Time-varying system identification via explicit filtering of the parameter estimates

The on-line identification of continuously adaptive rational models is considered for data records which are realizations of nonstationary processes. Emphasis is placed on the treatment of arbitrary time variations for the model coefficients. This motivates a novel approach to time-varying modeling, based only on limited a priori knowledge about the nature of the non- stationarity, namely the expected bandwidth of the time evolution for the parameter vector. The cost criterion considered is a constrained least squares cost functional which incorporates with equal weight all instantaneous errors up to the current time of observation. The constraint is specified from the expected time evolution bandwidth through explicit filtering of the parameters to be estimated. Computational considerations and associated trade-offs are discussed for the modeling of various nonstationary data.