High-speed train (HST) positioning plays a vital role in ensuring train safety, improving transportation efficiency and efficient dispatching. As the railway system has adopted and integrated 5G New Radio (NR) technology, higher requirements are placed on HST positioning accuracy. This paper presents a novel extended Kalman filter-based fusion positioning method which incorporates nonlinear high-order variable information from the train’s nonlinear positioning model. In this method, to capture and exploit the high-order variable information in nonlinear positioning models, an auxiliary model that focuses on high-order variables is introduced. The predicted values of the high-order variables obtained from the auxiliary model can be regarded as additional measurements of these variables. This approach thereby circumvents the identification of high-order variables under the condition of under-measurement, which is a common issue in existing methods. Meanwhile, to ensure the accuracy of the introduced auxiliary model, a real-time updating method for the statistical characteristics of the auxiliary model error is proposed. To intuitively compare the performance of the high-order extended Kalman filter under different expansion orders, this paper presents a novel performance index. The simulation results of train positioning under different motion modes and the rotor position of permanent magnet synchronous motors (PMSMs), demonstrate that the second-order extended filter designed in this paper achieves better estimation performance than existing second-order extended filters when only utilizing the second-order variables in the nonlinear model. Moreover, as the information of high-order variables is progressively incorporated, the proposed high-order extended filter exhibits superior performance.

This paper addresses the challenge of achieving high-precision headway estimation in virtual coupling trains by proposing a method utilising a high-order extended Kalman filter-based smoother. In this approach, the leading train uses a high-order extended Kalman filter to obtain its current operational state and then transmits historical state data to the following train. The following train then employs a high-order extended Kalman smoother to refine the state estimation and determine dynamic headway estimation. The high-order extended Kalman filter, based on Taylor series expansion, enhances state estimation accuracy by minimising truncation errors. It constructs a pseudo-linear representation of the full-space hidden variables and establishes high-order states, facilitating the modelling of measurements to align with the filtering derivation process. The high-order extended Kalman smoother continuously optimises current-state estimation using future measurement sequences, with the derivation process realised through the orthogonal theorem and innovation analysis. Ultimately, the headway estimation is updated based on the smoothed state provided by the smoother, and the effectiveness of the proposed method is validated through a multi-mode operating process of virtual coupling trains.

Fault diagnosis of railway assets has drawn the interest of both the scholarly and engineering communities. Federated learning (FL) enables training models across distributed assets to preserve data privacy and reduce high data transfer costs, which has been applied in fault diagnosis. However, the imperfect data transmission problem due to communication errors easily results in low accuracy of FL-based fault diagnosis in the railway system. To solve the problem, a sequential and asynchronous federated learning framework is proposed for fault diagnosis of railway point machines (RPMs) in this work. First, a dual-branch network is proposed as the global model in asynchronous FL for reducing parameters, while maintaining high accuracy. Second, a time cycle mechanism based on sequential Kalman filtering is proposed for reducing the negative impact of data communication errors. Finally, experimental results demonstrates that the proposed method enhances the applicability of online RPM fault diagnosis training in real deployment scenarios.

With the integration of 5G NR (New Radio) into railway systems, the demand for enhanced positioning and trajectory tracking performance in High-Speed Train (HST) networks has grown. However, many existing train positioning schemes rely on traditional algorithms like the Extended Kalman Filter (EKF), which may fall short of meeting the precision requirements, particularly in 5G HST scenarios. Addressing this limitation, this paper draws on the concepts presented by Ko et al. (2022) and introduces an Improved Extended Kalman Filter (IEKF) using the Least Squares of Undermeasurement (LSU) technique, specifically tailored for nonlinear systems. The IEKF, expanding step by step, theoretically captures statistical properties of the Knorr set for any order prediction error, providing richer information on higher-order terms compared to the traditional EKF. Additionally, for a more intuitive comparison of the IEKF unfolded to different orders, a novel performance indicator is introduced. In conclusion, to validate the effectiveness of our proposed algorithm in real-world scenarios, we demonstrate its superior localization performance by comparing Mean Squared Error (MSE) and Mean Absolute Error (MAE) with traditional nonlinear localization algorithms. The comparisons are based on simulation examples involving train localization tracking and an industrial device ablation system.

