Train running state estimation method and system based on high-order extended Kalman filter considering noise correlation

Abstract

The invention provides a train operation state estimation method and system based on a high-order extended Kalman filter considering noise correlation, and belongs to the technical field of rail transit train operation management. According to the method, correlation analysis between high-order terms is introduced, the filtering precision is remarkably improved, and particularly, excellent performance is shown under a strong nonlinear system; by establishing a multi-mode train state model, the dynamic characteristics of a train in operation modes such as traction, cruising, sliding and braking are comprehensively covered, and a more accurate input basis is provided for a filtering algorithm; by introducing a sliding window error criterion, the filter can quickly switch operation modes according to real-time errors, so that the filter is ensured to keep high adaptability in a complex and changeable operation environment; the comprehensive performance evaluation framework based on the error covariance matrix not only evaluates the mean square error and the mean absolute error, but also quantifies the contribution of the high-order correlation to the precision of the filter, and provides a more scientific and comprehensive evaluation system.

Description

Technical Field

[0001] The present invention relates to the technical field of rail transit train operation management, and particularly to a train operation state estimation method and system based on a high-order extended Kalman filter considering noise correlation. Background Art

[0002] Common filtering methods are difficult to provide high-precision state estimation when dealing with measurement data with noise. To solve the problem of noise interference, the Kalman filter, which combines the dynamic model of the system and measurement data and utilizes the minimum mean square error criterion, was thus born. It is updated continuously over time and currently includes but is not limited to the following types of Kalman filters:

[0003] The ordinary Kalman filter (KF) is a filtering method based on recursive estimation. It optimally estimates the state through a linear system model. Its core idea is to estimate the state of the system using observation data under the state space model and achieve the best estimate by minimizing the mean square error. The advantage of the Kalman filter lies in its high computational efficiency, which can handle noise interference in dynamic systems in real time and is widely used in fields such as navigation, control systems, and signal processing. However, the limitation of the ordinary Kalman filter is that it assumes that the system model and observation model are linear and the noise is Gaussian distributed, which makes it have certain limitations when dealing with nonlinear systems.

[0004] The extended Kalman filter (EKF) is an extension of the ordinary Kalman filter designed to handle nonlinear systems. In the extended Kalman filter, the state transition function and observation function of the nonlinear system are linearized by performing a first-order Taylor expansion, thereby transforming the nonlinear system into a local linear problem for applying the framework of the Kalman filter. Although the extended Kalman filter makes up for the defects of the ordinary Kalman filter to a certain extent, its linearization process is prone to introducing linearization errors and its performance is poor when the system is strongly nonlinear. Therefore, the performance of the extended Kalman filter may be limited in some cases. Based on the above methods, Li et al. first established a mathematical model of a single-point levitation system and designed a state observer using the extended Kalman filter algorithm to solve the problems of process noise, measurement noise, and state unpredictability. Then, combined with linear quadratic optimal control (LQR) and feedforward control, a levitation controller suitable for the complex environment of maglev trains was proposed.

[0005] The Unscented Kalman Filter (UKF) is an improved Kalman filter algorithm designed to enhance the estimation accuracy for strongly nonlinear systems. Different from the Extended Kalman Filter, the Unscented Kalman Filter propagates the state by selecting a set of representative sampling points (called unscented points), rather than through linearization approximation. This method approximates the higher-order statistics of the nonlinear function by determining the mean and covariance of these sampling points, thus avoiding the linearization error that may occur in traditional Kalman filtering when dealing with nonlinear systems. The Unscented Kalman Filter exhibits superior performance in applications with a high degree of nonlinearity and has been widely used in real-time applications such as positioning and tracking. Nazaruddin et al. proposed a multi-sensor data fusion method based on the Unscented Kalman Filter (UKF) to improve the accuracy of measurement data in railway system operations and ensure the reliability and safety of the system. This method fuses data from different on-vehicle and turnout sensors (such as indoor positioning systems, radio frequency identification, and rotary encoders) to obtain more accurate train position data.

[0006] The Centralized Kalman Filter (CKF) is a multi-sensor fusion technology that fuses the information of multiple sensors through centralized calculation to improve the state estimation accuracy of the system. In the Centralized Kalman Filter, the data of each sensor is processed and fused through a shared central node to provide a global state estimate of the system. This method is applicable when multiple sensors work together and can optimize the global state estimate in a centralized manner. However, the disadvantage of the Centralized Kalman Filter is its high computational complexity, and when the number of sensors increases, it may face communication and computational bottleneck problems. Therefore, the Centralized Kalman Filter is usually applicable to occasions where the number of sensors is relatively small and there is sufficient computing resources. Jukka et al. studied the positioning method of high-speed trains (HSTs) based on time difference of arrival (TDoA) and angle of arrival (AoA) measurements in a 5G new radio (NR) network. This method uses 5G NR reference signals for positioning in the millimeter wave (mmWave) band and employs an Extended Kalman Filter (EKF) to track the train position.

