Virtual marshalling train interval prediction method and system based on high-order extended Kalman smoother

Abstract

The invention provides a virtual marshalling train interval prediction method and system based on a high-order extended Kalman smoother, and belongs to the technical field of train operation management, real-time state data of a train in marshalling and historical state data of a leading train are obtained, and the state data comprise speed data, position data and acceleration data; on the basis of the obtained real-time state data of the vehicle and the historical state data of the leading vehicle, a high-order extended Kalman filter is adopted to predict the dynamic state of the vehicle; and based on the state after smooth optimization, dynamically calculating the train spacing based on the difference value of the position states of the leading train and the following train. According to the method, the real-time dynamic tracking of the train state and the high-precision estimation of the distance between the train and the head train are realized, and through the definition of the high-order hidden variables and the pseudo-linearization representation of the high-order hidden variables, the description capability of the nonlinear characteristic of the train system is improved, the calculation complexity of high-order expansion is reduced, and the robustness and the stability of the virtual coupling train system are ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of train operation management, and in particular to a method and system for predicting the interval between virtual marshaled trains based on a high-order extended Kalman smoother. Background Art

[0002] The Kalman filter series of methods have been widely used. The standard Kalman filter (KF) can solve many linear problems and is a recursive filter used to estimate the state of a dynamic system. It is based on the Bayesian filtering method with the minimum mean square error criterion. By combining the system's prior model and measurement data, it minimizes the mean square value of the estimation error and realizes real-time estimation of the system state. The core of KF lies in the two-stage cycle: prediction and update. In the prediction stage, the state transition equation of the system is used to predict the current state; in the update stage, the prediction result is corrected by combining the new measurement data. This method assumes that both the system noise and the measurement noise are Gaussian white noise, and the system model is linear.

[0003] The Extended Kalman Filter (EKF) is an extension of the standard Kalman filter and is used to handle state estimation of nonlinear systems. The EKF linearizes the state transfer equation and measurement equation of the nonlinear system by performing a first-order Taylor expansion, and then applies them to the framework of the Kalman filter for estimation. Specifically, the EKF calculates the Jacobian matrix of the state and observation equations at each moment to approximately describe the linear characteristics of the system. Jin et al. proposed a filtering method based on Gaussian theory and theoretical EKF to estimate the state and parameters of nonlinear systems, and applied it to the high-speed train control model.

[0004] Unscented Kalman Filter (UKF) is a filtering method for nonlinear systems that aims to overcome the limitations of EKF linearization. UKF uses unscented transformation to directly propagate nonlinear functions by selecting a set of deterministic sampling points called sigma points in the state space. These sigma points are used to re-estimate the state mean and covariance after nonlinear transformation to capture nonlinear characteristics. UKF does not need to calculate the Jacobian matrix, avoiding bias errors in the linearization process. Second-order unscented Kalman filters have been shown to have higher estimation accuracy and stability for nonlinear systems. Jayasin et al. used UKF as a predictive control tool for trains to calibrate train speed and position measurements.

[0005] Centralized Kalman Filter (CKF) is mainly used in multi-sensor data fusion scenarios. In CKF, the data of all sensors will be processed centrally to provide a global estimate of the system state. CKF incorporates the sensor's observation data and noise characteristics into a unified filtering framework and uses the recursive characteristics of Kalman filtering to achieve the optimal estimate of the system state.

[0006] Particle filter (PF) is a nonlinear filtering algorithm based on the Monte Carlo method, which is designed for state estimation technology. PF represents the probability distribution of the state by using a set of weighted particles, each particle corresponding to a possible system state. At each time step, the particles are sampled according to the state transition of the system, and then the weights of the particles are updated according to the observed data to reflect the degree of match with the real state. Particle filters are suitable for high-dimensional and non-Gaussian systems in the scenario of complex nonlinear systems. Similarly, Jin et al. proposed a train state estimation method based on a multi-sensor parallel filtering method.

