An Approach for a Faster GPS Tracking Extended Kalman Filter

GPS is capable of providing 100 m level accuracy for a great number of users worldwide. In GPS, range and range-rate data can be used with satellite position and velocity to compute user position and velocity using an extended Kalman filter (EKF). However, the EKF is computationally intensive, leading to difficulties in broadband real-time applications. Hence, it is necessary to resort to techniques to improve EKF speed. Therefore, in this paper, the EKF matrices are analyzed in detail, exploiting the sparsity and structure of the EKF matrices to reduce the number of computations. A typical trajectory is simulated, and a comparison of the computation speed of sequential implementations of EKF, both with and without the proposed reduction of computations, is reported. Further, an algorithm is developed to obtain an initial estimate of user position and velocity which is used to initialize the state vector of the EKF algorithm.