Recursive parameter estimation by means of the SG - algorithm ⋆

Recursive parameter estimation in linear regression models by means of the Stenlund-Gustafsson algorithm is considered. The manifold of stationary solutions to the parameter update equation is parameterized in terms of excitation properties. It is shown that the parameter estimation error vector does not diverge under lack of excitation, therefore achieving the purpose of anti-windup. Furthermore, an elementwise form of the parameter vector estimate is suggested revealing the effect of individual matrix entries in the Riccati equation on the parameter estimation updates. Simulations are performed to illustrate the loss of convergence rate in the estimates versus the decrease of computational power needed for two specific approximations of the Riccati equation in the elementwise form.