The optimal, in the mean-square error sense, estimate 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 which is obtained from Kalman filter and a nonlinear estimator. In addition the a-posteriori probability, P(x sub k/lambda sub k) is also given.
展开▼