[0007] The main idea of ​​the high-order extended Kalman filter (HEKF) is to use the simplified or ignored high-order information in the original system to enhance the filter's ability to overcome high-order nonlinearity in a reasonable way. For example, Sun et al. proposed corresponding HEKF design methods for different forms of nonlinear systems, treating high-order variables as independent pseudo-linear variables. The goal is to establish a dynamic pseudo-linear extended system to minimize the gap with the nonlinearity of the original system, thereby developing HEKF. In response to the nonlinear problem of the strong tracking filter (STF), a high-order strong tracking filter (HSTF) was proposed; in response to the nonlinear problem of the non-Gaussian maximum correlation entropy Kalman filter (MCKF), a maximum correlation entropy high-order extended Kalman filter (MCHEKF) was also proposed. However, under the requirements of VCTs, the state estimation of a single train is transformed into the state estimation of multiple trains, and the dynamic distance estimation between the lead train and the following train is crucial. Since there is always a time-space order relationship between the lead train and the following train, the historical state sequence and measurement sequence of the lead train are always more than the data of the following train. If the operation requirements are consistent, these data can be regarded as the future state and measurement of the following train. Therefore, this phenomenon conforms to the smoothing process of KF. That is, by continuously optimizing the historical state using future measurements, the optimal historical state estimate can be obtained. The optimal historical state estimate refers to the optimal historical state of the leading car obtained by the following car through the smoothing method, thereby solving the problem of inaccurate estimation of the filter caused by the operation of the nonlinear train system and environmental noise. In the end, the following car can obtain a more reasonable and accurate vehicle distance. Smoothers are divided into three types: fixed point smoothing, fixed delay smoothing, and fixed interval smoothing. Xiao et al. used these three Kalman smoothers to solve the multiplicative noise and data loss problems of wireless sensor systems in nonlinear dynamic systems. Smoothers can solve strong nonlinearity and noise problems in a delayed manner. At present, there are two different derivation methods for smoothing technology. One is based on the orthogonal theorem and information analysis of the Kalman smoothing algorithm, and the other is based on the Bayesian process of the Rauch-Tung-Striebel (RTS) smoothing algorithm. Geng et al. proposed an algorithm for calculating the fixed interval smoothed state estimate of a linear time-varying Gaussian random system, established sufficient conditions for the existence of Gaussian smoothing density, and was not restricted by existing algorithms, thereby improving versatility and estimation accuracy. Liu et al. combined Kalman filter and smoother with machine learning technology for online trajectory prediction and offline trajectory adjustment, thereby inferring the dynamic information of target motion. Yang et al. proposed a dual filter smoothing method (MRTFS) based on maximum entropy. For nonlinear systems with non-Gaussian noise, the estimation accuracy was improved by fusing the smoothing results without initial condition constraints, which was better than traditional methods such as EKF and RTS. Akhtar et al. proposed a smoothing algorithm based on UKF. Since the Jacobian matrix of UKF is not applicable, RTS smoothing based on Bayesian smoothing is adopted.Bruno et al. also verified the effectiveness of the smoothing algorithm in flight path reconstruction.

[0008] Insufficient nonlinear processing capability and accuracy Existing methods (such as EKF, UKF, and CKF) have limitations when dealing with strongly nonlinear systems. EKF linearizes the system through a first-order Taylor expansion, ignoring high-order nonlinear information, resulting in significant truncation errors and insufficient accuracy. Although UKF and CKF improve nonlinear problems through traceless transformation and spherical radial sampling, the sampling points are sparse and cannot fully capture the dynamic characteristics of complex systems. There are also weight selection problems and stability risks. Although particle filters (PFs) can handle complex nonlinear problems, they require a large number of particles, have high computational complexity, and suffer from serious particle degradation, which affects the estimation efficiency and stability of the system. Large dynamic distance estimation error and insufficient robustness In virtual coupled trains (VCTs), dynamic distance estimation between the lead train and the following train is crucial. However, existing technologies fail to fully utilize historical and future state information when dealing with the time-space order relationship in dynamic train interactions, resulting in large dynamic distance estimation errors. At the same time, environmental noise and data loss (such as multiplicative noise and random packet loss) significantly affect the robustness of existing filtering methods, making the estimation results not stable and reliable under complex working conditions. Insufficient computational efficiency and real-time performance Existing high-precision filtering methods (such as PF, UKF) often require high computing resources and are difficult to meet real-time requirements. Especially in multi-train collaborative systems, as the state dimension increases, the computational complexity increases exponentially. In addition, the existing methods fail to effectively balance the computational complexity and accuracy in smooth optimization, and are difficult to meet the application requirements of large-scale systems. Summary of the invention

[0009] The object of the present invention is to provide a method and system for predicting the interval between virtual train formations based on a high-order extended Kalman smoother, so as to solve at least one technical problem existing in the above-mentioned background technology.

[0010] In order to achieve the above object, the present invention adopts the following technical solutions:

[0011] In a first aspect, the present invention provides a method for predicting the interval between virtual marshaling trains based on a high-order extended Kalman smoother, comprising:

[0012] Acquire the real-time status data of the accompanying train in the marshaling and the historical status data of the leading train, wherein the status data includes speed data, position data and acceleration data;

[0013] Based on the acquired real-time status data of the accompanying vehicle and the historical status data of the leading vehicle, a high-order extended Kalman filter is used to predict the dynamic state of the accompanying vehicle; wherein the state is updated in combination with the real-time measured state data; wherein the predicted value is fused with the measured value by calculating the Kalman gain to minimize the prediction error and adjust the error covariance after the state update; a high-order extended Kalman smoother is used to smooth the historical state; wherein the historical state of the accompanying vehicle is backward optimized by using the future measurement data of the leading vehicle;

[0014] Based on the smoothed optimized state, the train spacing is dynamically calculated based on the position state difference between the leading train and the following train.

