A grid-based Bayesian tracking approach is proposed that uses the observed measurements to guide the sampling of the likelihood function during the measurement update step. This leads to computational savings over standard sampling methods while also pro-viding a more accurate estimate of the likelihood function. The likelihood model assumes an exponential distribution of returns with a mean based on a predictive model that incorporates an assumed signal-to-noise ratio (SNR) of the targets, background clutter, beam response, and waveform ambiguity functions. Two variations of an example based on simulated frequency modulated (FM) and continuous wave (CW) signals are used to assess target detection, localization, and computational performance.