Multi-dimensional particle filter-based estimation of phase line biases for single-differenced ambiguity resolution in GNSS-based attitude determination

Abstract

Global navigation satellite systems (GNSSs) have been widely used to provide real-time and high-precision attitude information for land vehicles, ships and aircraft over the past few decades. With the joint use of emerging multi-GNSS common-clock receivers and the single-differenced (SD) model, the accuracy of pitch and roll can be significantly improved to the same level as that of yaw. However, the prerequisite is that the frequency-dependent phase line biases (LBs) in multiple GNSS systems and frequencies are accurately and rapidly estimated. In this contribution, we intend to solve this problem by using a multi-dimensional particle filter (PF)-based approach. We first investigate the relationship between the ratio value and the multi-dimensional phase LBs. Results have revealed that the ratio value can be used to judge the quality of multi-dimensional phase LBs and represent the likelihood function of the observations. We then present the procedure of multi-dimensional PF-based phase LBs estimation for SD ambiguity resolution and attitude determination. An improved strategy is also proposed to reduce the computation time. Finally, we take the two-dimensional case as a representative example to evaluate the performance of the proposed method in aspects of the convergence and accuracy of phase LB estimates, the attitude determination accuracy, and the computation time. Experimental results from two static datasets have demonstrated that the two-dimensional phase LBs basically rapid converge within 20 epochs. Moreover, compared with the double-differenced method, the proposed multi-dimensional PF-based SD method could provide comparable yaw accuracy and much better pitch accuracy. The pitch accuracy is improved to the same level as yaw by approximately 42.9%–50.0%. With regard to the computation time, it is found that with the proposed modification strategy, the single-epoch computation times are significantly reduced by approximately 90.7%–93.5%, and they are mostly within 0.05 s for most of the epochs on a personal computer.