[0015] In a second aspect, the present invention provides a virtual marshaling train interval prediction system based on a high-order extended Kalman smoother, comprising:

[0016] An acquisition module is used to acquire real-time status data of the accompanying trains in the marshaling and historical status data of the leading trains, wherein the status data includes speed data, position data and acceleration data;

[0017] A prediction module is used to predict the dynamic state of the accompanying vehicle based on the acquired real-time state data of the accompanying vehicle and the historical state data of the leading vehicle by using a high-order extended Kalman filter; wherein the state is updated in combination with the real-time measured state data; wherein the predicted value is fused with the measured value by calculating the Kalman gain to minimize the prediction error and adjust the error covariance after the state update; and the historical state is smoothed by using a high-order extended Kalman smoother; wherein the historical state of the accompanying vehicle is backward optimized by using the future measurement data of the leading vehicle;

[0018] The calculation module is used to calculate the train spacing based on the smoothed optimized state; and dynamically calculate the train spacing based on the position state difference between the leading train and the following train.

[0019] In a third aspect, the present invention provides a non-transitory computer-readable storage medium, which is used to store computer instructions. When the computer instructions are executed by a processor, the virtual train-to-train prediction method based on a high-order extended Kalman smoother as described in the first aspect is implemented.

[0020] In a fourth aspect, the present invention provides a computer device comprising a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the virtual train interval prediction method based on the high-order extended Kalman smoother as described in the first aspect.

[0021] In a fifth aspect, the present invention provides an electronic device, comprising: a processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes instructions for implementing the virtual train interval prediction method based on the high-order extended Kalman smoother as described in the first aspect.

[0022] Beneficial effects of the present invention: The high-precision dynamic estimation framework combining filtering and smoothing of the present invention breaks through the limitation that the existing methods are only applicable to a single filter or a fixed model. By designing the collaborative working mechanism of the high-order extended Kalman filter (HEKF) and the smoother, the real-time dynamic tracking of the train state and the high-precision estimation of the head car spacing are realized, which significantly improves the applicability and estimation accuracy of the complex nonlinear system. At the same time, the three smoothing methods of fixed point, fixed lag and smoothing interval proposed can be dynamically selected according to the train operation requirements, taking into account the real-time and accuracy requirements. Compared with the traditional linear state-based filtering method, the present invention not only significantly improves the description ability of the nonlinear characteristics of the train system through the definition of high-order hidden variables and their pseudo-linear representation, but also effectively reduces the computational complexity of the high-order expansion. In addition, the dynamic spacing error correction mechanism and efficient matrix recursive algorithm of the present invention further optimize the safety and energy efficiency of train operation, and ensure the robustness and stability of the virtual coupled train system.

[0023] Additional advantages of the present invention will be more clearly given in the following description or learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0025] Figure 1 This is a schematic diagram of the multidimensional Taylor network structure described in an embodiment of the present invention.

[0026] Figure 2 It is a schematic diagram of the principle of a fixed-point high-order extended Kalman smoother for the train running state according to an embodiment of the present invention.

[0027] Figure 3 It is a schematic diagram of the principle of a fixed-lag high-order extended Kalman smoother for the train running state according to an embodiment of the present invention.

[0028] Figure 4It is a schematic diagram of the principle of a fixed-interval high-order extended Kalman smoother for train running status according to an embodiment of the present invention.

[0029] Figure 5 A schematic diagram of dynamic interval estimation and interval error boundary of virtual coupled trains according to an embodiment of the present invention. DETAILED DESCRIPTION

[0030] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below by the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

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

[0032] It should also be understood that terms, such as those defined in commonly used dictionaries, should be understood to have a meaning consistent with that in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless as defined herein.

[0033] Those skilled in the art will appreciate that, unless otherwise stated, the singular forms "a", "an", "said" and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements and / or groups thereof.

[0034] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. Different embodiments or examples described in this specification and features of different embodiments or examples may be combined and combined by those skilled in the art without contradiction.

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

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

[0037] The present invention provides a virtual marshaling train interval prediction method and system based on a high-order extended Kalman smoother. The proposed high-order extended Kalman filter combined with dynamic smoothing method (HEKF-HEKS) shows significant advantages. First, by introducing nonlinear modeling of high-order Taylor expansion, the truncation error is greatly reduced, so that the filter can capture the high-order nonlinear characteristics of the complex system, and combined with dynamic smoothing technology, the relationship between the historical state and the future measurement is further optimized, thereby significantly improving the accuracy and robustness of dynamic vehicle distance estimation. Second, by combining fixed point smoothing, fixed delay smoothing and fixed interval smoothing, the time-space order relationship between the historical state sequence and the train system is optimized by future measurements, thereby solving the problem of inaccurate estimation caused by data loss and environmental noise. Third, by reasonably selecting the weights and parameters of the high-order building blocks, the computational complexity is effectively reduced. Compared with complex methods such as particle filtering, the dependence on a large number of samples is reduced, and the real-time and stability of the system are improved. Especially in the multi-train collaborative scenario, this method can effectively adapt to the significant demand for an efficient smoothing-filtering integrated mechanism, making it suitable for real-time application scenarios of large-scale systems.

