Theoretical Analysis and Experimental Evaluation of Wide-Lane Combination for Single-Epoch Positioning with BeiDou-3 Observations

Multi-frequency signals can enable some wide-lane (WL) observations to achieve instantaneous ambiguity resolution (AR) in complex scenarios, but simply adding WL observations will also place additional pressure on real-time kinematic data transmission. With the official service of the third-generation Beidou Navigation Satellite System, which broadcasts five-frequency signals, this dilemma has become increasingly evident. It is significant to explore multi-frequency observation combination methods that take into account both positioning precision and data transmission burden. In this work, we use the least squares method to derive the theoretical precision of the single-epoch WL combination of 16 schemes with varying frequency numbers (three or more) under the ionosphere-fixed model and the ionosphere-float model. The baseline solutions of 4.3 km and 93.56 km confirm that the positioning results are broadly consistent with the theoretical derivations under both models. In the ionosphere-fixed mode, the five-frequency scheme (B1C, B1I, B3I, B2b, B2a) yields the best positioning performance, improving the 3-dimensional positioning error standard deviation, circle error probable (CEP), and spherical error probable at 75% probability by 7.8%, 11.5%, and 6.7%, respectively, compared with the optimal triple-frequency scheme (B1C, B3I, B2a). Under the ionosphere-float model, the quad-frequency scheme (B1C, B3I, B2b, B2a) provides the best positioning performance, with only the CEP at 75% improving by 1.3% over the triple-frequency scheme. Given that the optimal triple-frequency scheme has a lower data volume, this work recommends it as the preferred scheme.