0205] 1) To construct the label sample data set for deep learning training, the REKF results obtained above are used. To maximize the utilization of the system model information, the state prediction error including the system model information and the state interval error are introduced as a result of including the system model information. Therefore, according to the state update process of the Kalman filter, are selected as the four input information of the first neural network model, as the output information, which will be used to predict the system state estimate value. In addition, according to the Kalman filter state estimation error covariance update process, are selected as the two input information of the second neural network model, as the output information, which is used to predict the system estimation error covariance matrix. Among them, means expanding the elements of into a column vector in sequence by columns. P k+1|k+1 represents the true estimation error covariance.

[0206] Note: The prediction error obeys the normal distribution, that is Therefore, the prediction error can be obtained through Monte Carlo sampling.

[0207] 2) Construction of the deep neural network Kalman filter model. Through the input features designed in 1), two neural network models for predicting the system state estimate value and the estimation error covariance are established as shown in the following formulas (67) and (68):

[0208]

[0209] where G(·) and F(·) represent two neural network models for predicting the system state estimate and the estimation error covariance. Here, and respectively represent the neural network models for predicting the system state estimate and the estimation error covariance, while ω and b respectively represent the weights and biases of the neural network model for predicting the system state estimate. Similarly, α and β respectively represent the weights and biases of the neural network model for predicting the estimation error covariance, and η k+1 and represent the random perturbations of the two neural network models.

[0210] Then, the specific architecture of the neural network model is designed. The neural network model mainly consists of three parts. First, a fully connected layer is used to linearly map the input features to a higher dimension. The middle layer uses an LSTM network, which is the core part of the whole model, to realize the non-linear combination of the input features to the target output. The third part uses a fully connected layer to linearly map its feature dimension to one dimension. Finally, the predicted value of the network is output through a non-linear regression layer.

[0211] Let X and Y respectively represent two sample data sets of the neural network model for predicting the state estimate and the neural network model for predicting the state estimation error covariance. The length of the data set is set to M1, that is and Then there are:

[0212] X k =[I k ,x k+1 T ; k = 0, 1, …, M1 (69)

[0213] Y k =[S k ,st(P k+1|k+1 )] T ; k = 0, 1, …, M1 (70)

[0214] Based on the deep neural network Kalman filter established above, an offline iterative prediction solution process can be established starting from the (M1 + 1)-th moment. The state estimate and the estimation error covariance at each moment are respectively expressed as shown in the following formulas (71) and (72):

[0215]

[0216]

[0217] where the state estimation error covariance​ Solve as follows

[0218]

[0219] If the system working environment changes at time M1 + M2, then the deep network model needs to be retrained at time M1 + M2 + 1 to adapt to the future state update process.

[0220] Design of the Kalman filter (FDREKF) that fuses the results of DREKF and REFK

[0221] Based on the above content, the REFK estimated value and the DREKF estimated value at time k + 1 are combined as shown in the following formula:

[0222] l k+1 = C k+1 x k+1 + η k+1 (74)

[0223] Where

[0224]

[0225] And respectively represent the state estimation errors solved by REKF and DREKF at time k + 1. η k+1 obeys a normal distribution with a mean of 0 and a variance of That is

[0226] By transposing and rearranging Equation (74), the expression of x k+1 can be obtained as follows:

[0227]

[0228] Then the state estimation value of the fusion filter at time k + 1 can be solved as:

[0229]

[0230] Continue to solve the state estimation error of the fusion filter at time k + 1 as

[0231]

[0232] According to the definition, the state estimation error covariance matrix

[0233]

[0234] According to Equation (78), the following conclusions can be drawn:

[0235]

[0236] Therefore, the estimation result of the fusion filter (FDREKF) is superior to that of REKF and DREKF at the same time.

[0237] Embodiment 2

[0238] Embodiment 2 provides a non-transitory computer-readable storage medium for storing computer instructions, which when executed by a processor, implement the train operation state estimation method based on the depth neural network fusion residual extended Kalman filter as described above.

[0239] Embodiment 3

[0240] Embodiment 3 provides a computer device including a memory and a processor, where 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 train operation state estimation method based on the depth neural network fusion residual extended Kalman filter as described above.

[0241] Embodiment 4

[0242] Embodiment 4 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 runs, the processor executes the computer program stored in the memory so that the electronic device executes the instruction to implement the train operation state estimation method based on the depth neural network fusion residual extended Kalman filter as described above.

[0243] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer-usable program code.

[0244] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows 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 the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices produce means for implementing the functions specified in one or more flows and / or blocks Figure 1 in one or more flows and / or blocks Figure 1 or in one or more blocks.

[0245] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including instruction means that implement the functions specified in one or more flows and / or blocks Figure 1 in one or more flows and / or blocks Figure 1 or in one or more blocks.

[0246] These computer program instructions can also be loaded onto a computer or other programmable data processing device to perform a series of operation steps on the computer or other programmable device to generate a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more flows and / or blocks Figure 1 in one or more flows and / or blocks Figure 1 or in one or more blocks.

[0247] Although the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation to the protection scope 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 deformations that can be made by those skilled in the art without creative efforts should be covered within the protection scope of the present invention.