Recently, Ko et al. (2022) proposed a high-speed railway positioning scheme based on an improved Kalman filter using 5G NR signals. Although the proposal was promising, our research and analysis have revealed that the method has serious design flaws in the proposed filtering principles, rendering the algorithm infeasible. Specifically, the flaws are related to the computation and usability of high-order terms in the prediction error after Taylor expansion and prediction error derivation.

The key equipment in a cyber-physical system (CPS) can be changed or replaced by untrusted equipment, which causes the system to make incorrect decisions, which threatens people's lives and property security. Inspired by the identification of human genes, this research establishes a data fingerprint identification method for equipment. This method provides a security guarantee for the operation of a CPS. Thus, this research makes three contributions. First, it is the first attempt to represent device data information with a mathematical representation model based on multiorder terms. Second, we originally attempt to establish a multigranularity feature extraction method. Then, for the first time, we try to propose different scale matching methods for different granularity features. In addition, an F-404 aircraft example is used to verify the new method. The experimental results show that stealthy false data attacks can bypass the${\chi ^{2}}$detector and destroy the operation of key equipment. However, the method proposed in this article can detect stealthy false data attacks and alert managers so that they can deal with the attacks in time; hence, the method proposed in this article is better than the${\chi ^{2}}$detector. Similarly, we contrast the proposed method with recent competitor schemes and provide tangible evidence of the effectiveness of the proposed solution.

This paper investigates the problem of path following with prescribed performance for autonomous underwater vehicles subjects to unknown actuator dead-zone nonlinearity. To cope with this practical problem abstracted from hydrodynamic noise measurement, an adaptive command filtered backstepping method with actuator dead-zone compensation is proposed. By introducing a damped exponential barrier functions, new tracking errors are defined to satisfy the prescribed performance requirements. The path following control method is theoretically based on the command filtered backstepping technique for handling the complexity explosion problem attribute to the repeating derivations. Moreover, the filter compensation mechanism is designed to eliminate the negative effect of the filter errors. To deal with the actuator dead-zone nonlinearity, a fuzzy logic system based dead-zone compensation method is developed that dose not need the inverse of the dead-zones. Numerical simulations are conducted to demonstrate the theoretical analysis, and the usefulness and potential of the new design scheme is revealed.

Suspension systems are significant for safe and comfort operation of high-speed trains. Health assessment is a useful tool to schedule maintenance plans of suspension systems, and furthermore ensure safety operation of high-speed railway transportation. In real operating condition, two problems, i.e. data imbalance and shortage of labelled data, result in difficult for health assessment of the suspension system using deep learning. In this work, a multi-sensor information fusion method, called as multi-sensor graph transfer network (MSGTN), is proposed in basis of deep transfer learning and graph neural network. In the proposed method, a domain-share multi-sensor graph neural network (MSGNN) is firstly proposed to extract features from vibration signals collected from three different positions in train vehicles. A graph-based fusion layer in MSGNN is proposed to fuse multi-sensor information by combining frequency response curves of the suspension system. The MSGTN mainly includes two parts in source and target domains respectively. In the source domain, a simple physical dynamic model of high-speed rail suspension system is built to generate labelled simulation datasets to pre-train MSGNN. In the target domain, the initial hyper-parameters of MSGNN are that of the pre-train model in the source domain. The labelled data in the target domain is fed to fine-tune MSGNN and then the final model for health assessment can be obtained by minimizing the loss function. The effectiveness of the proposed method was verified using real-work operation data.

With the increasing demand for rail transit, wireless communication technologies are playing a growing significant role in train control systems, which enables the railway systems to provide a higher capacity and more efficient services. However, due to the nature of radio frequency propagation, the quality of the train-to-ground wireless connections is highly dependent on a well-planned deployment of the wayside access points. To improve both the accuracy and the efficiency in railway network planning, in this paper, a deep learning technology is exploited to model the wireless propagation, which was very difficult to deterministically predict at a fast speed in our previous research due to the high computation demanding. In this proposed wireless propagation model, Kalman filter is utilized to update the neural network parameters online, which makes this model can meet the variation of the environment. The numeric evaluation result shows that the deep neural network based wireless channel model can precisely predict the outage probability with a very low computational cost.