[0038] In view of the complex and strong nonlinear characteristics of the dynamic running state of trains in virtual coupled train systems, the present invention proposes an accurate dynamic estimation method for inter-vehicle spacing through the collaborative modeling and estimation of high-order extended Kalman filter (HEKF) and high-order extended Kalman smoother (HEKS). This method can capture the precise spacing state of trains under different operating conditions in real time, ensure that the accuracy of train spacing estimation meets the requirements of efficient and safe operation, and achieve high-precision estimation even if the running state of trains continues to change in a dynamic environment. In the virtual coupled train operation environment, train operation data is often affected by complex noise interference (such as environmental noise, measurement noise) and data loss during communication. In view of these problems, the high-order extended Kalman smoother (HEKS) proposed in the present invention combines future measurement information with historical status, optimizes the dynamic estimation process of train status, and greatly improves the estimation stability and robustness of the system under noise and incomplete data conditions, thereby providing technical guarantee for the reliable control of train spacing. By introducing high-order extended modeling and filtering methods, the present invention significantly reduces the problem of high computational complexity in traditional methods while achieving high-precision state estimation. The high-order expansion method of Taylor series is used to optimize the computational efficiency of train state estimation, so that it can meet the high real-time and high-efficiency operation requirements of the virtual coupled train system in a practical environment with limited resources, and achieve the best balance between estimation accuracy and computational complexity. This not only improves the engineering applicability of the system, but also provides reliable support for large-scale train operation optimization.

[0039] Example 1

[0040] In this embodiment 1, a virtual marshaling train interval prediction system based on a high-order extended Kalman smoother is first provided, including: an acquisition module, which is used to acquire the real-time state data of the accompanying car in the marshaling and the historical state data of the leading car, and the state data includes speed data, position data and acceleration data. A prediction module is used to use a high-order extended Kalman filter to predict the dynamic state of the accompanying car based on the acquired real-time state data of the accompanying car and the historical state data of the leading car; wherein the state is updated in combination with the real-time measured state data; wherein the predicted value and the measured value are fused by calculating the Kalman gain to minimize the prediction error and adjust the error covariance after the state update; a high-order extended Kalman smoother is used to smooth the historical state; wherein the historical state of the accompanying car is backward optimized by using the future measurement data of the leading car. A calculation module is used to dynamically calculate the train spacing based on the state after smoothing optimization and the position state difference between the leading car and the accompanying car.

[0041] In this embodiment, the above-mentioned system is used to implement a virtual marshaling train interval prediction method based on a high-order extended Kalman smoother, including: obtaining real-time status data of the accompanying car in the marshaling and historical status data of the leading car, wherein the status data includes speed data, position data and acceleration data; based on the acquired real-time status data of the accompanying car and the historical status data of the leading car, a high-order extended Kalman filter is used to predict the dynamic state of the accompanying car; wherein the state is updated in combination with the real-time measured state data; wherein the predicted value and the measured value are fused by calculating the Kalman gain to minimize the prediction error and adjust the error covariance after the state update; a high-order extended Kalman smoother is used to smooth the historical state; wherein the historical state of the accompanying car is backward optimized by using the future measurement data of the leading car; based on the state after smoothing optimization, the train spacing is dynamically calculated based on the position state difference between the leading car and the accompanying car.

[0042] The overall process of train state estimation and train spacing prediction can be summarized as a complete set of operations from system initialization, data acquisition to state estimation and optimization. High-precision prediction of train running status and dynamic spacing estimation can be achieved through high-order extended Kalman filter (HEKF) and high-order extended Kalman smoother (HEKS).

[0043] First, a mathematical model of train operation is established during the system initialization phase, including state equations and measurement equations to describe the relationship between the dynamic state of the train and the sensor measurements. The state equations are used to represent the evolution of train states such as speed, position, and acceleration, while the measurement equations describe the nonlinear mapping relationship between sensor measurements and state variables. At this stage, 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). In addition, the initial state v(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.

[0044] Data acquisition is the core foundation of train state estimation. The system obtains the real-time speed, acceleration and position data of the train through various sensors on the train, such as wheel sensors, Doppler radars, inertial measurement units (IMUs), etc. At the same time, the historical status information of the lead train, including speed, position and acceleration, is obtained through vehicle-to-vehicle communication (V2V). In addition, environmental data such as track curvature, slope and weather information can also be collected, which may affect the operating status of the train. In order to ensure data quality, the system will pre-process the collected data, including denoising, cleaning outliers, completing missing data, and normalizing data of different dimensions. These operations can effectively improve the reliability of the data and the consistency of the model input.

