Unbiased parameter estimation by means of autocorrelation functions

A new method for obtaining an on-line unbiased estimate of the parameter vector of linear systems in the presence of additive uncorrelated output noise is described. The method, which is based on the equation error, is developed for continuous variables and then formulated both for continuous and discrete representations. Instead of the conventional least squares approach, the autocorrelation function of the error serves as the cost function to be minimized. It is shown that for comparatively wide-band noise, this cost function yields unique and practically unbiased estimates. On-line identification from system input and output is feasible. Bias suppression as a function of the time-delay in the cost function is demonstrated by numerical examples. Convergence of the estimates is demonstrated by means of simulated continuous and discrete examples.