[0007] Particle Filter (PF) is a filtering algorithm based on the Monte Carlo method, which is suitable for processing systems with non-linear and non-Gaussian noise. Particle Filter represents the probability distribution of the system state by using a set of randomly sampled particles, and updates the distribution of these particles through weights, so as to achieve the estimation of the system state. The advantage of Particle Filter is that it can handle highly non-linear and complex dynamic systems without the need for linearization or Gaussian noise assumptions. Therefore, Particle Filter has achieved remarkable applications in fields such as target tracking, positioning, and robot navigation in complex environments. However, the computational cost of Particle Filter is relatively large, especially in high-dimensional state spaces, where a large number of particles may be required to maintain the estimation accuracy, which may become a bottleneck in real-time processing. Yang et al. proposed a new adaptive filter to solve the problems of system model error and non-Gaussian noise interference in complex train environments. This filter is based on the Particle Filter (PF), constructs an equivalent weight function using the IGG method, and introduces an adaptive factor to optimize the importance density function, thereby reducing the sensitivity of the algorithm to measurement environment interference.

[0008] Improved Extended Kalman Filter (IEKF) is based on the Extended Kalman Filter. It unfolds the non-linear measurement function layer by layer, and uses higher-order Taylor expansion terms to extract more statistical feature information. Compared with the traditional EKF that only uses the first-order term, it can handle highly non-linear systems more accurately. The IEKF algorithm proposed by Wen et al. is based on 5G NR (New Radio) signals. By introducing a higher-order Taylor expansion formula, it captures the higher-order statistical features of the non-linear measurement function, thereby improving the positioning accuracy. This algorithm combines the Least Squares method (ULS) and the step-by-step expansion technique to extract more information of the measurement function without adding additional information, so as to meet the high-precision requirements of High-Speed Train (HST) positioning.

[0009] Taking traditional filtering methods as an example, the EKF linearizes the nonlinear system through first-order Taylor expansion. This approximation may lead to significant errors when the system is highly nonlinear, affecting the filtering accuracy. The UKF is sensitive to the parameters generated by the Sigma points (such as the expansion coefficient, the number of sampling points, etc.). Improper parameter selection may result in poor filtering performance. The performance of the CKF is greatly affected by parameters such as the number of sampling points and the expansion coefficient. Improper parameters may lead to poor filtering effects. Thus, it is found that traditional filtering methods have certain limitations. Existing nonlinear filtering techniques generally ignore the correlation between the system state noise and the measurement noise, which significantly affects the accuracy of the filtering results. For example, although the Iterated Extended Kalman Filter (IEKF) proposed in the literature improves some problems by introducing higher-order terms, it does not solve the correlation problem between the higher-order terms, reducing the reliability and estimation accuracy of the method. Trains have multiple operating modes (such as traction, cruise, coasting, braking). Traditional filtering methods are difficult to quickly switch to an appropriate state model according to the real-time operating mode of the train, resulting in a decrease in filtering accuracy and being unable to meet the requirements of practical applications. Summary of the Invention

[0010] The object of the present invention is to provide a train operation state estimation method and system based on a high-order extended Kalman filter considering noise correlation to solve at least one of the technical problems existing in the above-mentioned background technology.

[0011] To achieve the above object, the present invention adopts the following technical solutions:

[0012] In a first aspect, the present invention provides a train operation state estimation method based on a high-order extended Kalman filter considering noise correlation, including:

[0013] Obtain the operation state data of the train at the current moment, including the running speed, position, and environmental data under the current operation state;

[0014] Based on the obtained operation state data of the train at the current moment, use the prediction model of the high-order extended Kalman filter considering noise correlation to predict the dynamic state of the train; wherein, the high-order extended Kalman filter considering noise correlation linearizes the nonlinear state equation to higher-order terms through the Taylor expansion formula, and then substitutes it into the measurement equation to obtain the standard form of the least squares, so as to obtain the high-order dynamic characteristics.

[0015] Update the state by combining the real-time measured operation state data; wherein, the predicted state and the real-time operation state data are weighted and fused through the dynamic calculation of the Kalman gain, and the gain coefficient optimally integrates the two according to the minimum mean square error criterion by balancing the confidence of the prediction model and the measurement noise.

[0016] As a further limitation of the first aspect of the present invention, the mathematical model of train operation includes a state equation and a measurement equation, which are used to describe the relationship between the dynamic state of the train and the sensor measurement values; the state equation is used to represent the evolution process of the train speed, position, and acceleration states, and the measurement equation describes the non-linear mapping relationship between the measurement values and the state variables.

