This thesis presents a paradigm for accelerating the Cauchy Estimator using high performance computing for discrete linear systems with scalar process and measurement noises. The Cauchy Estimator is developed in such a way that is conducive to parallelization and thus presents an opportunity to leverage the graphics processing unit (GPU) to bring the algorithm closer to a real time environment. This work compartmentalizes the estimator into smaller routines and presents algorithms that were developed to accelerate the computations across several independent terms. First, the serial implementation is given for comparison and to help build intuition. Then, the GPU implementation is given along with the parameter sending and receiving requirements for each function. Simulations demonstrate that parallelization does eventually outpace the serial implementation along with an almost linear scaling in time after each subsequent measurement.