Triple-Frequency Code-Phase Combination Determination: A Comparison with the Hatch-Melbourne-Wübbena Combination Using BDS Signals

Abstract

Considering the influence of the ionosphere, troposphere, and other systematic errors on double-differenced ambiguity resolution (AR), we present an optimal triple-frequency code-phase combination determination method driven by both the model and the real data. The new method makes full use of triple-frequency code measurements (especially the low-noise of the code on the B3 signal) to minimize the total noise level and achieve the largest AR success rate (model-driven) under different ionosphere residual situations (data-driven), thus speeding up the AR by directly rounding. With the triple-frequency Beidou Navigation Satellite System (BDS) data collected at five stations from a continuously-operating reference station network in Guangdong Province of China, different testing scenarios are defined (a medium baseline, whose distance is between 20 km and 50 km; a medium-long baseline, whose distance is between 50 km and 100 km; and a long baseline, whose distance is larger than 100 km). The efficiency of the optimal code-phase combination on the AR success rate was compared with that of the geometry-free and ionosphere-free (GIF) combination and the Hatch-Melbourne-Wübbena (HMW) combination. Results show that the optimal combinations can always achieve better results than the HMW combination with B2 and B3 signals, especially when the satellite elevation angle is larger than 45 • . For the wide-lane AR which aims to obtain decimeter-level kinematic positioning service, the standard deviation (STD) of ambiguity residuals for the suboptimal combination are only about 0.2 cycles, and the AR success rate by directly rounding can be up to 99%. Compared with the HMW combinations using B1 and B2 signals and using B1 and B3 signals, the suboptimal combination achieves the best results in all baselines, with an overall improvement of about 40% and 20%, respectively. Additionally, the STD difference between the optimal and the GIF code-phase combinations decreases as the baseline length increases. This indicates that the GIF combination is more suitable for long baselines. The proposed optimal code-phase combination determination method can be applied to other multi-frequency global navigation satellite systems, such as new-generation BDS, Galileo, and modernized GPS.

Characteristics of BeiDou Navigation Satellite System (BDS) Code Observations for Different Receiver Types and Their Influence on Wide-Lane Ambiguity Resolution

“…For dual-frequency users, the Melbourne–Wübbena (MW) combination is usually used to resolve wide-lane ambiguity. The MW combination is a linear combination of both carrier phase and code observables, which is defined as [ 7 , 9 , 21 , 22 , 23 ]: …”

Reliable real-time triple-frequency cycle slip detection and recovery with adaptive detection thresholds

“…Besides the above three combinations, an additional determination of cycle slips on a code-phase combination is employed, to reduce the ill-conditioned problem caused by the large conditional number of the coefficient matrix in the original observation equations. The fourth combination T 4 is also geometry-free, with the phase observation ϕ (1,1,−2) = ϕ 1 + ϕ 2 − 2ϕ 3 and three original code observables, and can be referred to in [16]. If the ionosphere residual on B1 between adjacent epochs is no more than 10 cm, this combination can achieve a 99.99% success rate of ambiguity resolution by directly rounding.…”

Reconstructing GNSS Meta-Signal Observations Using Sideband Measurements

“…This characteristic has opened several possibilities at both the measurement and signal processing levels. Significant work has been performed to optimally combine measurements from several frequencies (Deng et al, 2018;Li, 2018;Richert & El-Sheimy, 2007) in efforts to eliminate the impact of ionospheric delay, reduce noise, and improve the ambiguity resolution process in carrier-phase positioning. At the signal processing level, the concept of meta-signals (Issler et al, 2010;Paonni et al, 2014) has been introduced: A meta-signal is obtained when two (or more) GNSS components are considered together and processed as a single entity to obtain better tracking performance and high-accuracy code measurements.…”