[0017] As a further limitation of the first aspect of the present invention, the speed state estimation of the train is described by the following model:

[0018]

[0019] Where x(k) represents the train speed, y(k + 1) represents the speed measurement value; f(·) is a non-linear continuously differentiable function, and H(k + 1) is a linear function; w(k) and v(k + 1) are the state noise and measurement noise respectively, and their error covariance matrices are Q(k) and R(k + 1) respectively, and the error covariance matrix of the initial state estimation is P(0); the initial state x(0) is determined by the initial speed, position, and acceleration of the train.

[0020] As a further limitation of the first aspect of the present invention, using high-order Taylor expansion, the state model of the vehicle speed is extended to a higher order to model the train state; the high-order information in the state equation in modeling the train state using the measurement equation is obtained, that is, the high-order extended Kalman filter prediction related to the noise, to obtain the high-order expansion information.

[0021] As a further limitation of the first aspect of the present invention, speed estimation is performed based on the obtained high-order information to obtain the posterior estimation value:

[0022] As a further limitation of the first aspect of the present invention, the updated error covariance matrix:

[0023]

[0024] In the second aspect, the present invention provides a train operation state estimation system based on a high-order extended Kalman filter considering noise correlation, including:

[0025] An acquisition module, configured to acquire the train operation state data at the current moment, including the running speed, position, and environmental data under the current running state;

[0026] A prediction module, configured to predict the dynamic state of a train based on the obtained operation state data of the train at the current moment, by using a prediction model of a high-order extended Kalman filter considering noise correlation; wherein, the high-order extended Kalman filter considering noise correlation linearizes the non-linear state equation to high-order terms through Taylor expansion, and then substitutes it into the measurement equation to obtain the standard form of least squares, so as to obtain high-order dynamic characteristics.

[0027] An update module, configured to update the state by combining the operation state data measured in real time; wherein, the predicted state and the operation state data measured in real time are weighted and fused through dynamic calculation of the Kalman gain, and the gain coefficient optimally integrates the two according to the minimum mean square error criterion by balancing the confidence degrees of the prediction model and the measurement noise.

[0028] In a third aspect, the present invention provides a non-transitory computer-readable storage medium, which is used to store computer instructions, and when the computer instructions are executed by a processor, the train operation state estimation method based on a high-order extended Kalman filter considering noise correlation as described in the first aspect is implemented.

[0029] 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 based on a high-order extended Kalman filter considering noise correlation as described in the first aspect.

[0030] 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 based on a high-order extended Kalman filter considering noise correlation as described in the first aspect.

[0031] Advantages of the present invention: Based on the existing improved extended Kalman filter (IEKF), the present invention significantly improves the performance of the filtering algorithm in complex nonlinear systems through multiple innovations. First, compared with IEKF that simply relies on Taylor expansion to extract high-order terms, the proposed correlated noise-induced extended Kalman filter (CIEKF) method not only improves the traditional EKF by considering the influence of high-order terms, but also systematically introduces the correlation analysis between high-order terms for the first time, significantly improving the filtering accuracy, especially showing excellent performance in strongly nonlinear systems. At the same time, the present invention establishes a multi-mode train state model to comprehensively cover the dynamic characteristics of the train in operation modes such as traction, cruise, coasting, and braking, providing a more accurate input basis for the filtering algorithm. In addition, the introduction of the sliding window error criterion enables the filter to quickly switch the operation mode according to the real-time error, thus ensuring that the filter maintains high adaptability in complex and changeable operating environments. The present invention also designs a comprehensive performance evaluation framework based on the error covariance matrix, which not only evaluates the mean square error (MSE) and mean absolute error (MAE), but also quantifies the contribution of high-order correlations to the filter accuracy, forming a more scientific and comprehensive evaluation system.

[0032] The advantages of the additional aspects of the present invention will be more clearly given in the following description part, or can be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings 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.

[0034] Figure 1 It is a flowchart of the train operation state estimation method based on the correlated noise-induced extended Kalman filter according to the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0035] The following details the embodiments of the present invention. The examples of the embodiments 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 embodiments described below with reference to the drawings are exemplary only for explaining the present invention and should not be construed as limiting the present invention.

[0036] 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 technical field to which the present invention belongs.

[0037] It should also be understood that terms such as those defined in a general dictionary should be understood as having a meaning consistent with their meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless defined as here.

[0038] Those skilled in the art can understand that, unless specifically stated otherwise, the singular forms "a", "an", "the", and "said" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the specification of the present invention means the presence of the recited features, integers, steps, operations, elements, and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0039] In the description of this specification, the description referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. means 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 can 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.

[0040] 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.

[0041] 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.

