Optimal and self-tuning white noise estimators with applications to deconvolution and filtering problems (Q1911251)

Using the innovation analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model, this paper presents a unified white noise estimation theory that includes both input and measurement white noise estimators, and presents a new steady-state optimal state estimation theory. Non-recursive optimal state estimators are given, whose recursive version gives a steady-state Kalman filter, and a new algorithm to obtain the Kalman filter gain is proposed. Two new algorithms for the Kalman predictor gain are also derived. Local asymptotic stability of the Kalman filter is proved. To illustrate, three simulation examples are given.