In this paper, we demonstrate fixed-point FPGA implementations of state space systems using Particle Filters, especially multi-target beating and range tracking systems. These trackers operate either as independent organic trackers or as a joint tracker to estimate a moving target's state in the x-y plane. For the efficiency of the particle filter, we consider factorized posterior approximations based on the Laplacian approximation, which uses a Newton-Raphson search. We delineate the computation and memory resources needed for real-time performance of the range and bearing particle filter trackers. Our implementations are demonstrated using the Xilinx System Generator. As part of the FPGA implementation, a floating-point, soft- and hard-core implementation of the Newton search algorithm is also developed.