Optimal state-vector estimation for non-Gaussian initial state-vector
DEMETRIOS G. LAINIOTIS, S. Park, R. Krishnaiah · IEEE Transactions on Automatic Control · 1971
The optimal estimate, in the mean-square-error sense, of state-vector of a linear system excited by zero-mean white Gaussian noise with non-Gaussian initial state-vector is obtained. Both the optimal estimate and the corresponding error covariance matrix are given. It is shown that the optimal estimator consists of two parts: a linear estimator that is obtained from a Kalman filter and a nonlinear estimator. In addition, the a posteriori probabilityp(x_{k}/\lambda_{k})is also given.