Improving GNSS triple-frequency cycle slip repair using ACMRI algorithm

Abstract

The processing of GNSS triple-frequency cycle slips is an important prerequisite for providing high-precision location services. Cycle slip detection is achieved by constructing a group of detection combinations, namely two geometry-free phase combinations and one pseudo-range phase combination of GNSS observations. However, cycle slip estimation would be strongly affected by ill-conditioned equations, which means that even a slight fluctuation in the observations will cause large biases to the final results. To deal with this problem, a new cycle slips estimation algorithm of adjusting coefficient matrix based on residual information (ACMRI algorithm) is proposed. In our algorithm, a parameter k is utilized to adjust the coefficient matrix of the normal equation to compensate for the deviation of the observations, so as to reduce the influence of the ill-conditioned normal equation. However, it is significantly challenging to search for the value of k. To solve this difficulty, we firstly developed a new way to obtain the search region of the parameters using the method of statistics–verification–optimization based on numerous experiments. Then, a new two-order search method, based on the principle of minimum least-square residual and rounding residual, is proposed. Once the cycle slips are determined, the two residuals are used as the reliability index of cycle slips repair. Two geometry-free phase combinations [1 1– 2], [1 –2 1] and one pseudo-range phase combination [1 4 –5] are selected for the experiments using BDS2, BDS3, GPS, and Galileo observations. Experimental results show the proposed algorithm improves the success rates of triple-frequency cycle slips repair from least-squares solution rates of 89.3% (Galileo), 14.5% (BDS2), and 48.1% (BDS3) to 100% for all systems, and reduces the RMS error of the residual between the float solutions of cycle slips and their true values more than 90% compared with the least-squares method. To further evaluate the feasibility of the algorithm, 60 groups of combinations are set for the four GNSS systems. Results indicate that the proposed algorithm can significantly improve the triple-frequency cycle slip estimation and the success rate of cycle slip repair for all combinations of all the four systems.