Efficient Mapping of a Kalman Filter into an FPGA using Taylor Expansion

The Kalman filter is widely used as an estimator in many modern applications. In the case where its implementation in hardware is required, the computational complexity of the algorithm dictates the use of many resources. This paper presents an approximation of the conventional Kalman filter by using Taylor expansion and matrix calculus in order to remove the hardware expensive part of the algorithm. The Bierman-Thornton algorithm, as the exact counterpart of our proposed Approximate Kalman filter algorithm, is also implemented for comparison purposes. Comparing to the Bierman-Thornton algorithm, the FPGA implementation results demonstrate that our proposed Approximate Kalman filter implementation achieves one order of magnitude higher throughput using less hardware resources, obtaining similar convergence rate and accuracy.