[0042] The present invention solves the problem of insufficient processing ability of traditional filtering methods (such as EKF, UKF, CKF) for strongly nonlinear systems by introducing high-order terms on the basis of the Extended Kalman Filter (EKF). By means of high-order Taylor expansion and making full use of high-order characteristic quantities, the filtering accuracy is improved, and the system estimation error is significantly reduced. Aiming at the problem of the second unconsidered noise correlation, the proposed High-precision Extended Kalman Filter (CIEKF) model in the present invention considers the correlation between state noise and measurement noise in the filtering algorithm for the first time. By introducing the cross-correlation covariance matrix, the state estimation accuracy and reliability are improved, and the deficiency that the traditional IEKF algorithm increases the estimation error due to the unconsidered noise correlation is overcome. Aiming at the problem of insufficient model adaptability in the third aspect, the present invention proposes an error criterion based on a sliding window, which can discriminate the train operation mode (such as traction, cruise, coasting, braking) in real time and dynamically adjust the filtering model according to the operation mode. This method can effectively cope with the problem of the decrease in filtering accuracy caused by the frequent switching during the multi-mode operation of the train, and improves the applicability and real-time performance of the filter.

[0043] The high-order extended Kalman filter related to noise in the present invention is mainly used in the fields of train transportation, sensor design, train dynamics modeling, etc. The main technical problems it solves are as follows: Aiming at the characteristics of complex and highly non-linear dynamic operating states of trains in the Harmony 3 train system, an accurate high-speed train speed estimation method is proposed through the estimation of the noise-related high-order extended Kalman filter (CIEKF). This method can capture the accurate train speed state of trains under different operating conditions in real time, ensuring that the accuracy of train speed estimation meets the requirements of efficient and safe operation. Even when the operating state of the train continuously changes in a dynamic environment, high-precision estimation can be achieved. Regarding the optimization of the estimation accuracy and robustness of high-speed trains, this noise-related high-order extended Kalman filter is mainly extended from the high-order extended Kalman filter, considering the correlations existing between high-order terms that were not considered in the original high-order extended Kalman filter and between process noise and high-order terms, improving the theoretical derivation. And according to the experimental conclusions, it has higher estimation accuracy compared with traditional extended Kalman filters, unscented Kalman filters, and high-order extended Kalman filters. Among them, the third-order noise-related high-order extended Kalman filter has improved by about 50% compared with the ordinary EKF and by about 10% compared with the third-order high-order extended Kalman filter. Regarding the robustness problem of train speed estimation, due to the interference problem of train speed, the noise-related high-order extended Kalman filter (CIEKF) proposed in the present invention combines measurement information and state information to optimize the dynamic estimation problem of train states, greatly improving the estimation stability and robustness of trains under noise interference. Aiming at the existing problem of the conversion of train operation modes, trains may switch operation modes too early or too late. Therefore, a sliding window error model is proposed, which can dynamically adjust the operation mode of trains during real-time operation, avoiding inaccurate state estimation caused by premature mode switching and ensuring the stability and reliability of the system under various operating conditions.

[0044] Embodiment 1

[0045] In Embodiment 1, a train operation state prediction system based on a high-order extended Kalman filter considering noise correlation is first provided, including: an acquisition module for acquiring the operation state data of the train at the current moment, including the running speed, position, and environmental data under the current operation state; a prediction module for predicting the dynamic state of the train based on the acquired operation state data of the train at the current moment by using a prediction model of a high-order extended Kalman filter considering noise correlation; wherein, the high-order extended Kalman filter considering noise correlation linearizes the nonlinear state equation to a high-order term through a Taylor expansion, and then substitutes it into the measurement equation to obtain the standard form of the least squares, so as to obtain the high-order dynamic characteristics; an update module for updating the state by combining the operation state data measured in real time; wherein, the predicted state and the operation state data measured in real time are weighted and fused through the dynamic calculation of the Kalman gain, and the gain coefficient optimally integrates the two according to the minimum mean square error criterion by balancing the confidence degrees of the prediction model and the measurement noise.

[0046] In Embodiment 1, using the above system, a train operation state estimation method based on a high-order extended Kalman filter considering noise correlation is realized, including: using the acquisition module to acquire the operation state data of the train at the current moment, including the running speed, position, and environmental data under the current operation state; using the prediction module to predict the dynamic state of the train based on the acquired operation state data of the train at the current moment by using a prediction model of a high-order extended Kalman filter considering noise correlation; wherein, the high-order extended Kalman filter considering noise correlation linearizes the nonlinear state equation to a high-order term through a Taylor expansion, and then substitutes it into the measurement equation to obtain the standard form of the least squares, so as to obtain the high-order dynamic characteristics. Using the update module to update the state by combining the operation state data measured in real time; wherein, the predicted state and the operation state data measured in real time are weighted and fused through the dynamic calculation of the Kalman gain, and the gain coefficient optimally integrates the two according to the minimum mean square error criterion by balancing the confidence degrees of the prediction model and the measurement noise.

[0047] In this embodiment, in the system initialization stage, the speed state estimation of the high-speed train is described by the following model:

[0048]

[0049] Wherein, x(k) represents the train state (speed), and y(k + 1) represents the sensor (speed) measurement value. f(·) is a nonlinear continuously differentiable function, and H(k + 1) is a linear function; w(k) and v(k + 1) are the state noise and measurement noise respectively, both of which are zero-mean Gaussian white noises. Their error covariance matrices are Q(k) and R(k + 1) respectively, and the error covariance matrix of the initial state estimate is P(0).

