A Dual Progressive Extended Kalman Filter for Nonlinear Systems With Unknown Noises

Abstract

Kalman filtering works well in theory, but in practice, unknown noise from complex environments often degrades its performance—sometimes causing outright divergence. A Dual Progressive Extended Kalman filter (DPEKF) method is proposed for nonlinear systems with unknown noise. The existence of unknown noise will amplify the linearization error in nonlinear filtering, especially when the outliers in the equivalent test significantly reduce the overlap between the prior probability density distribution and the likelihood distribution. In order to solve this problem, the pseudo-time variable is introduced into the prior probability density and likelihood function at the same time, and the update equation of the Dual Progressive Extended Kalman filter (DPEKF) is derived. The robustness and estimation accuracy of the filter are effectively improved by extending the overlap region of prior distribution and the likelihood distribution and adopting a reasonable path function strategy. Furthermore, the introduction of convergence termination conditions effectively improves the computational efficiency and adaptive ability of the algorithm. Theoretical analysis shows that this method can maintain the boundedness of the state estimation error in the filtering process. Finally, simulation results based on a nonlinear target tracking example show that, compared with traditional methods such as EKF, IEKF, PEKF, HMKF, and MCCKF, DPEKF achieves superior robustness and estimation accuracy.