FAST TRACKING RLS ALGORITHM USING NOVEL VARIABLE FORGElTING FACTOR WITH UNITY ZONE

Introduction: An important requirement of recursive estimators for adaptive control and adaptive signal processing lies in their ability to track parameter changes. From this viewpoint, the famous standard RLS algorithm which is known to have the optimal properties in stationary environments is unsuitable for nonstationary environments. Thus many attempts have been directed to the development of modified versions of the RLS algorithm to include tracking capability in timevarying environments. '-' Among these modified RLS algorithms, the best known is an exponential data weighting RLS algorithm using a forgetting f a ~ t o r . ~ However, in certain situations, this algorithm can lead to a problem often referred to as the blow-up problem.',* Also the lower the value of the forgetting factor, the higher the tracking velocity but the higher the influence of the noise, that is, the larger the parametric errors. To avoid these difficulties, the idea of a variable forgetting factor was introduced? We present a new exponentially weighted RLS (EWRLS) algorithm using a novel form of variable forgetting factor. The method presented has an excellent tracking adaptability with a low forgetting factor in the nonstationary situation and less error variance than other algorithms with a unity forgetting factor in stationarv environments. The additional comwhere N I N T [ 3 is defined as the nearest integer to [ 1, and p is a design parameter which controls the width of a unity zone, which will be discussed later. In eqn. 5, the minimum value of the forgetting factor is obtained when a goes to infinity, and when a decreases to zero the forgetting factor goes to unity at an exponential rate. This rate is controlled by the sensitivity gain p. The additional computational burden with respect to the standard RLS algorithm is only a few arithmetic calculations and some hit shift operations in digital processors for the calculation of the Lth power of 2. Thus this new algorithm is numerically computationally efficient compared with other EWRLS algorithms. This is verified in the following computer simulations.