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

The celebrated least squares and 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. However when there is model uncertainty present, the performance of these algorithms can be poor. Here we propose a “modified” weighted least squares algorithm that is geared towards 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. Also, a similar H_∞ (worst-case) estimation algorithm is proposed in the paper for the same objective of identification in the presence of modeling uncertainty