Modified least squares algorithm incorporating exponential resetting and forgetting

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Abstract
In this paper we present the general analysis of a class of least squares algorithms with emphasis on their dynamic performance particularly in the presence of poor excitation. The analysis is carried out in a deterministic framework and stresses geometrical interpretations. The core of this paper is the proposal and analysis of a new algorithm which incorporates exponential forgetting and resetting to an unprejudiced treatment of data when excitation is poor. The algorithm is particularly suitable for tracking time-varying parameters and is similar in computational complexity to the standard recursive least squares algorithm. The superior performance of the algorithm is verified via simulation studies.

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