A Novel Fast GNSS Positioning Algorithm

Classic GNSS pseudo-range positioning algorithm, Gauss-Newton iteration algorithm, largely dependent on the initial-value. A bad initial-value of Gauss-Newton iteration algorithm will need more iterations calculation for algorithm converging and each iterative calculation involves matrix multiplication and inversion, which will lead to a calculation surge. An important parameter of receiver, TTFF (Time to First Fix), is directly affected. Direct calculation method doesn’t require initial-value and iteration calculation, characteristic of small amount of calculation, however it’s positioning accuracy worse than Gauss-Newton iteration’s. To address the issue mentioned above, a two-step fast positioning algorithm is proposed in this paper. The first, calculate the initial position by the direct solution algorithm. The second, expand the distance equations using Taylor expansion at the initial position, then calculate corrective position with weighted least squares. Initial position adjusted with corrective position is the receiver position. The new algorithm significantly reduces computation under the premise of guarantee of positioning accuracy. The new algorithm has important engineering significance. Simulation results show the effectiveness of the new algorithm.