In this article, we propose kernel maximum correntropy based nonlinear 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 the 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.