Matrix forgetting factor with adaptation
Alexander S. Poznyak, J. J. Medel Juárez · International Journal of Systems Science · 1999
We suggest an approach to provide time-varying parameter estimates in ARMA (Auto Regression Moving Average) models of a stochastic nature based on the use of the recursive version of theInstrumental Variable Method (IVM) with a MatrixForgetting Factor (MFF) . We demonstrate that there exists the best selection of MFFminimizing the error strip bound. This optimal MFF depends in a complex manner on a group of unknown parameters. An adaptation procedure is suggested to obtain asymptotically this optimal value using only the available measurements. The adaptation procedure is based on one Gaussian smoothing technique. The combination of IVM with adaptive MFFis a tool for estimating the entries of a non-stationary parameter matrix involved in the ARMA model. An asymptotic analysis of the error matrix is presented. Simulation results demonstrate the effectiveness of the suggested approach.