[0045] In the high-order state prediction stage, a high-order extended Kalman filter (HEKF) is used to predict the dynamic state of the train. HEKF linearizes the nonlinear state equation to high-order terms through Taylor expansion, capturing the high-order dynamic characteristics ignored in traditional methods. By using the historical state data of the lead car and the real-time measurement data of the follower car, the system predicts the future state of the follower car and calculates the error covariance to reflect the uncertainty of the predicted value. This high-order modeling method can significantly reduce the error caused by nonlinear truncation and improve the accuracy of state prediction.

[0046] After the prediction is completed, the system updates the state in combination with the real-time measurement data. At this stage, the predicted value is fused with the sensor measurement value by calculating the Kalman gain to minimize the prediction error. The error covariance after the state update is also adjusted synchronously to reflect the corrected uncertainty. This step corrects the predicted value with real-time measurement data to ensure that the model can closely track the actual operating status of the train.

[0047] To further optimize the state estimation, the system uses a high-order extended Kalman smoother (HEKS) to smooth the historical state. HEKS backward optimizes the historical state of the following vehicle by using the future measurement data of the lead vehicle. The smoother can combine historical, current, and future information to significantly improve the robustness and accuracy of the state estimation. This is particularly important for solving the problem of inaccurate estimation caused by data loss or noise.

[0048] After completing the state estimation, the system calculates the train spacing by smoothing the optimized state. The dynamic calculation of the spacing is based on the position state difference between the lead train and the following train. The prediction results can provide real-time information on the spacing between trains and compare it with the safety threshold. If the spacing is lower than the safety threshold, the system will issue a warning signal to remind the dispatcher or driver to take measures.

[0049] In this embodiment, the state of the virtual coupled train is described by the following model:

[0050]

[0051] in, Indicates the train status (speed), z (k+1) represents the sensor (speed) measurement value; the subscript (1) represents the original state variable, which is used to distinguish the hidden state variable introduced later. f(·) and h(·) are nonlinear continuous differentiable functions; and Y (k+1) are state noise and measurement noise, respectively, both are zero-mean Gaussian white noise. The error covariance matrices are R (k+1) , the error covariance matrix of the initial state estimate is

[0052] Assuming that the measurement sequence of the speed sensor has been obtained according to formula (2), the following formula can be obtained:

[0053]

[0054] In this embodiment, a high-order extended Kalman filter (HEKF) is designed. The extended Kalman filter (EKF) is based on a first-order Taylor expansion, and this embodiment derives a high-order extended Kalman filter (HEKF) expanded to the rth order.

[0055] According to formula (1), exist Where to proceed Figure 1 The multidimensional Taylor series expansion shown is as follows:

[0056]

[0057] Assumptions as well as The formula is rewritten as:

[0058]

[0059] Among them, 0<l<r represents the order of Taylor expansion, l j Representation variables The specific power of are the coefficients of the Taylor series:

[0060]

[0061] By transforming the state estimation problem from Convert to error variable The estimation problem can effectively avoid the complex calculation caused by polynomial expansion.

[0062] Define a set of hidden variables:

[0063]

[0064] Among them, n l is the total number of l-order hidden variables. The formula can be rewritten in vector form:

[0065]

[0066] Furthermore, the state update formula can be rewritten in pseudo-linear form:

[0067]

[0068] in,

[0069]

[0070] For each hidden state variable The linear dynamic model with all variables needs to establish the following relationship:

[0071]

[0072] Among them, A (l,u) is the weight matrix. To identify this matrix, a multidimensional Taylor network (MTN) is required. The structure of MTN is as follows: Figure 1 shown.

[0073] Assume that the input state vector of MTN is The output state vector is Its form is as follows:

[0074]

[0075] Each input state vector exists in the form of a weighted sum in the intermediate layer, where the weight variable between the output layer and the intermediate layer is At the same time, a minimum error objective function is needed to identify The formula is as follows:

[0076]

[0077] Formula 14 can be derived from Formula 13, as follows:

[0078]

[0079] in,

[0080]

[0081] To model the error, its statistical characteristics can be modeled as follows

[0082]

[0083] about According to formula 14, the simple least squares method or gradient descent method can be used to solve it. When there is no prior information, and A(k|k) (l,u) is consistent, A(k|k) (l,u) It can be assumed that:

[0084]

[0085] The extended high-order hidden state variables need to be properly represented in the state space to properly utilize their high-order information. The linear matrix form of the extended state variables in the full space is shown below:

[0086]

[0087] in

[0088]

[0089] By combining formula 3, we can get

[0090]

[0091] The initial estimation error covariance matrix of the extended high-order state hidden variables is

