An Improved Square Root Unscented Kalman Filter for Nonlinear Positioning in Space-Based Pseudolite Systems

Introduction: As a backup system for satellite navigation, pseudolite systems can effectively compensate for its shortcomings due to their flexible application and regional enhancement. Method: In terms of positioning and tracking algorithms, it highlights the limitations of Kalman filtering algorithms in handling nonlinear systems, as well as those of traditional improved filtering algorithms such as the EKF(Extended Kalman Filter) and UKF(Unscented Kalman Filter) algorithm. When dealing with strong nonlinear systems, UKF has significant errors and serious divergence. Based on the unscented Kalman filtering algorithm, an improved algorithm is proposed and used in data processing. Results: It replaces the square root of the covariance matrix in the recursive process to ensure non-negative determinacy and symmetry in the process. It establishes a comprehensive testing and evaluation environment consisting of software simulation, sports car testing, and an indoor navigation test field. MATLAB simulation software is used to compare and analyze the performance differences between the improved algorithm and the traditional target-tracking algorithm in dealing with strong nonlinear systems. Discussion: In terms of positioning and tracking, an improved Kalman filter-based algorithm is proposed to address its limitations in dealing with nonlinear systems. It is shown that the unscented Kalman filter algorithm exhibits large errors and serious divergence when dealing with strong nonlinear systems. In the recursive process, the square root of the covariance matrix is used to participate in the recursive process, which can ensure non-negative definiteness and symmetry in the process. Conclusion: The superiority of the algorithm was verified through movement testing, dynamic tracking, and positioning experiments in navigation test fields.