Wide-Sense Martingale Approach to Linear Optimal Estimation
H. Kara, Vidyadhar S. Mandrekar, G. L. Park · SIAM Journal on Applied Mathematics · 1974
It is shown how to recursively compute linear least-squares estimates for a signal $x_t = \phi (t)u_t $, where $\phi (t)$ is an $n \times n$ matrix and $u_t $ is a wide-sense martingale, based on noisy observations. Assuming that the observation process has full rank, the recursive equations are derived for prediction, filtering and smoothing. It is also shown that the solution of the Kalman problem follows from these more general equations.