[0092]

[0093] Similar to Formula 5, The multidimensional Taylor series expansion of is shown in formula 19

[0094]

[0095] Assumptions and but Can be expressed as

[0096]

[0097] Similar to the pseudo-linearization process of the state model, is the prediction error All l-order latent variables of is the corresponding weight, and there is

[0098]

[0099] Combined with Definition 1, Formula 2 can be expressed as

[0100]

[0101] Furthermore, Equation 2 has the following linear expression:

[0102]

[0103] in,

[0104]

[0105] The i-th component of the measurement model can be expressed according to Formula 23, and Formula 24 is the expression of the entire measurement model. Then, the linearized matrix form of Formula 2 is as follows:

[0106]

[0107] in

[0108]

[0109] In order to realize the linear representation of nonlinear models, the concept of full space is introduced here. The full space is defined as the original variables and hidden variables The space composed of two terms Tr(f(ξ (k|k) ) and Tr(h(ξ (k+1|k) ) contain unknown terms, and they themselves are high-order infinitesimals and Referring to the traditional extended Kalman filter (EKF), equations 16 and 25 can be simplified to:

[0110]

[0111] To formally describe the design of a high-order extended Kalman filter, it is necessary to assume that Y (k+1) and Some statistical properties of:

[0112]

[0113] Assume that it is known Then we can deduce recursively by induction that

[0114]

[0115] The initial estimation error covariance matrix of the high-order extended system is denoted as P0:

[0116]

[0117] in By deriving Equation 31, all necessary conditions for filter design based on Equations 26 and 27 can be obtained:

[0118]

[0119] The high-order extended Kalman filter (HEKF) proposed in this embodiment is applicable to systems where both the state and the measurement are nonlinear, has wider applicability, and more accurately propagates high-order variables by using polynomial nonlinear transformation (MTN), solving the problem that the linear state of the high-speed train positioning system with linear state and nonlinear measurement does not consider the pseudo-linear propagation in the measurement. In addition, by establishing a high-order expansion of the state error, high-order information is provided, while avoiding redundant derivative calculations.

[0120] In this embodiment, for the development and integration of a high-order extended Kalman smoother (HEKS), a bidirectional filtering structure is required to obtain a smoothed state estimate of the leading vehicle in a virtual coupled train system (VCTs). During the normal operation of the high-order extended Kalman forward filter, time information can be collected. and At the same time, smooth estimation can be achieved in the reverse smoothing process.

[0121] For a high-order extended Kalman forward filter

[0122]

[0123] According to formula 26, the one-step forward state prediction of the preceding vehicle can be calculated:

[0124]

[0125] Then the state prediction estimation error can be obtained:

[0126]

[0127] The covariance matrix of the forecast estimation error can be obtained

[0128]

[0129] According to Formula 27, the one-step forward measurement prediction of the preceding vehicle can be calculated,

[0130]

[0131] Then the measurement prediction estimation error can be obtained,

[0132]

[0133] A high-order extended Kalman forward filter for virtual coupled train systems (VCTs) is designed. The formula is as follows

[0134]

[0135] Where K (k+1) is the optimal Kalman gain matrix to be determined.

[0136] Orthogonality Principle: If the dot product of two vectors is zero, then they are orthogonal.

[0137] According to LM.1, the Kalman gain matrix K can be solved (k+1)

[0138]

[0139] Substituting equations 27 and 37 into equation 38, we obtain equation 39.

[0140]

[0141] The error covariance matrix of will be updated in Equation 40.

[0142]

[0143] The high-order extended Kalman filter (HEKF) obtained by orthogonality theorem and innovation analysis is a necessary step for its smoother. It should be noted that the HEKF state based on Taylor series is expressed as $\hat\tilde v_{(\cdot)}^+$, which is the extended expansion error. The real-time design of the forward filter has been completed, which means that in virtual coupled trains (VCTs), each train can estimate its own state in real time. In order to achieve dynamic distance estimation and distance error margin between VCTs, a smoother needs to be introduced. It is the combination of filter and smoother that makes high-precision distance estimation of the entire VCTs possible.

[0144] At present, three smoothing methods have been developed based on the smoothing idea: fixed point smoothing, fixed lag smoothing and fixed interval smoothing. The difference between them lies in the different sizes of the future measurement sequences used, which leads to different complexity of the iterative algorithm. The fixed point smoothing algorithm uses all future measurement sequences to smooth a point; the fixed lag smoothing algorithm uses the future measurement sequences within the fixed lag interval to smooth the historical state; by properly controlling the length of the lag interval, the error covariance of the smoother within the lag interval converges, which can maximize the smoothing accuracy. The fixed interval smoothing algorithm uses all subsequent future measurements to smooth each historical state. This algorithm is based on the intervalization mode of fixed point smoothing, and the future measurement sequences used will gradually decrease.

