Least squares type algorithms for identification in the presence of modeling uncertainty

The celebrated least squares and LMS (least-mean-squares) are system identification approaches that are easily implementable, need minimal a priori assumptions, and have very nice identification properties when the uncertainty in measurements is only due to noises and not due to unmodeled behavior of the system. When there is uncertainty present due to an unmodeled part of the system as well, however, the performance of these algorithms can be poor. Here the authors propose a “modified” weighted least squares algorithm that is geared toward identification in the presence of both unmodeled dynamics and measurement disturbances. The algorithm uses very little a priori information and is easily implementable in a recursive fashion. Through an example the authors demonstrate the improved performance of the proposed approach. Motivated by a certain worst-case property of the LMS algorithm, an H_∞ estimation algorithm is also proposed for the same objective of identification in the presence of modeling uncertainty