[0050] Initial state x(0): Determined by the initial velocity, position, and acceleration of the train.

[0051] Initial error covariance matrix P(0): Reflects the uncertainty of the initial state.

[0052] State noise covariance Q(k) and measurement noise covariance R(k + 1): Set based on experimental data.

[0053] For the data source, the data acquisition method is as follows: Use on - vehicle sensors to obtain the real - time state data of the train, such as speed, acceleration, and position information. Use a speedometer to monitor speed changes. Doppler radar provides the accurate speed of the train relative to the track. The data collected is the real - time speed v of the train.

[0054] In the high - order state prediction stage (forward calculation of CIEKF), use high - order Taylor expansion to model the train state: Use high - order Taylor expansion to extend the state model of vehicle speed to a higher order:

[0055]

[0056] Then, use OLS to obtain high - order information: Use the measurement equation to obtain the high - order information in the state equation, that is, the high - order extended Kalman filter prediction related to noise, and obtain the high - order expansion information of the l - th order:

[0057]

[0058] Among them, the high - order extended Kalman filter considering noise correlation (CIEKF):

[0059] After obtaining the high - order information of CIEKF, this can use this high - order information to further improve the estimation accuracy. At the same time, using the filtering process of CIEKF can ensure that the speed accuracy estimated by CIEKF is closer to the true value, and obtain the posteriori estimation value:

[0060]

[0061] The updated error covariance matrix is:

[0062]

[0063] In summary, the overall process of train state estimation can be summarized as a complete set of operations from system initialization, data acquisition to state estimation and optimization, and high - precision prediction of the train operation state is achieved through the high - order extended Kalman filter considering noise correlation (CIEKF).

[0064] First, during the system initialization phase, a mathematical model of train operation is established, including state equations and measurement equations, to describe the relationship between the dynamic state of the train and sensor measurement values. The state equations are used to represent the evolution process of states such as train speed, position, and acceleration, while the measurement equations describe the non-linear mapping relationship between sensor measurement values and state variables. In this phase, system noise and measurement noise are added to the model, and the uncertainty in the system is characterized by defining the noise covariance matrices Q(k) and R(k + 1). In addition, the initial state x(0) and initial error covariance P(0) of the train need to be initialized to ensure that the model can accurately reflect the dynamic characteristics of the train.

[0065] Data acquisition is the core foundation of train state estimation. The system obtains the real-time speed of the train through various sensors on the train, such as wheel sensors, Doppler radars, etc. In addition, environmental data can also be collected, such as track curvature, slope, and weather information, which may affect the running state of the train. To ensure data quality, the system preprocesses the collected data, including denoising, cleaning outliers, filling in missing data, and normalizing data with different dimensions. These operations can effectively improve the reliability of the data and the consistency of model inputs.

[0066] In the high-order state prediction process phase, a high-order extended Kalman filter considering noise correlation (CIEKF) is used to predict the dynamic state of the train. CIEKF linearizes the non-linear state equation to high-order terms through Taylor expansion, and then substitutes it into the measurement equation to obtain the standard form of the least squares, thus capturing the high-order dynamic characteristics ignored in traditional methods. This high-order modeling method can significantly reduce the errors caused by non-linear truncation and improve the accuracy of state prediction.

[0067] After the prediction is completed, the system updates the state by combining real-time measurement data. In this process, the dynamic calculation of the Kalman gain realizes the weighted fusion of the predicted state and sensor observation data. This gain coefficient optimally integrates the two based on the minimum mean square error criterion by balancing the confidence levels of the prediction model and measurement noise. At the same time, the synchronous update of the posterior error covariance matrix accurately quantifies the uncertainty level of the corrected state estimate. This recursive correction mechanism based on real-time observation data effectively improves the accuracy of state estimation and enables the system to dynamically adapt to the real-time changes in the train operation state.

[0068] The real-time speed of the train is obtained through speed sensors on high-speed trains (such as Doppler radars, wheel hub sensors); then high-order terms are obtained through Taylor expansion, and the information of the high-order terms is estimated using the least squares method. After obtaining the high-order terms, they are substituted into the state equation to improve the prediction information of the state equation. Finally, the final filtering result is obtained through the filtering process of CIEKF, which is specifically expressed as follows:

[0069]

[0070] Posterior error covariance matrix

[0071]