[0145] like Figure 2 As shown, the fixed-point high-order extended Kalman smoother is:

[0146]

[0147] In a given measurement sequence middle, Indicates at time The optimal smoothing estimate of is expressed as follows:

[0148]

[0149] Based on the definition and new information analysis, the The fixed point smoother for is designed as follows:

[0150]

[0151] where Θ (·) is the optimal Kalman smoothing gain matrix. According to Lemma 1, we can get Formula 42 and further solve Θ (·) .

[0152]

[0153] in

[0154]

[0155] After derivation, the fixed point Kalman smoother is obtained:

[0156]

[0157] in

[0158] like Figure 3 As shown, for a fixed lag high-order extended Kalman smoother:

[0159]

[0160] in and t=l,l+1,l+2,…,k; t l =tl

[0161] like Figure 4 As shown, for a fixed interval high-order extended Kalman smoother:

[0162]

[0163] in

[0164] If the three smoothing methods have enough future measurement sequences to smooth the historical states, their final smoothing effects are the same, which means that the smoothing effect is limited. Through the recursive error covariance of future states, the error information from future states becomes smaller and smaller. This is mainly manifested in the convergence of the error covariance to the minimum value. Because the smoothed states are usually correlated in the time series, the errors of the finite future sequence cannot violate the state transition law. In other words, the determinism and stability of the model determine that the smoothed error must converge.

[0165] When the operating conditions of the virtual coupled trains are consistent, L headway represents the dynamic interval estimation between the preceding train and the following train, L headwayerrorrepresents the error margin of the dynamic interval estimation between the preceding train and the following train. In order to consider the safety of the train, the error margin must be greater than zero. In the case of inconsistent operating conditions of the virtual coupled trains or the virtual coupling is reconstructed, L headway and L headwayerror represents the reference interval estimate and reference error of the subsequent train

[0166] like Figure 5 As shown, in order to achieve dynamic interval estimation, it is necessary to make the best estimate of the train ahead and make real-time estimates of the following trains. By using a high-order extended smoother, a more accurate estimate can be obtained than a high-order extended Kalman filter. Therefore, the interval estimation is also the most accurate, and it can be obtained:

[0167]

[0168] in, and The difference is and The first-level state variable, L train is the length of the train ahead.

[0169] Example 2

[0170] This embodiment 2 provides a non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the virtual marshaling train interval prediction method based on a high-order extended Kalman smoother as described above is implemented. The method includes:

[0171] Acquire the real-time status data of the accompanying train in the marshaling and the historical status data of the leading train, wherein the status data includes speed data, position data and acceleration data;

[0172] Based on the acquired real-time status data of the accompanying vehicle and the historical status data of the leading vehicle, a high-order extended Kalman filter is used to predict the dynamic state of the accompanying vehicle; wherein the state is updated in combination with the real-time measured state data; wherein the predicted value is fused with the measured value by calculating the Kalman gain to minimize the prediction error and adjust the error covariance after the state update; a high-order extended Kalman smoother is used to smooth the historical state; wherein the historical state of the accompanying vehicle is backward optimized by using the future measurement data of the leading vehicle;

[0173] Based on the smoothed optimized state, the train spacing is dynamically calculated based on the position state difference between the leading train and the following train.

[0174] Example 3

[0175] This embodiment 3 provides a computer device, including a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, the processor calls the program instructions to execute the virtual marshaling train interval prediction method based on the high-order extended Kalman smoother as described above, the method comprising:

[0176] Acquire the real-time status data of the accompanying train in the marshaling and the historical status data of the leading train, wherein the status data includes speed data, position data and acceleration data;

[0177] Based on the acquired real-time status data of the accompanying vehicle and the historical status data of the leading vehicle, a high-order extended Kalman filter is used to predict the dynamic state of the accompanying vehicle; wherein the state is updated in combination with the real-time measured state data; wherein the predicted value is fused with the measured value by calculating the Kalman gain to minimize the prediction error and adjust the error covariance after the state update; a high-order extended Kalman smoother is used to smooth the historical state; wherein the historical state of the accompanying vehicle is backward optimized by using the future measurement data of the leading vehicle;

[0178] Based on the smoothed optimized state, the train spacing is dynamically calculated based on the position state difference between the leading train and the following train.

[0179] Example 4

[0180] This 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 is running, the processor executes the computer program stored in the memory, so that the electronic device executes instructions for implementing the virtual marshaling train interval prediction method based on the high-order extended Kalman smoother as described above, the method comprising:

[0181] Acquire the real-time status data of the accompanying train in the marshaling and the historical status data of the leading train, wherein the status data includes speed data, position data and acceleration data;

[0182] Based on the acquired real-time status data of the accompanying vehicle and the historical status data of the leading vehicle, a high-order extended Kalman filter is used to predict the dynamic state of the accompanying vehicle; wherein the state is updated in combination with the real-time measured state data; wherein the predicted value is fused with the measured value by calculating the Kalman gain to minimize the prediction error and adjust the error covariance after the state update; a high-order extended Kalman smoother is used to smooth the historical state; wherein the historical state of the accompanying vehicle is backward optimized by using the future measurement data of the leading vehicle;

[0183] Based on the smoothed optimized state, the train spacing is dynamically calculated based on the position state difference between the leading train and the following train.

