Parametric Estimation: Improvement of the RLS Algorithm using a Differential Approach
Résumé
This paper describes a new computational method for recursive least squares (RLS) algorithm. It is well known that the initial values for computing RLS estimates should be chosen to guarantee the existence of the estimates at each step, that the initial covariance matrix may affect the convergence rate, and that a blow-up phenomenon (infinite increase of the covariance matrix) can appear. Much research has focused on each of these problems, but heavy computations and different specific design parameters result from the most common solutions. We propose an alternative simple algorithm that reaches a trade-off between the advantages of the well-known RLS algorithms and of the more complex computations. The proposed algorithm modifies the prior additional term used in the cost function. This modified term is updated during the recursion, in the context of a differential formalism. The aim of this formalism is, first, to provide valid computations and properties in both discrete and continuous time domains, and to yield the variations of the parameters at each step. Second, in the particular case of discrete time this formalism provides very good numerical properties. The methodology in developing this approach is quite different from the previous work on RLS estimation. We demonstrate that our algorithm, compared with RLS algorithm, leads to a higher convergence rate. It also offers a closer tracking of parameters in nonstationary case and satisfactory results in the presence of blow-up situations. This goal is achieved without significant additional computations, and the behaviour of the approach is illustrated through simulations.