FAST INTEGER AMBIGUITY RESOLUTION IN GPS KINEMATIC POSITIONING USING LEFT NULL SPACE AND MULTI-TIME (INVERSE) PAIRED CHOLESKY DECORRELATION

Abstract

Aiming at the problems that huge amount of computation in ambiguity resolution with multiple epochs and high-order matrix inversion occurred in the GPS kinematic relative positioning, a modified algorithm for fast integer ambiguity resolution is proposed. Firstly, Singular Value Decomposition (SVD) is applied to construct the left null space matrix in order to eliminate the baselines components, which is able to separate ambiguity parameters from the position parameters efficiently. Kalman filter is applied only to estimate the ambiguity parameters so that the real-time ambiguity float solution is obtained. Then, sorting and multi-time (inverse) paired Cholesky decomposition are adopted for decorrelation of ambiguity. After diagonal elements preprocessing and diagonal elements sorting according to the results of Cholesky decomposition, the efficiency of decomposition and decorrelation is improved. Lastly, the integer search algorithm implemented in LAMBDA method is used for searching the integer ambiguity. To verify the validity and efficacy of the proposed algorithm, static and kinematic tests are carried out. Experimental results show that this algorithm has good performance of decorrelation and precision of float solution, with computation speed also increased effectively. The final positioning accuracy result with static baseline error less than 1 cm and kinematic error less than 2 cm, which indicates that it can be used for fast kinematic positioning of high precision carrier.