Optimal Kalman Filtering in the Presence of Time-Correlated Process Noise

Abstract

Kalman filtering (KF), in previous works, assumes that system noises are white Gaussian noises (WGN) and are uncorrelated with each other. This assumption, however, is not reasonable in real-world navigation applications. This paper dedicates to develop an optimal Kaman filtering navigation algorithm in the time-correlated contained dynamic system. Efforts are made on its stochastic model establishment and the corresponding recursive formulae derivations. First, as a popular sort of time-correlated noise-whitening method, the principle of state augmentation based KF (SAKF) is reviewed and presented. Alternative method second moment information based KF (SMIKF) which directly compensates the variances through stochastic model is proposed and developed. To precisely establish the stochastic model of time-correlated process noise, a refined SMIKF (RSMIKF) is further rigorously proposed and derived from continuous-time dynamic model. We also investigate the numerical computation burden for these developed methods compared with conventional KF (CKF). Finally, a simulation experiment is carried out to illustrate the performances of our proposed algorithm. The accuracies of CKF and our proposed methods are all computed and analyzed for comparison purpose. The results show that the proposed RSMIKF algorithm adapts to the time-correlated process noise very well and obtains the accurate and reliable solutions compared with other methods as expected.