Adaptive estimation of external fields in reproducing kernel Hilbert spaces

Abstract

SummaryThis article studies the distributed parameter system that governs adaptive estimation by mobile sensor networks of external fields in a reproducing kernel Hilbert space (RKHS). The article begins with the derivation of conditions that guarantee the well‐posedness of the ideal, infinite dimensional governing equations of evolution for the centralized estimation scheme. Subsequently, convergence of finite dimensional approximations is studied. Rates of convergence in all formulations are established using history‐dependent bases defined from translates of the RKHS kernel that are centered at sample points along the agent trajectories. Sufficient conditions are derived that ensure that the finite dimensional approximations of the ideal estimator equations converge at a rate that is bounded by the fill distance of samples in the agents' assigned subdomains. The article concludes with examples of simulations and experiments that illustrate the qualitative performance of the introduced algorithms.