Claims

1. A train operation state estimation method integrating a residual extended Kalman filter, characterized in that Including: Obtain train status information, including spatial coordinates, speed information, and heading angle; And obtain the real-time status instruction information output by the train ATP / ATO control system, and sample and organize all the observed data into a sequence input at a fixed time interval; Based on the obtained train status information, the intermediate state estimation result of the train is predicted based on the non-linear state space model of the train; among them, the state transition function in the model is x k+1 = f(x k , u k ) + w k , the observation model is y k = h(x k ) + v k , the model retains the high-order remainder terms ignored in the Taylor expansion, and corrects the error covariance matrix P k of the state estimation based on its statistical characteristics, so as to optimize the Kalman gain K k ; Based on the deep neural network module with the LSTM structure, using the intermediate state estimation result, error covariance, Kalman gain, and system residual as input features, learn the model error distribution through non-linear combination, and output a set of optimized state estimation results; Perform weighted fusion on the intermediate state estimation result and the optimized state estimation result to obtain the final state estimation result.

2. The train operation state estimation method of the fusion residual extended Kalman filter according to claim 1, characterized in that, In the nonlinear state space model, the extended Kalman filter REKF is designed to consider the remainder term. In order to make greater use of the information of the system's nonlinear state model and nonlinear observation model, REKF takes into account the Taylor high-order remainder term discarded in the linearization process during the state estimation process; first, the high-order residual term estimation of the state and measurement equations is carried out; after completing the solution of the estimated value and estimated error covariance of u k+1 , through the projection algorithm, the estimated value and estimated error covariance of the original estimated variable state are given; first, using the unilateral projection operator, the estimated value of the first-order Taylor expansion remainder term of the state equation is obtained and the estimated value of the first-order Taylor expansion remainder term of the observation equation ξ k+1|k+1 ; then, using the double unilateral projection operator, the estimated error covariance matrices of the original system state variables ζ k and ξ k+1 are obtained and Complete the estimation of the first-order Taylor expansion remainder terms of the nonlinear state equation and nonlinear measurement observation.

3. The train operation state estimation method of the fusion residual extended Kalman filter according to claim 2, wherein The implementation steps of the filter include: obtaining the initial value of the system and calculating the estimates and covariances of the higher-order neglected terms in the nonlinear state equation, denoted as and as well as the estimates and covariances of the higher-order neglected terms in the nonlinear measurement equation, denoted as and calculating the system state prediction and its error covariance matrix obtaining the system measurement prediction value and the measurement error combining with the Kalman gain to obtain the filter estimate and the estimation error covariance and using them as the initial values for the filter estimation at the next moment.

4. The train operation state estimation method using the fusion residual extended Kalman filter according to claim 3, characterized in that, Use the result of the REKF process as the input of the deep learning network model, and iteratively train its most suitable non-linear combination to formulate the formula of the deep Kalman filter; including two neural network models, one for predicting the system state estimation value, and the other for predicting the estimation error covariance.

5. The train operation state estimation method of the fusion residual extended Kalman filter according to claim 4, characterized in that Construct a label sample data set for deep learning training using the results of REKF, and introduce the state prediction error containing system model information and the state interval error as a result of containing system model information; therefore, according to the state update process of the Kalman filter, select as the four input information of the first neural network model, as the output information, which will be used to predict the system state estimate; according to the Kalman filter state estimation error covariance update process, select as the two input information of the second neural network model, as the output information, which is used to predict the system estimation error covariance matrix; where, means to The elements of are expanded into column vectors in sequence by columns, and P k+1|k+1 represents the true estimation error covariance.

6. The train operation state estimation method of the fusion residual extended Kalman filter according to claim 5, characterized in that, For the two input information of the second neural network model, respectively establish two neural network models for predicting the system state estimation value and the estimation error covariance; the neural network model includes three parts of the structure: the first part uses a fully connected layer to linearly map the input features to a higher dimension, the middle layer uses an LSTM network, which is the core part of the whole model, to realize the non-linear combination of the input features to the target output, and the third part uses a fully connected layer to linearly map its feature dimension Linearly map to one dimension; output the predicted value of the network through the non-linear regression layer.

7. A train operation state estimation system integrating a residual extended Kalman filter, characterized in that, Including: An acquisition module for obtaining train status information, including spatial coordinates, speed information, and heading angle; And obtain the real-time status instruction information output by the train ATP / ATO control system, and sample and organize all the observed data into a sequence input at a fixed time interval; An estimation module for predicting an intermediate state estimation result of a train based on the obtained train state information and a non-linear state space model of the train; wherein, the state transition function in the model is x k+1 = f(x k , u k ) + w k , the observation model is y k = h(x k ) + v k , the model retains the high-order remainder terms ignored in the Taylor expansion and corrects the error covariance matrix P k of the state estimation based on its statistical characteristics, thereby optimizing the Kalman gain K k ; An optimization module for, based on the deep neural network module with the LSTM structure, using the intermediate state estimation result, error covariance, Kalman gain, and system residual as input features, learning the model error distribution through non-linear combination, and outputting a set of optimized state estimation results; A fusion module for performing weighted fusion on the intermediate state estimation result and the optimized state estimation result to obtain the final state estimation result.

8. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the train operation state estimation method of the fusion residual extended Kalman filter described in any one of claims 1-6 is implemented.

9. A computer device, characterized in that, Including 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 train operation state estimation method of the fusion residual extended Kalman filter described in any one of claims 1-6.

10. An electronic device, characterized in that, 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 operates, the processor executes the computer program stored in the memory so that the electronic device executes instructions for implementing the train operation state estimation method of the fusion residual extended Kalman filter according to any one of claims 1-6.

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