TRACKING RANDOMLY VARYING PARAMETERS - ANALYSIS OF A STANDARD ALGORITHM

In linear stochastic system identification, when the unknown parameters are randomly time varying and can be represented by a Markov model, a natural estimation algorithm to use is the Kalman filter. In seeking an understanding of the properties of this algorithm, existing Kalman-filter theory yields useful results only for the case where the noises are gaussian with covariances precisely known. In other cases, the stochastic and unbounded nature of the regression vector (which is regarded as the output gain matrix in state-space terminology) precludes application of standard theory. Here we develop asymptotic properties of the algorithm. In particular, we establish the tracking error bounds for the unknown randomly varying parameters, and some results on sample path deviations of the estimates.