Improving the tracking ability of KRLS using Kernel Subspace Pursuit

We present a new Kernel Recursive Least Squares (KRLS) algorithm that is able to efficiently track time-varying systems. In order to alleviate the detrimental effect of a large dictionary size on the algorithm´s tracking ability, we decouple the equality between dictionary size and weight vector size, an equality that has been encountered in all previous KRLS algorithms. In the proposed method, the maximum size of the weight vector is fixed and is independent from the dictionary size. We introduce the Kernel Subspace Pursuit algorithm which we use to choose a subset of the dictionary that tracks best the most recent received data samples. The selected dictionary elements are then used in the KRLS iterations. We show through simulations that our algorithm outperforms existing KRLS algorithms in tracking time-varying systems.