Particle filtering for target tracking using multi-input multi-output (MIMO) pulse-Doppler radars faces three long-standing obstacles: a) the absence of reliable likelihood models for raw radar data; b) the computational and statistical complications that arise when nuisance parameters (e.g., complex path gains) are augmented into state vectors; and c) the prohibitive computational burden of extracting noisy measurements of range, Doppler, and angles from snapshots. Motivated by an optimization-centric interpretation of Bayes' rule, this article addresses these challenges by proposing a new particle filtering framework that evaluates each hypothesized state using a tailored cost function, rather than relying on an explicit likelihood relation. The framework yields substantial reductions in both running time and tracking error compared to existing schemes. In addition, we examine the implementation of the proposed particle filter in MIMO orthogonal frequency-division multiplexing (OFDM) systems, aiming to equip modern communication infrastructure with integrated sensing and communications (ISAC) capabilities. Experiments suggest that MIMO-OFDM with pulse-Doppler processing holds considerable promise for ISAC, particularly when wide bandwidth, extended on-target time, and large antenna aperture are utilized.