Radar tracking filters are generally computationally expensive, involving the manipulation of large matrices and deeply nested loops. In addition, they must generally work in real-time to be of any use. The now-common Kalman Filter was developed in the 1960's specifically for the purposes of lowering its computational burden, so that it could be implemented using the limited computational resources of the time. However, with the exponential increases in computing power since then, it is now possible to reconsider more heavy-weight, robust algorithms such as the original nonrecursive Gauss-Newton filter on which the Kalman filter is based. This dissertation investigates the acceleration of such a filter using FPGA technology, making use of custom, reduced-precision number formats.