Adaptive MSSRCPF filtering based on constrained optimization and fading memory for SINS/GNSS integrated navigation

To address particle degeneracy and the challenge of selecting importance density functions in traditional particle filters for complex nonlinear systems, we propose an adaptive mixed-order spherical simplex-radial cubature particle filter algorithm based on constrained optimization and fading memory. This algorithm integrates constrained optimization, an adaptive fading memory strategy, adaptive adjustment of particle numbers and weights, and the advantages of mixed-order spherical simplex-radial cubature Kalman filtering. By designing the importance density function using a mixed-order integration method, the algorithm significantly improves filtering accuracy over traditional cubature Kalman filters while maintaining lower computational complexity than high-order cubature Kalman filter methods. The adaptive fading memory strategy dynamically adjusts the covariance matrix, enhancing sensitivity to current measurement information and reducing the influence of historical data. By dynamically adjusting the noise covariance matrix and constraining the ratio between the error covariance and measurement noise covariance, the algorithm improves the convergence speed and accuracy of state estimation. An adaptive particle number and weight adjustment strategy based on effective sample size and entropy regularization dynamically adjusts the number of particles to reduce computational complexity while ensuring filtering accuracy, and employs entropy regularization to suppress weight over-concentration, thereby reducing the impact of outliers on the filtering results. Simulation results demonstrate that in complex SINS/GNSS integrated navigation systems, especially under high-noise and nonlinear conditions, the proposed algorithm significantly improves positioning accuracy compared to the CPF method, with the maximum latitude error reduced by approximately 54.8%, the maximum longitude error reduced by approximately 40.5%, and the maximum altitude error reduced by approximately 68.3%. Compared to the FMCPF method, the proposed algorithm also shows clear advantages in positioning accuracy, convergence speed, and computational efficiency, validating its effectiveness and practicality in complex environments.