STABILITY OF RECURSIVE STOCHASTIC TRACKING ALGORITHMS

First, the paper gives a stability study for the random linear equatio n x(n+1) = (I - A(n))x(n). It is shown that for a quite general class of random matrices {A(n)} of interest, the stability of such a vector equation can be guaranteed by that of a corresponding scalar linear eq uation, for which various results are given without requiring stationa ry or mixing conditions. Then, these results are applied to the main t opic of the paper, i.e., to the estimation of time varying parameters in linear stochastic systems, giving a unified stability condition for various tracking algorithms including the standard Kalman filter, lea st mean squares, and least squares with forgetting factor.