A Kalman Filter with Progressive Measurement Update

Under the condition of large initial error and / or accurate measurement, due to the decrease of the accuracy of the joint Gauss distribution hypothesis, the moment approximation filtering methods based on Gauss hypothesis have the problem of posteriori error matrix overestimated, which means the error of the filter is much lower than the actual error, resulting in filtering divergence. In view of this problem, a Kalman filter with progressive measurement update is proposed. Firstly, based on Gauss hypothesis, under the framework of Daum-Huang filter, the progressive Bayesian formal description of the state evolution equation is given, the linear Gauss solution of the state evolution equation is derived. Secondly, by means of the first order Taylor expansion, the approximate solution of the nonlinear condition is obtained, and at last a Kalman filter with progressive measurement update and its nonlinear extend form are proposed. Simulation results show that in the large initial error and / or accurate measurement conditions, proposed method improves position estimation accuracy by 90% than UKF(Unscented Kalman Filter) and CKF(Cubature Kalman Filter), by 17% than EKF(Extended Kalman Filter), by 30% than similar method when progressive step is 0.1 and by 17% when progressive step is 0.01; proposed method improves velocity estimation accuracy by 66% than UKF and by 73% than CKF, by 53% than EKF, by 23% than similar method when progressive step is 0.1 and equivalent accuracy when progressive step is 0.01.