The federated learning (FL) method based on model aggregation can balance data and protect data privacy, but the existing method is difficult to achieve the same effectiveness as the centralized learning method under data sharing. In addition, it is difficult for the existing federated model to realize the real-time update of the clients' network parameters, because it inhibits the optimal performance of the client. Therefore, this article proposes an asynchronous update paradigm of FL with real-time identification of the client's network parameters to tackle the shortcomings. First, we adopt the linear fusion method based on sequential filtering and fuse the parameters of federated center asynchronously considering communication delay, which can approach the diagnostic accuracy based on the centralized learning. Second, we establish the real-time identification method for the clients based on linear filtering with the new labeled samples obtained at nonequal intervals, which expects the client to acquire better performance. Finally, we test the fault classification ability of the proposed method based on the actual collected fault dataset and the test platform of bearing fault dataset.

Conventionally, the transition probabilities in the interacting multiple model (IMM) are often fixed based on the prior information. However, this conservative setting may result in inaccurate state estimations. To solve this problem, a Bayesian-based online correction function is proposed in this paper, which can adaptively adjust the transition probabilities. To deal with the response lag and the short-term peak estimation error problem during the respond to model jump, a model jumping threshold is defined, so that the current information of the models can be fully utilized by the IMM algorithm and the correction function of the transition probabilities can be further improved. Subsequently, an adaptive transition probability-based parallel IMM algorithm is proposed in this paper. Finally, three maneuvering target tracking simulations are conducted to verify the performance of the proposed algorithm, the results show that the proposed algorithm can improve the response speed of the system model jump and the state estimation accuracy. The effectiveness and feasibility of the algorithm are proven.

Communication-based train control (CBTC) systems have been playing a progressively significant role in metro signaling in recent years. As safety-critical systems, CBTC systems have very strict requirements on the wireless communication performance between train and wayside access points (AP), which is highly dependent on the deployment of the APs. In this paper, by customizing and adopting a decomposition-based multiobjective evolutionary algorithm, the proposed AP deployment optimization method has been implemented, verified, and its implementation accuracy has been assessed. A real-world case study is carried out in an integrated simulation platform, in which the optimized AP deployments are verified and show better performance than the original planning.

In railway condition monitoring, feature classification is a very critical step, and the extracted features are used to classify the types and levels of the faults. To achieve better accuracy and efficiency in the classification, the extracted features must be properly selected. In this paper, maximal information coefficient is employed in two different stages to establish a new feature selection method. By using this proposed two-stage feature selection method, strong features with low redundancy are reserved as the optimal feature subset, which results in the classification process having a more moderate computational cost and good overall performance. To evaluate this proposed two-stage selection method and prove its advantages over others, a case study focusing on the rolling bearing is carried out. The result shows that the proposed selection method can achieve a satisfactory overall classification performance with low-computational cost.

Train positioning is of critical importance for communication-based train control (CBTC) systems. The objective of this paper is to provide an algorithm to generate the precise estimates of the train position and velocity for CBTC systems with carrier-sense multiple access (CSMA) protocol scheduling, thereby improving the accuracy of train positioning as well as the availability of CBTC systems. First, the dynamics of a train with N cars linked by couplers is described based on Newton's motion equations. Then, the transmission model reflecting the behaviors of p-persistent CSMA protocol is presented by using a Bernoulli distributed sequence whose probability distribution is dependent on the number of trains sharing with one communication channel [i.e., N(k)]. Furthermore, the value of N(k) is assumed to be unknown but bounded by two known positive integers. The purpose of the problem addressed is to design an estimator, such that the estimation error is exponentially ultimately bounded (with a certain asymptotic upper bound) in mean square subject to the external resistive force. By utilizing the stochastic analysis approach, sufficient conditions are established to guarantee the ultimate boundedness of the estimation error in mean square. For the purpose of designing the desired estimator gains under different requirements (e.g., smallest ultimate bound and fastest decay rate), two optimization problems are solved in terms of linear matrix inequalities. Finally, a simulation example is given to illustrate the effectiveness of the estimator design scheme.

Communication-based train control (CBTC) systems are a new generation of metro signaling system dependent on wireless technology with appropriate access point (AP) deployment. Improved AP deployment can improve the reliability of wireless CBTC systems. This paper proposes a method for optimizing the AP deployment in the data communication system of CBTC. To validate the optimal AP deployment, an integrated simulation environment is used to test the performance of the optimized AP deployments.