[0072] Embodiment 2

[0073] In this Embodiment 2, a train operation state estimation method based on a high-precision extended Kalman filter considering noise correlation (CIEKF) is provided, which mainly solves the problems of insufficient nonlinear processing accuracy, neglect of noise correlation, and poor multi-mode real-time adaptability in the state estimation of high-speed trains (CRH3). Traditional filtering methods (such as EKF, UKF, CKF) have first-order linearization errors and parameter sensitivities when dealing with strong nonlinear dynamic systems of trains, resulting in a decrease in estimation accuracy. In this embodiment, high-order characteristic quantities are introduced through high-order Taylor expansion, significantly improving the nonlinear modeling accuracy. At the same time, the correlation between state noise and measurement noise is considered for the first time, and the robustness of the filtering algorithm is improved through the cross-correlation covariance matrix. In addition, this embodiment proposes an error criterion method based on a sliding window, which can real-time identify the train operation mode and dynamically adjust the filtering model, effectively solving the adaptability problem in multi-mode switching. In a complex noise environment, this embodiment improves the filtering performance through a high-precision extended Kalman filter considering noise correlation (CIEKF). Experiments show that it is significantly superior to traditional methods in terms of accuracy, robustness, and real-time performance, providing more reliable technical support for train state estimation.

[0074] In this embodiment, the state of the high-speed train is described by the following model:

[0075]

[0076] where f(x(k)) is a nonlinear state function, H(k + 1) is a measurement transfer matrix, and f(x(k)) has continuous differentiability of any order; x(k + 1) represents the train speed, w(k) is the disturbance in the train state model, y(k + 1) is the monitored quantity of the sensor, and v(k + 1) is the disturbance received by the sensor. Given that the initial speed of the train is x(0), the disturbance w(k) in the state model and the measurement error vector v(k + 1) are statistically independent and each has statistical characteristics;

[0077]

[0078] In this embodiment, the high-order extended Kalman filter prediction related to noise correlation includes:

[0079] For the original non-linear state model, the state model needs to be expanded step by step. Expand the above equation (1.1) at to perform a second-order Taylor expansion:

[0080]

[0081] Substitute equation (1.2) into the measurement equation for combination and rearrangement, and the measurement equation about can be obtained:

[0082]

[0083] Among them, the new modeling error has the following statistical characteristics:

[0084]

[0085] Convert the measurement equation (1.3) into the standard least squares calculation mode to solve the statistical characteristics:

[0086]

[0087] Among them

[0088]

[0089] In the above equation

[0090]

[0091] In this embodiment, it is noted that while being related to both v(k + 1) and w(k). However, the literature Wen T, Jiang H, Cai B, et al. High-Speed Train Positioning Using Improved Extended Kalman Filter With 5G NR Signals[J]. IEEE Transactions on Intelligent Transportation Systems, 25[2025 - 01 - 09]. DOI: 10.1109 / TITS.2024.3357101 does not consider this correlation. For the algorithm design that does not consider the noise correlation, the correlation between the state noise and the measurement noise will not be considered, which will affect the final state accuracy.

[0092] According to the derivation of the above formula, the statistical characteristics of the (l + 1)-th feature can be continuously derived based on the statistical characteristics of the l-th feature of the state prediction estimation error that has been obtained and used in the prediction stage of the filtering process. The specific derivation process is as follows:

[0093] Expand the state equation at to obtain a Taylor expansion of order l + 1

[0094]

[0095] Combine and organize Equation (1.5) to obtain a measurement equation for :

[0096]

[0097] where

[0098]

[0099] The modeling error of the above equation has the following statistical properties:

[0100]

[0101] Its variance will show modeling error when l + 1 > 2 and the elements in

[0102]

[0103] become correlated. Attention should be paid to the correlation between its elements, and the covariance matrix will be obtained as follows After obtaining the above preconditions, the statistical properties of

[0104]

[0105] In the above equation

[0106]

[0107] In this embodiment, is related to both v(k + 1) and w(k) simultaneously. Therefore is related to All are relevant. However, the literature Wen T, Jiang H, Cai B, et al. High-Speed Train Positioning Using Improved Extended Kalman Filter With 5G NR Signals[J]. IEEE Transactions on Intelligent Transportation Systems, 25[2025-01-09]. DOI: 10.1109 / TITS.2024.3357101. does not consider this correlation. For the algorithm design that does not consider the noise correlation, the correlation between the state noise and the measurement noise will not be considered, which will affect the final state accuracy.

[0108] In this embodiment, the high-order extended Kalman filter update regarding noise correlation includes:

[0109] Based on the above prediction step, the l-order statistical information has been obtained, and thus the equation obtained by high-order expansion of Equation (1.1) can be converted into the following expression

[0110]

[0111] Before formally performing the Kalman filter update process, it is necessary to obtain the state estimate, state estimation error, initial state error, initial state estimate, and estimation error covariance matrix, that is:

[0112]

[0113] Similar to the traditional Kalman filter process, regarding the Kalman filter update process, it is not only related to the state variables but also related to the measurement variables. Therefore, it is necessary to derive the following equations related to the measurement variables.

[0114]

[0115] In this embodiment, the relationship between the high-order state term and the measurement noise is considered. Therefore, the relationship between the state variables and the measurement variables must also be considered during the Kalman filter update process.

