The problem of estimating the state of a stationary Gauss-Markov sequence observed in uncorrelated Gaussian noise of constant, hut unknown, covarianeeRis considered. A non-informative prior density is assigned to the prior innovations covariancoM, which is unknown by virtue of the uncertainty inR.Thea posterioridensity ofMevolves as an inverted Wishart, censored to account for the fact thatMis 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 aposteriori(MAP) estimate of the innovations covarianee,