Research on utilizing inexpensive and personal-level parallel computing architectures to speed up the implementation of the class of particle filters is proposed. This study will leverage NVIDIA Graphics Processing Units (GPUs) and multi-core CPUs that are quickly becoming commonly available for engineering communities. Parallelization of the Unscented Kalman filter and the bootstrap particle filter with applications in INS/GPS integration and the orbital determination problem will be the focus of the phase I research. This research will contribute to upgrading the current fleet of NASA navigation software which heavily rely on Kalman filters and EKF and are quickly becoming outdated. Over the last couple of decades, great advancement has been made in improving filter accuracy in nonlinear applications with non-Gaussian noise models. One of the advanced techniques is particle filters which, if properly applied, are more accurate than the EKF for nonlinear and non-Gaussian applications. One drawback of the particle filters is the excessive computational burden if implemented on a serial computer. However, since the majority of the computation can be carried out simultaneously, the particle filters inherently are well suited for parallel computing. The objective of the Phase I effort is to leverage GPUs and multi-core CPUs to exploit such parallelism. With the performance of these devices improving at a rapid pace, it is anticipated that they will quickly find their way to onboard avionics, and this research paves the way for implementing particle filters in real-time applications. This will bring unprecedented accuracy and applicability of particle filters to aircraft and spacecraft navigation analyses for NASA and a wide range of non-NASA applications.