On the use of the extended least squares with simultaneous filtering to identify time-varying ARMAX model

A novel method, based on the combination of weighted extended least squares (WELS) and explicit filtering, for tracking the time-varying parameters of a linear stochastic system is presented. The properties and tracking capability of WELS combined with filtering are analyzed for time-varying linear stochastic system. It is shown that the proposed algorithm has exactly the same tracking capability as WELS if the weighting sequence is appropriately defined. The main advantages of the algorithm are that it improves the parameter estimates and provides the flexibility of using the combined identification scheme and adaptive filtering to track the time-varying parameters