Kalman滤波的一种改型

对于n维状态x∈R~n与不完全观测y∈R~m(m

A Modification of Kalman's Filter

At the filter formula of the kalman recursive algorithm, optimal weight A_k is the important factor. We choose this factor that may minimize the error covarience, but calculate A_k to be rather complex.In this paper, we use optimal weight Bk+ in sense of minimizing the Frobenious norm with constraint that the weight update must satisfy the quasi-Newton linear equation at instant time. We also calculate the correspond. optimal error covariance estimate P_k+ by means of minimizing the Frobenious norm with constraint that P_k+ satisfies the linear relation with P_k/k-1. From above results, we can compare the P_k+ to the P_k/k if the incomp1ete observe equation is linear with added white noise. We can find that Ricatti equation of error covarience has the important role at the linear filter whatever we use A_k or B_K⁺ as the optimal weight.