| Abstract: | In this paper, we propose a new nonlinear set‐membership recursive least‐squares algorithm. The algorithm draws on a linear set‐membership filter in conjunction with kernels for nonlinear processing. Set‐membership algorithms exploit a priori model information that directly, or indirectly, prescribes dynamic constraints on the solution space. Such information is disregarded by conventional approaches. Kernel methods provide an implicit mapping of the data in a high‐dimensional feature space where linear techniques are applied. Computations are done in the initial space by means of kernel functions. In this work, we develop a kernel‐based version of a set‐membership filter that belongs to a class of optimal bounding ellipsoid algorithms. Optimal bounding ellipsoid algorithms compute ellipsoidal approximations to regions in the parameter space that are consistent with the observed data and the model assumptions. Experiments involving stationary and nonstationary data are presented. Compared with existing kernel adaptive algorithms, the proposed algorithm offers an enhanced performance and sparsity, conjugated with better tracking capabilities. |
