Complexity reduction of the Kalman filter-based tracking loops in GNSS receivers
In modern GNSS receivers, using a Kalman filter in each signal tracking loop presents remarkable advantages in terms of accuracy and robustness against malicious noise sources, but poses critical issues in real-time applications due to the high computational cost. For this reason, we propose an efficient method to dramatically reduce the number of operations involved in the execution of the Kalman filter. In particular, the relationship between Kalman gain and noise covariances is analyzed in detail, showing that the gain computation can be greatly simplified by using an appropriately calibrated, small-size lookup table (LUT). The loss of performance of the proposed method, due to its inherent approximations, is shown to be negligible with respect to a traditional implementation upon careful system model and LUT calibration. Furthermore, a very fast signal tracking recovery after an outage is guaranteed. The implementation complexity of the simplified LUT-based method is compared with traditional approaches, proving that the proposed method has a tremendous advantage in terms of computational and storage requirements.