Statistical Filtering

This paper is a tutorial survey which focuses on some developments introduction in statistical filtering achieved since the of Wiener and Kalman filters for linear gaussian problems. Kalman are reviewed with filters (including reference to their smoothers and predictors) interesting properties and also their fundamental limitations in nonlinear or unknown environments. For nonlinear filtering problems, the relevance of the near optimal extended Kalman filters and gaussian sum filters, and bound optimal filters are discussed. For adaptive linear filtering and prediction, connections gaussian theory with recursive least squares of the linear parameter estimation theory are seen to yield adaptive filtering algorithms which are asymptotically optimum, and connections with recursive a posteriori probability updating algorithms are seen to yield optimal solutions to model approximation, fault detection, and adaptive filtering problems.