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. 2020 Mar 10;20(5):1534.
doi: 10.3390/s20051534.

Extra-Wide Lane Ambiguity Resolution and Validation for a Single Epoch Based on the Triple-Frequency BeiDou Navigation Satellite System

Jian Deng  1   2 , Aiguo Zhang  1   2 , Nenghui Zhu  3 , Fuyang Ke  4
Affiliations

Extra-Wide Lane Ambiguity Resolution and Validation for a Single Epoch Based on the Triple-Frequency BeiDou Navigation Satellite System

Jian Deng et al. Sensors (Basel). .

Abstract

The ambiguity resolution (AR) and validation of the global navigation satellite system (GNSS) have been challenging tasks for some decades. Considering the reliability problem of extra-wide-lane (EWL) ambiguity in the triple-carrier ambiguity resolution (TCAR), a method for validating the reliability of the EWL ambiguity using a single epoch was proposed for the BeiDou Navigation Satellite System (BDS). For the initial EWL ambiguity, obtained using a rounding estimator with a geometry-free (GF) model, the double-difference ionospheric delay was first estimated to construct a relative positioning model with an initial fixed ambiguity. Second, based on the theory of gross error detection and the AR characteristics of EWL, the second-best ambiguity candidate was constructed. Finally, among the two sets of ambiguities, the one with the smaller posterior variance was taken as the reliable ambiguity. The study showed that, for a single epoch, when only one or two satellites had incorrect ambiguities, the AR success rate after ambiguity validation and correction could reach 100% for medium baselines. For long baselines, due to the increase of atmospheric error, the validation was affected to some extent. However, the AR success rates for two long baselines increased from 96.82% and 98.44% to 98.80% and 99.67%, respectively.

Keywords: BDS; EWL ambiguity resolution; gross error detect; reliability; triple-frequency.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Ambiguity resolution (AR) success rate using four observations with different noise levels and double-difference (DD) ionospheric delays: (a) DD ionospheric delay ΔI=40cm and (b) DD ionospheric delay ΔI=100cm.
Figure 2
Figure 2
Ambiguity ΔN(1,4,−5) biases with four different combined observations: (a) using observation ΔP(−5,2,2.65), (b) using observation ΔP(1,0,0), (c) using observation ΔP(0,1,1), and (d) using observation Δϕ(0,−1,1).
Figure 3
Figure 3
Performance of fixed ambiguity (a) and DD ionospheric delay (b) for satellite C05.
Figure 4
Figure 4
Method for validating the reliability of the EWL ambiguity ΔN(1,4,−5). LS: Least-squares estimation.
Figure 5
Figure 5
Distribution of BeiDou Navigation Satellite System (BDS) satellites at station TAOY.
Figure 6
Figure 6
Performance of fixed ambiguity (a) and standardized residuals (b) for satellites C07, C12, and C14.
Figure 7
Figure 7
Fixed ambiguity from the 1490th to the 1600th epoch for satellites C07, C12, and C14.
Figure 8
Figure 8
The performance of the posterior variance (a) with the initial ambiguity, (b) with candidate ambiguity during the first detection, (c) with the ambiguity after the first detection, and (d) with the final ambiguity.
Figure 9
Figure 9
Performance of the float ambiguity for the satellites C01, C02, and C04.
Figure 10
Figure 10
The performance for the posterior variance (a) with the initial ambiguity, (b) with the candidate ambiguity, and (c) with the final ambiguity.
Figure 11
Figure 11
The performance for the fixed ambiguity for satellite C04 (a) without ambiguity validation and (b) with ambiguity validation.
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