NOTE ON THE KALMAN FILTER WITH ESTIMATED PARAMETERS

N. Watanabe

Journal of Time Series Analysis, 1985, vol. 6, issue 4, 269-278

Abstract: Abstract. State estimation and prediction problems are considered for a stochastic process represented by a state space form which involves unknown parameters. We first study the stability of the Kalman filter corresponding to the state space form without assuming the stationarity of the process. Second, we consider the state estimation and prediction when the process is stationary, and show some asymptotic properties of the state estimates and predicted values obtained by the Kalman filter with estimated parameters which converge to the true parameters or to the equivalent classes of the true parameters with probability one.

Date: 1985
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