Assessment of Quad-Frequency Long-Baseline Positioning with BeiDou-3 and Galileo Observations

Abstract

Quad-frequency signals have thus far been available for all satellites of BeiDou-3 and Galileo systems. The major benefit of quad-frequency signals is that more extra-wide-lane (EWL) combinations can be formed with quad-frequency than with triple- or dual-frequency, of which the ambiguities can be fixed instantaneously in medium and long baselines. In this paper, the long-baseline positioning algorithm based on optimal triple-frequency EWL/wide-lane (WL) combinations of BeiDou-3 and Galileo is proposed. First, the theoretical precision of multi-frequency combinations of BeiDou-3 and Galileo is studied, and EWL/WL combinations with a small noise amplitude factor and a small ionospheric scalar factor are selected. Then, geometry-free methods are used to estimate the a priori precision of EWL/second EWL/WL signals for different combination schemes. Second, the double-differenced (DD) geometry-based function models of quad-frequency configurations and three different triple-frequency configurations are given, and the DD ionospheric delays are estimated as unknown parameters. In the end, the real BeiDou-3 and Galileo data are used to evaluate the positioning preference. The results show that, when using fixed EWL observations to constrain WL ambiguities, the proposed triple-frequency EWL/WL signals composed of (B1I,B3I,B2a) of BeiDou-3 and (E1,E5a,E6) of Galileo can achieve the same precision as the quad-frequency signals. Therefore, the method proposed in this article can realize long-baseline instantaneous decimeter-level positioning while reducing the dimension of matrix and improving calculation efficiency.

Single-Epoch Decimeter-Level Precise Point Positioning with a Galileo Five-Frequency Ionosphere-Reduced Combination

“…For the E1/E5a/E6/E5b/E5 five-frequency case, the linear combination of observation based on integer coefficients can be expressed as [22,29]:…”

Application of Variational Bayesian Filtering Based on T-Distribution in BDS Dynamic Ambiguity Resolution

“…Geng [9] used 31 days of three-frequency multi-GNSS data from 76 stations in Asia and Oceania, replaced the pseudo-range observation values of ultra-wide lane and wide lane with fixed ambiguity, improved the convergence of narrow lane ambiguity, and shortened the average initialization time of narrow lane by 3 minutes. Liu [10] respectively used two four-frequency high-quality ultrawide lane combined observations of BDS-3 and Galileo with fixed ambiguity to constrain the solution of wide lane ambiguity, and increased the precision of floating point solution of wide lane ambiguity. At present, the relative positioning under dynamic conditions mostly uses the combination of three frequency signals, and four frequency signals can form more high-quality combined observations than three frequency signals.…”