Identification of time-varying systems using combined parameter estimation and filtering

The problem of tracking time-varying parameters of a linear stochastic system is considered, and an identification method based on parameter estimation and filtering is described. The proposed algorithm combines the standard weighted least squares (WLS) identification with low-pass filtering of parameter estimates. It is shown that the parameter tracking properties of the combined estimation-filtering method are exactly the same as the tracking capabilities of the WLS estimator characterized by the appropriately defined weighting sequence and can be analyzed in terms of the associated frequency characteristics. The main advantage of the method is that it allows for efficient implementation of banks of adaptive filters characterized by different memory lengths without compromising the good tracking capabilities of WLS estimators. Additionally, it provides the designer with much greater flexibility in shaping the window.