Modifications to the sliding-window kernel RLS algorithm for time-varying nonlinear systems: Online resizing of the kernel matrix

Abstract

A kernel-based recursive least-squares algorithm that implements a fixed size ldquosliding-windowrdquo technique has been recently proposed for fast adaptive nonlinear filtering applications. We propose a methodology of resizing the kernel matrix to assist in system identification of time-varying nonlinear systems. To be applicable in practice, the modified algorithm must preserve its ability to operate online. Given a bound on the maximum kernel matrix size, we define the set of all obtainable sizes as the resizing range. We then propose a simple online technique that resizes the kernel matrix within the resizing range. The modified algorithm is applied to the nonlinear system identification problem that was used to evaluate the original algorithm. Results show that an increase in performance is achieved without increasing the original algorithm's computation time.