Parametric Estimation: Improvement Of The Rls Algorithm Using A Differential Approach

AbstractThis 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 do...