On-line parameter identification algorithms based on Householder transformation

A fast online least-squares algorithm for both order determination and parameter identification of linear single-variable dynamic systems is introduced. An exponential weighting scheme is used to place heavier emphasis on the more recent data in the case of a time-varying system. This algorithm is derived on the basis of an orthogonal transformation, the Householder transformation, rather than the matrix pseudoinverse in the solution of a normal equation, so as to avoid worsening of the ill-conditioning, which occurs with most present online algorithms. For parameter estimation from noisy measurements in complex stochastic environments, a fast online generalized least-squares algorithm, a fast online extensive matrix algorithm, and a fast online maximum-likelihood algorithm are developed according to the proposed fast online least-squares algorithm. These algorithms can also estimate the order simultaneously with the parameters of a system to be identified