Bayesian outlier rejection and state estimation

An outlier is a data point that contains no information about the system to be estimated. A procedure is developed, using a Bayesian cost criterion, to detect and eliminate outliers from a data base and at the same time provide estimates of the state of a dynamical system. The approach is applied to a Gauss-Markov discrete-time system and to a parameter estimation problem. For the latter case, exact solutions of estimator bias and convariance are obtained and conditions for filter divergence are discussed. The approach in this paper differs from others in that a maximum a posteriori estimate is obtained over long block lengths of data so that clustering schemes can be employed.