Estimation of the forgetting factor in kernel recursive least squares

Abstract

In a recent work we proposed a kernel recursive least-squares tracker (KRLS-T) algorithm that is capable of tracking in non-stationary environments, thanks to a forgetting mechanism built on a Bayesian framework. In order to guarantee optimal performance its parameters need to be determined, specifically its kernel parameters, regularization and, most importantly in non-stationary environments, its forgetting factor. This is a common difficulty in adaptive filtering techniques and in signal processing algorithms in general. In this paper we demonstrate the equivalence between KRLS-T's recursive tracking solution and Gaussian process (GP) regression with a specific class of spatio-temporal covariance. This result allows to use standard hyperparameter estimation techniques from the Gaussian process framework to determine the parameters of the KRLS-T algorithm. Most notably, it allows to estimate the optimal forgetting factor in a principled manner. We include results on different benchmark data sets that offer interesting new insights.