Non-linear state estimation in observation noise of unknown covariance†
Louis L. Scharf, DANIEL L. ALSPACH · International Journal of Control · 1978
The problem of estimating the state of a stationary Gauss-Markov sequence observed in uncorrelated Gaussian noise of constant, hut unknown, covarianee R is considered. A non-informative prior density is assigned to the prior innovations covarianco M, which is unknown by virtue of the uncertainty in R. The a posteriori density of M evolves as an inverted Wishart, censored to account for the fact that M is bounded from below by a positive definite matrix. The resulting non-linear state estimator involves a canonical integral which can be approximated to yield an attractive parallel filtering structure. The structure can be used to approximate the maximum a posteriori (MAP) estimate of the innovations covarianee,