A single difference-based multi-GNSS inter-system model with consideration of inter-frequency bias and inter-system bias

Ambiguity resolution (AR) is fundamental to achieve high-precision solution in GNSS (Global Navigation Satellite System) relative positioning. Extensive research has shown that systematic errors are associated with the performance of AR. However, due to the physical complexity, some systematic errors would inevitably remain in the observation equations even after processed with some popular models and parameterization. In the medium and long baselines, these unmodeled errors are the leading cause of the slow or even incorrect fixation of ambiguity. Therefore, to improve the AR performance in the medium and long baselines, we present a procedure with the careful consideration of unmodeled errors. At first, we develop a method to estimate the unmodeled errors based on the float ambiguity bias. Then, the overall procedure and key steps to fix the float solutions corrected by the unmodeled error estimate is designed. Finally, some real-measured baselines (from 68 km to 120 km) are utilized to validate the proposed procedure. The experimental results are analyzed and discussed from the aspects of AR and positioning, respectively. For the AR performance, the time required for the first fixation have been reduced by about 41.58% to 83.51%, from 12 to 100 min. Besides, 12.72% to 48.59% and 2.96% to 36.28% improvements of the ambiguity-fixed rate and the ambiguity-correct rate can be respectively obtained in the four baselines. As for the positioning performance, the mean values and RMSEs have improved by 0.2 to 4.8 cm (1.63% to 22.43%) and 0.2 to 2.8 cm (1.47% to 10.57%), respectively.

Section: Discussionmentioning

confidence: 99%

“…Global navigation satellite system (GNSS) is essential for a wide range of fields in human society [1,2]. Carrier phase observation plays a critical role in the achievement of highprecision positioning and navigation [3].…”

Section: Introductionmentioning

confidence: 99%

Improving the ambiguity resolution with the consideration of unmodeled errors in GNSS medium and long baselines

Wang,

2024

“…The global navigation satellite system (GNSS) is widely used in many aspects of geodesy, engineering measurements, and precise navigation owing to its unique advantages [1][2][3][4]. However, unmodeled errors are commonly present in GNSS data processing models owing to interference or imperfections in the mathematical models [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A method for separating unmodeled errors in GNSS based on the constraint of the prior variance of unit weight

Wang

2023

In Global Navigation Satellite System (GNSS) positioning, some unmodeled errors critically affect the accuracy and reliability of positioning solutions. When the unmodeled errors are significant in the mathematical model, they are mainly processed by choosing the adjustment models with additional systematic error parameters or semiparametric estimation. However, many existing methods tend to require knowledge of the prior information of unmodeled errors; otherwise, achieving better processing results is difficult. To address this problem, this paper proposes a GNSS unmodeled error separation method that does not rely on prior information of unmodeled errors. This method is built based on the constraint of the prior variance of unit weight. To begin with, the method effectively separates the effect of unmodeled errors in the residuals under this constraint. Secondly, the initial estimate of unmodeled errors in the observation domain is used as a virtual observation. Thus, the optimal estimate and variance of unmodeled errors are obtained. Finally, the observations are effectively corrected by combining the ideas of mean shift and variance inflation. In this paper, multiple sets of experiments are conducted. The results show that the proposed method can effectively weaken the impact of unmodeled errors on the float and fixed solutions of GNSS positioning, whether the unmodeled errors exist in a single observation or multiple observations.

“…Gao et al [24] proposed an ambiguity transfer program to overcome this problem, and the method was utilized by Liu et al [25,26] to calculate the interfrequency biases between GPS and BDS. Mi et al [27] and Shang et al [28] adopted a single difference (SD) model to maintain consistency of F-ISPB. The SD model can also be used to calculate the F-ISPB between frequency division multiple access (FDMA) signals and code division multiple access (CDMA) signals after correcting GLONASS inter-frequency phase bias [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Multi-GNSS inter-system model for complex environments based on optimal state estimation

Shang¹,

Gao²,

Gao³

et al. 2021

Self Cite

When calibrating inter-system biases (ISB), especially the fractional part of inter-system phase biases (F-ISPB), a multi-GNSS inter-system model can effectively improve positioning performance under a complex environment. Usually, the F-ISPB is estimated after fixing the intra-system ambiguities. However, this approach seems inapplicable when it is difficult to obtain intra-system ambiguities under a complex environment. A multi-dimensional particle filter (PF)-based F-ISPB estimate method has been proposed to overcome the problem. Nevertheless, the multi-dimensional PF involves a great quantity of computations. In this contribution, four state optimal estimate-based F-ISPB handling schemes are proposed: step-by-step PF, step-by-step particle swarm optimization (PSO), multi-dimensional PF, and multi-dimensional PSO-based F-ISPB estimate methods. Two baselines were selected to investigate the F-ISPB estimate performance in both open and complex environments. The results show that due to the potential of the wrong F-ISPB to bring about the maximum ratio for a long time during the initial stage, the step-by-step PF method can achieve better performance than step-by-step PSO. Besides, the two-dimensional results show that all of the F-ISPB still cannot be extracted under complex environments by multi-dimensional PSO. Furthermore, compared with step-by-step PF, the multi-dimensional PF method costs too much to obtain the right value. For example, in the two-dimensional case, the step-by-step PF searches 200 times for each epoch, while the two-dimensional PF requires 40 000 times for each epoch, so it is difficult for receivers to provide hardware support for this method. In addition, the step-by-step PF can obtain the right F-ISPB with about 100 epochs no matter what scenario. Thus, under challenging observation scenarios, a step-by-step PF method is recommended to extract the F-ISPB.