College of Information and Navigation, Air Force Engineering University, Xi’an 710077, China.

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Abstract—According to the dynamic GPS rapid positioning ambiguity resolution problems, a modified algorithm for rapid integer ambiguity resolution is proposed. Firstly, a method of QR decomposition is applied on the observation matrix to construct the left null space matrix in order to construct the left null space matrix, so as to decrease dimensions of the matrix and to satisfy rapid ambiguity resolution by matrix transformation that can separate out the ambiguity parameter from the position parameter. Kalman filter is applied only to estimate the ambiguity parameters in order to acquire the real-time ambiguity float solution. Then, ordering and multi-time (inverse) paired Cholesky decomposition are adopted for decorrelation of ambiguity. One applies diagonal elements preprocessing, sorts diagonal elements according to the results of Cholesky decomposition, thus to improve the efficiency of decomposition and decorrelation. Lastly, the LAMBDA method is used for searching the fixed integer ambiguity. To verify the correctness and effectiveness of the proposed algorithm, the static and kinematic tests are carried out. Experimental results show that this algorithm has good performance of decorrelation and precision of float solution. It also can effectively improve computation speed. The final positioning accuracy result with static baseline error less than 1cm and kinematic error less than 2cm.The method may be used in areas requiring accurate positioning such as kinematic navigation and geodesy.

Index Terms—GPS, Integer ambiguity, QR decomposition, multi-time (inverse) paired Cholesky decomposition.

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Cite: Rong Duan , Xiubin Zhao, Chunlei Pang, Ang Gong, "Rapid Ambiguity Resolution for Single Frequency GPS Kinematical Positioning Based on Left Null Space Theory," Journal of Computers vol. 11, no. 1, pp. 52-61, 2016.