Relationship between the delay and Doppler shift with the radar return is non-linear in nature. Therefore a non-linear estimator based on sparse kernel least mean square algorithm is proposed. Further, an adaptive kernel width optimization technique is proposed to lower the computational complexity and for simple implementation. An expression for the Cramer-Rao lower bound is derived and validated for the proposed estimator over linear frequency modulated, and orthogonal frequency division multiplexed radar systems.

In this work we propose, kernel maximum correntropy based non-linear estimators for range and velocity estimation in non-Gaussian clutter and system-nonlinearity. The proposed estimators are analyzed for linear frequency modulated and stepped frequency radar systems. Additionally, an adaptive update equation is derived for optimization of the kernel-width, which further lowers the dictionary-size, and variance of the proposed estimators. For performance evaluation of the proposed estimators, an expression is derived for the Cramer-Rao lower bound using a modified Fisher information matrix.

In this paper, a kernel minimum error entropy (KMEE) based estimator is proposed for the estimation of multiple targets' direction of departure (DOD), the direction of arrival (DOA), and the Doppler shift with multiple input multiple output radar in the presence of non-Gaussian clutter. Most existing estimation approaches are based on optimization of a complex cost function which often leads to a sub-optimum solution. Therefore, for the accurate estimation of DOD, DOA and Doppler shift, an efficient, kernel adaptive filter (KAF) based estimation approach is proposed. The proposed estimator utilizes the minimum error entropy (MEE) criterion and minimizes the error entropy function. The MEE, being an information-theoretic criterion, optimizes the higher-order statistics of error and thus makes the proposed estimator robust against the effects of outliers like clutter. The KMEE based estimator without any sparsification suffers from a linear increase in computational complexity. Thus, subsequently, the computational complexity of the proposed KMEE based estimator is reduced by incorporation of novelty criterion (NC) based sparsification technique, and the resulting estimator is called KMEE-NC. The performance of the proposed KMEE-NC based estimator is compared with the recently introduced sparse estimators based on kernel maximum correntropy criterion, and kernel minimum mean square error criterion. Additionally, KMEE-NC based estimator is also compared with other existing conventional estimators. Further, for assessing the accuracy of the proposed estimator, the modified Cramer-Rao lower bound is derived using the modified Fisher information matrix.

In radar, the measurements (like the range and radial velocity) are determined from the time delay and Doppler shift. Since the time delay and Doppler shift are estimated from the phase of the received echo, the concerned estimation problem is nonlinear. Consequently, the conventional estimator based on the fast Fourier transform (FFT) is prone to yield high estimation errors. Recently, nonlinear estimators based on kernel least mean square (KLMS) are introduced and found to outperform the conventional estimator. However, estimators based on KLMS are susceptible to incorrect choice of various system parameters. Thus, to mitigate the limitation of existing estimators, in this paper, two efficient low-complexity nonlinear estimators, namely, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are proposed. The EKF is advantageous due to its implementation simplicity; however, it suffers from the poor representation of the nonlinear functions by the first-order linearization, whereas UKF outperforms the EKF and offers better stability due to exact consideration of the system nonlinearity. Simulation results reveal improved accuracy achieved by the proposed EKF- and UKF-based estimators.