[0184] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0185] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0186] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0187] These computer program instructions can also be loaded onto a computer or other programmable data processing device, and a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0188] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative work on the basis of the technical solution disclosed in the present invention should be included in the scope of protection of the present invention.

Claims

1. A virtual marshaling train interval prediction method based on a high-order extended Kalman smoother, characterized in that: include: Acquire the real-time status data of the accompanying train in the marshaling and the historical status data of the leading train, wherein the status data includes speed data, position data and acceleration data; Based on the acquired real-time status data of the accompanying vehicle and the historical status data of the leading vehicle, a high-order extended Kalman filter is used to predict the dynamic state of the accompanying vehicle; wherein the state is updated in combination with the real-time measured state data; wherein the predicted value is fused with the measured value by calculating the Kalman gain to minimize the prediction error and adjust the error covariance after the state update; a high-order extended Kalman smoother is used to smooth the historical state; wherein the historical state of the accompanying vehicle is backward optimized by using the future measurement data of the leading vehicle; Based on the smoothed optimized state, the train spacing is dynamically calculated based on the position state difference between the leading train and the following train.

2. The virtual marshaling train interval prediction method based on high-order extended Kalman smoother according to claim 1 is characterized in that: The state of the virtual coupled train is described by the following model: in, represents the train speed, z (k+1) represents the sensor speed measurement value; the subscript (1) represents the original state variable, which is used to distinguish the hidden state variable introduced later; f(·) and h(·) are nonlinear continuous differentiable functions; and Y (k+1) are state noise and measurement noise respectively, both are zero-mean Gaussian white noise, and their error covariance matrices are R (k+1) , the error covariance matrix of the initial state estimate is Initial state Determined by the initial speed, position and acceleration of the train, the initial error covariance matrix Reflects the uncertainty of the initial state.

3. The virtual marshaling train interval prediction method based on high-order extended Kalman smoother according to claim 1 is characterized in that: A high-order extended Kalman filter is used to model the state of the leading vehicle. A high-order Taylor expansion is used to expand the state model of the leading vehicle to a higher order to capture the nonlinear characteristics of the system. The state of the following vehicle is predicted based on the historical state data of the leading vehicle.

4. The virtual marshaling train interval prediction method based on high-order extended Kalman smoother according to claim 3 is characterized in that: Use future measurement data to smooth and optimize the historical state, calculate the smoothed error covariance, and calculate the train spacing based on the smoothed estimate.

5. The method for predicting virtual train intervals based on a high-order extended Kalman smoother according to claim 4, characterized in that: The smooth optimization of historical states using future measurement data is: The smoothed error covariance is calculated as: P(k∣N)=P(k∣k)+A(k) T (P(k+1∣k) -1 )(P(k+1∣N)-P(k+1∣k))(P(k+1∣k) -1 )A(k)。 6. The method for predicting virtual train intervals based on a high-order extended Kalman smoother according to claim 5, characterized in that: In order to achieve dynamic interval estimation, it is necessary to make the best estimate of the preceding train and make real-time estimates of the following trains. By using a high-order extended smoother, a more accurate estimate than a high-order extended Kalman filter is obtained, and the interval estimate is: in, and The difference is and The first-level state variable, L train is the length of the train ahead.

7. A virtual train marshaling interval prediction system based on a high-order extended Kalman smoother, characterized in that: include: An acquisition module is used to acquire real-time status data of the accompanying trains in the marshaling and historical status data of the leading trains, wherein the status data includes speed data, position data and acceleration data; A prediction module is used to predict the dynamic state of the accompanying vehicle based on the acquired real-time state data of the accompanying vehicle and the historical state data of the leading vehicle by using a high-order extended Kalman filter; wherein the state is updated in combination with the real-time measured state data; wherein the predicted value is fused with the measured value by calculating the Kalman gain to minimize the prediction error and adjust the error covariance after the state update; and the historical state is smoothed by using a high-order extended Kalman smoother; wherein the historical state of the accompanying vehicle is backward optimized by using the future measurement data of the leading vehicle; The calculation module is used to dynamically calculate the train spacing based on the state after smooth optimization and the difference in the position states of the leading train and the following train.

8. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, the method for intelligent estimation of virtual train intervals based on a high-order extended Kalman smoother as described in any one of claims 1 to 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 virtual marshaling train interval intelligent estimation method based on the high-order extended Kalman smoother as described in any one of claims 1-6.

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

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