Improved Multi-GNSS PPP Partial Ambiguity Resolution Method Based on Two-Step Sorting Criterion

Abstract

Multi-GNSS PPP partial ambiguity resolution (PAR) can improve the fixing success rate and shorten the time to first fix (TTFF). Ambiguity subset selection based on the bootstrapping success rate sorting criterion (BSSC) is widely used in PPP PAR due to its ease of computation and comprehensive evaluation of the global quality of ambiguity solutions. However, due to the influence of unmodeled errors, such as atmospheric residuals and gross errors, ambiguity parameter estimation will inevitably introduce bias. For ambiguity parameters with bias, their variance will converge incorrectly and will not accurately reflect the estimation accuracy. As a result, the selected ambiguity subset based on the BSSC becomes inaccurate, affecting the fixing success rate and TTFF. Therefore, we proposed an improved multi-GNSS PPP PAR method based on a two-step sorting criterion (TSSC). This method aims to address the influence of inaccurate variance of ambiguity parameters, particularly those with low observation quality, on the ambiguity subset selection based on the BSSC. The ambiguity subset satisfying the preset success rate threshold is selected to reduce the influence of unconverged ambiguity on the TSSC. In the first step of the sorting process, the observations whose elevation angle is below 30° or whose posterior residual falls into the IGG3 model reduction domain are clustered together. The posterior observation weight criterion (POWC) instead of the BSSC is adopted to sort ambiguities to overcome the false convergence of variance of ambiguity parameters. In the second step of the sorting process, the remaining ambiguities with reasonable variances are sorted based on the BSSC. Finally, the bottom ambiguity is removed one by one from the ambiguity subset sorted based on the two-step sorting criterion (TSSC) until the requirements of the ratio test for LAMBDA are met. The static data from 10 MGEX stations over a period of 30 days, along with urban kinematic data, were collected to validate the proposed method. Compared with the PAR based on the BSSC, the static experiments demonstrated a reduction of 8.7% and 16.8% in the TTFF and convergence time, respectively. Additionally, the positioning accuracy in the east, north, and up directions was improved by 20.1%, 17.1%, and 4.67%, respectively. Furthermore, the kinematic experiment revealed that the TTFF and convergence time decreased from 1.65 min and 10.5 min to 1.3 min and 1.8 min, respectively, with higher positioning accuracy.