[0116]

[0117] Due to the existence of terms during the expansion process, they will finally be combined with the process noise w(k) to form a new process noise, and its correlation relationship with the measurement noise is shown in the following equation:

[0118]

[0119] Based on the above inferences, the following new Kalman filter process can be obtained. Since the core formula of the Kalman filter is as follows:

[0120]

[0121] According to the calculation

[0122]

[0123] Finally, it is simplified to the following formula:

[0124]

[0125] Therefore, the filtering process in this embodiment is as follows:

[0126] A priori value:

[0127]

[0128] A priori error covariance:

[0129]

[0130] Kalman gain:

[0131] K r (k + 1) = P xy,rr (k + 1|k)P yy,rr (k + 1|k) -1

[0132] Posteriori error covariance:

[0133]

[0134] Optimal estimate:

[0135]

[0136] Embodiment 3

[0137] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium, which is used to store computer instructions. When the computer instructions are executed by a processor, the train operation state estimation method based on the high-order extended Kalman filter considering noise correlation as described above is implemented. The method includes:

[0138] Obtain the train operation state data at the current moment, including the running speed, position, and environmental data under the current operation state;

[0139] Based on obtaining the operation status data of the train at the current moment, a prediction model of a high-order extended Kalman filter considering noise correlation is used to predict the dynamic state of the train; among them, the high-order extended Kalman filter considering noise correlation linearizes the nonlinear state equation to high-order terms through Taylor expansion, and then substitutes it into the measurement equation to obtain the standard form of least squares, so as to obtain high-order dynamic characteristics;

[0140] Update the state in combination with the operation status data measured in real time; among them, the predicted state and the real-time operation status data are weighted and fused through the dynamic calculation of the Kalman gain, and the gain coefficient optimally integrates the two with the least mean square error criterion by balancing the confidence of the prediction model and the measurement noise.

[0141] Embodiment 4

[0142] 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 executable by the processor, and the processor calls the program instructions to execute the train operation state estimation method based on the high-order extended Kalman filter considering noise correlation as described above. This method includes:

[0143] Obtain the operation status data of the train at the current moment, including the running speed, position, and environmental data under the current operation state;

[0144] Based on obtaining the operation status data of the train at the current moment, a prediction model of a high-order extended Kalman filter considering noise correlation is used to predict the dynamic state of the train; among them, the high-order extended Kalman filter considering noise correlation linearizes the nonlinear state equation to high-order terms through Taylor expansion, and then substitutes it into the measurement equation to obtain the standard form of least squares, so as to obtain high-order dynamic characteristics;

[0145] Update the state in combination with the operation status data measured in real time; among them, the predicted state and the real-time operation status data are weighted and fused through the dynamic calculation of the Kalman gain, and the gain coefficient optimally integrates the two with the least mean square error criterion by balancing the confidence of the prediction model and the measurement noise.

[0146] Embodiment 5

[0147] This Embodiment 5 provides an electronic device, including: a processor, a memory, and a computer program; among them, 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 high-order extended Kalman filter considering noise correlation as described above. This method includes:

[0148] Obtain the operation status data of the train at the current moment, including the running speed, position, and environmental data under the current operation status;

[0149] Based on the obtained operation status data of the train at the current moment, use the prediction model of the high-order extended Kalman filter considering noise correlation to predict the dynamic state of the train; among them, the high-order extended Kalman filter considering noise correlation linearizes the nonlinear state equation to high-order terms through the Taylor expansion, and then substitutes it into the measurement equation to obtain the standard form of the least squares, so as to obtain the high-order dynamic characteristics;

[0150] Update the state by combining the operation status data measured in real time; among them, the predicted state and the operation status data in real time are weighted and fused through the dynamic calculation of the Kalman gain, and the gain coefficient optimally integrates the two with the minimum mean square error criterion by balancing the confidence of the prediction model and the measurement noise.

[0151] In summary, the high-precision extended Kalman filter (CIEKF) considering noise correlation of the present invention proposes a new extended Kalman filter method, utilizes the high-order terms omitted in the traditional EKF filter, and further considers the correlation between the high-order terms. It solves the problem of insufficient accuracy of the traditional EKF in a strongly nonlinear system and significantly improves the accuracy of system state estimation. The sliding window error criterion is introduced for real-time model discrimination, and a train operation mode discrimination method based on the sliding window error is proposed, which can judge the operation mode of the train in real time and dynamically adjust the filtering parameters. This criterion can quickly switch the filtering model to ensure that the filter can maintain high accuracy in different operation modes. Based on the filtering improvement of Gaussian noise, the correlation between the processed state noise and the measurement noise is considered, and a filtering algorithm with higher accuracy and robustness is proposed. Through theoretical derivation and simulation experiments, it is verified that when considering noise correlation, the performance of the filter is significantly better than traditional methods (EKF, UKF, PF, etc.). The identification of high-order characteristic statistics is carried out during the filtering process, and the high-order characteristic statistics of the prediction estimation error (such as the error characteristics of the second-order and third-order expansions) are solved step by step, and the accuracy improvement effect is verified by combining the actual model. A variety of model validations are carried out for different scenarios (such as constant speed - adhesion braking, air braking, acceleration, etc.) to prove the effectiveness of high-order characteristic identification. A comprehensive performance index based on the error covariance matrix is designed to evaluate the estimation accuracy of the filter and the system robustness. Through this index, the advantages and disadvantages of different filtering methods can be more intuitively compared.

