Particle filtering algorithms have enabled practical solutions to problems in autonomous robotics (self-driving cars, UAVs, warehouse robots), target tracking, and econometrics, with further applications in speech processing and medicine (patient monitoring). Yet, their inherent weakness at representing the likelihood of the observation (which often leads to particle degeneracy) remains unaddressed for real-time resource-constrained systems. Improvements such as the optimal proposal and auxiliary particle filter mitigate this issue under specific circumstances and with increased computational cost. This work presents a new particle filtering method and its implementation, which enables tunably-approximative representation of arbitrary likelihood densities as program transformations of parametric distributions. Our method leverages a recent computing platform thatcan perform deterministic computation on probability distributionrepresentations (UxHw) without relying on stochastic methods. For non-Gaussian non-linear systems and with an optimal-auxiliary particle filter, we benchmark the likelihood evaluation error and speed for a total of 294840 evaluation points. For such models, the results show that the UxHw method leads to as much as 37.7x speedup compared to the Monte Carlo alternative. For narrow uniform measurement uncertainty, the particle filter falsely assigns zero likelihood as much as 81.89% of the time whereas UxHw achieves 1.52% false-zero rate. The UxHw approach achieves filter RMSE improvement of as much as 18.9% (average 3.3%) over the Monte Carlo alternative.