Constrained Time-Varying System Modelling

Tools are presented to reliably identify a time-varying autoregressive (AR) model for a realization of a stochastic process with an arbitrary non-stationarity. Only limited a priori knowledge about the nature of the non-stationarity, namely the expected maximum rate of change of the model parameters, is necessary to estimate these parameters on-line. The criterion considered is a constrained least squares cost functional which incorporates with equal weight all instantaneous errors up to the time of observation. The constraint is specified from the maximum rate of change using a (non-unique) backward state-space description for the parameter variation. A doubly recursive algorithm based on smoothing theory is derived to find a quasi-optimal solution to the recursive parameter estimation problem. Associated trade-offs are discussed for various non-stationary environments.