Adaptive estimation of time-varying parameters in linear systems

Estimation of time-varying parameters via local polynomial approximations in linearly parameterized systems is considered. A strategy for approximating a time-varying parameter locally by a polynomial is given. The estimation time is divided into small intervals; in each interval the time-varying parameter is approximated by a time polynomial with unknown constant coefficients. A condition for resetting the parameter estimate at the beginning of each interval is derived; the condition ensures that the estimate of the time-varying parameter is continuous and allows for the coefficients of the polynomial to be different in various time intervals. Modifications of the least-squares and the gradient algorithms are provided to estimate the time-varying parameters. Stability of the proposed algorithms is shown and discussed. Simulation results on an example are given.