A Kalman Filter Method for Train Operation State Estimation that Use Underdetermined Least Squares Estimation Model Error

In the problem of estimating the operating status of trains, achieving precise modeling is extremely challenging. Due to the complexity of the train operating environment and the inherent defects of the sensors, the model inevitably has some errors. Due to the lack of a priori information, these errors are difficult to be accurately derived, which affects the accuracy of the Kalman filtering method or even the results do not converge. To address this problem, we introduce an error variable into the system model, construct an error estimation equation, and propose undetermined least squares Kalman Filter (ULS-KF) algorithm. The undetermined least squares method is able to get the minimum paradigm solution for the underdetermined system of equations. By estimating the unknown error and incorporating it into the Kalman filtering process, the effect of modeling error on the estimation results is compensated and the accuracy of the filtering results is improved. Through simulation experiments, the results show the effectiveness of the method proposed in this paper.