Fixed Budget Kernel LMS based Estimator using Random Fourier Features

Abstract

Accurate estimation of delay and Doppler shift are essential for target detection and tracking in a radar system. In this regard, online reproducing kernel Hilbert space (RKHS) based estimation techniques have emerged as viable for radar systems, due to guarantees of universal representation, and convergence to low estimator variance. However, existing RKHS based estimation techniques for radar rely on growing dictionary of observations, which makes it difficult to predict the memory requirement beforehand. Furthermore, online dictionary based learning techniques are prone to erroneous observations in the high-noise regime. In this work, a finite implementation-budget estimator is proposed, which utilizes an explicit mapping to RKHS using random Fourier features (RFF). The proposed RFF based estimator achieves equivalent/better performance as compared to its dictionary-based counterpart and has a finite memory requirement that makes the estimator attractive for practical implementation. Simulations are performed over realistic radar scenarios, that suggest the viability of the proposed RFF based estimator.