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A number of extensions of the famous Kalman filter exist for recursive Bayesian estimation of state vectors with nonlinear update equations and non-Gaussian prior probability density functions. Two of the most powerful are the particle filter, which uses a direct Monte Carlo approach, and the histogram filter, which uses a grid-based approach. Both filters are numerical implementations of recursive Bayesian estimation. The histogram filter uses a grid based approach that is analogous to midpoint rectangular integration, while the particle filter uses a Monte Carlo approach. Their performance is compared for a passive, model-based localization problem in which the target is broadcasting a low-frequency tonal signal while moving through a shallow water waveguide. The state vector being estimated includes range, depth, and source level. Target dynamic models allow for slow changes in velocity, depth, or source level. The example uses RAM realizations with additive noise as a synthetic received signal. In situations where computational power is restricted, the particle filter consistently outperforms the histogram filter in localizing the target. However, with sufficient computational power the performance is equivalent. [This work was sponsored by ONR Undersea Signal Processing.]