[0152] 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 storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0153] 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 flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams, 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 generate means for implementing the functions specified in Figure 1 one or more of the flows Figure 1 or blocks or the combination of blocks.

[0154] 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 generate a manufactured article including instruction means that implement the functions specified in Figure 1 one or more of the flows Figure 1 or blocks or the combination of blocks.

[0155] 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 Figure 1 one or more of the flows Figure 1 or blocks or the combination of blocks.

[0156] Although the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation on 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 running state estimation method based on a high-order extended Kalman filter considering noise correlation, characterized in that: include: Obtain the current running status data of the train, including running speed, position and environmental data under the current running status; Based on the acquired running status data of the train at the current moment, the prediction model of the high-order extended Kalman filter considering noise correlation is used to predict the dynamic state of the train; wherein, the high-order extended Kalman filter considering noise correlation linearizes the nonlinear state equation to high-order terms through Taylor expansion, and then substitutes it into the measurement equation to obtain the standard form of least squares, thereby obtaining high-order dynamic characteristics; The state is updated in combination with the real-time measured operating state data; the predicted state is weightedly fused with the real-time operating state data through dynamic calculation of the Kalman gain, and the gain coefficient optimally integrates the two by balancing the confidence of the prediction model and the measurement noise with the minimum mean square error criterion.

2. The train running state estimation method based on the high-order extended Kalman filter considering noise correlation according to claim 1 is characterized in that: The mathematical model of train operation includes state equations and measurement equations, which are used to describe the relationship between the dynamic state of the train and the sensor measurement values; the state equation is used to represent the evolution process of the train speed, position and acceleration state, and the measurement equation describes the nonlinear mapping relationship between the measurement value and the state variable.

3. The train running state estimation method based on the high-order extended Kalman filter considering noise correlation according to claim 2 is characterized in that: The train speed state estimation is described by the following model: Where x(k) represents the train speed, y(k+1) represents the speed measurement value; f(·) is a nonlinear continuously differentiable function, and H(k+1) is a linear function; w(k) and v(k+1) are the state noise and measurement noise, respectively, and their error covariance matrices are Q(k) and R(k+1), respectively. The error covariance matrix of the initial state estimation is P(0); the initial state x(0) is determined by the initial speed, position, and acceleration of the train.

4. The train running state estimation method based on a high-order extended Kalman filter considering noise correlation according to claim 1 is characterized in that: The state model of vehicle speed is expanded to a higher order by using high-order Taylor expansion to model the train state. The high-order information in the state equation used to model the train state is obtained by using the measurement equation, that is, the high-order extended Kalman filter prediction related to noise is used to obtain high-order expansion information.

5. The train running state estimation method based on a high-order extended Kalman filter considering noise correlation according to claim 3 is characterized in that: The velocity is estimated based on the obtained high-order information to obtain the posterior estimate:

6. The train running state estimation method based on the high-order extended Kalman filter considering noise correlation according to claim 5 is characterized in that: Updated error covariance matrix:

7. A train running state estimation system based on a high-order extended Kalman filter considering noise correlation, characterized in that: include: The acquisition module is used to obtain the running status data of the train at the current moment, including the running speed, position and environmental data under the current running state; A prediction module is used to predict the dynamic state of the train based on the acquired running state data of the train at the current moment, using a prediction model of a high-order extended Kalman filter that considers noise correlation; wherein the high-order extended Kalman filter that considers noise correlation linearizes the nonlinear state equation to a high-order term through a Taylor expansion, and then substitutes it into the measurement equation to obtain the standard form of the least squares, thereby obtaining high-order dynamic characteristics; The update module is used to update the state in combination with the real-time measured operating state data; wherein, the predicted state and the real-time operating state data are weightedly fused through the dynamic calculation of the Kalman gain, and the gain coefficient is used to balance the confidence of the prediction model and the measurement noise, and optimally integrate the two with the minimum mean square error criterion.

8. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, the train operation state estimation method based on the high-order extended Kalman filter considering noise correlation as described in any one of claims 1-6 is implemented.

9. A computer device, characterized in that: It includes a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the train operation state estimation method based on the high-order extended Kalman filter considering noise correlation as described in any one of claims 1-6.

10. An electronic device, characterized in that: include: A processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes instructions for implementing a train operation state estimation method based on a high-order extended Kalman filter considering noise correlation as described in any one of claims 1 to 6.

Images