WF-LLL: An LLL Method Based on Whitening Filter for GPS Ambiguity Decorrelation

Ambiguity resolution of GPS carrier phase observables is crucial in high precision geodetic positioning and navigation applications. In order to achieve high precision results within a short observation time span, the integer nature of the ambiguity has to be exploited. In this paper, An LLL method based on whitening filter (WF-LLL) is presented by analyzing the LLL method for ambiguity decorrelation. This method uses whitening filter algorithm and the sort matrix to improve the performance of LLL method. The sort matrix includes both an ascending and a descending matrix. Comparisons have been made between the performances of the LLL, WF-LLL and LAMBDA method, using 300 symmetric and positive definite matrixes derived from a random simulation. Numerical simulations show that the proposed WF-LLL method has the same performace with LAMBDA method on decreasing matrix condition number, while achiving better result than LLL method. Thus, the WF-LLL algorithm can reduce the searching time of ambiguity solutions.