Analysis and development of modified recursive least squares algorithms for estimation of time-dependent parameters (Q1369628)

The recursive least squares method is considered and the modifications capable of tracking time-dependent parameters in the presence of unobservable noise and inexact model specification are proposed. The algorithms preserve global convergence while ensuring a covariance (gain) matrix with nonzero elements. This is achieved, first, by keeping the trace of the matrix constant and applying variable forgetting or, second, by combining exponential forgetting with a modification of the covariance matrix by adding a positive definite constant matrix to the updated gain matrix. The accuracy and convergence of the algorithms are investigated and their numerical implementation is discussed.