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The positioning accuracy of the BeiDou Navigation Satellite System (BDS) can reach up to 10 m (95% confidence level) in both horizontal and vertical components. In order to improve the positioning performance for metre-level navigation, BDS pseudorange differential positioning has been proposed. We introduce the basic principles of BDS pseudorange differential positioning. Then based on the traditional Hatch filter, a modified Hatch filter for dual-frequency phase-smoothed pseudorange is introduced. The phase-smoothed pseudorange differential positioning, whose observations are smoothed by the modified Hatch filter using BDS B1 and B3 and Global Positioning System (GPS) L1 and L2 carrier-phase observations, are applied to determine the roving station's position. Three strategies are used for results analysis. The results show that the longer the baseline length is, the poorer positioning accuracy gets, and the positioning accuracy decline rate of the BDS B3 signal is higher than that of the BDS B1 signal, especially for long baselines. The percentages of the position deviations less than 3 m in horizontal component and 5 m in vertical component for BDS signals can reach up to 95 %.2. Phase-smoothed pseudorange differential positioning. 3. Dual-frequency phase smoothing.4. Baseline length.

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The loose combination (LC) and the tight combination (TC) are two different models in the combined processing of four global navigation satellite systems (GNSSs). The former is easy to implement but may be unusable with few satellites, while the latter should cope with the inter-system bias (ISB) and is applicable for few tracked satellites. Furthermore, in both models, the inter-frequency bias (IFB) in the GLObal NAvigation Satellite System (GLONASS) system should also be removed. In this study, we aimed to investigate the performance difference of ambiguity resolution and position estimation between these two models simultaneously using the single-frequency data of all four systems (GPS + GLONASS + Galileo + BeiDou Navigation Satellite System (BDS)) in three different environments, i.e., in an open area, with surrounding high buildings, and under a block of high buildings. For this purpose, we first provide the definition of ISB and IFB from the perspective of the hardware delays, and then propose practical algorithms to estimate the IFB rate and ISB. Thereafter, a comprehensive performance comparison was made between the TC and LC models. Experiments were conducted to simulate the above three observation environments: the typical situation and situations suffering from signal obstruction with high elevation angles and limited azimuths, respectively. The results show that in a typical situation, the TC and LC models achieve a similar performance. However, when the satellite signals are severely obstructed and few satellites are tracked, the float solution and ambiguity fixing rates in the LC model are dramatically decreased, while in the TC model, there are only minor declines and the difference in the ambiguity fixing rates can be as large as 30%. The correctly fixed ambiguity rates in the TC model also had an improvement of around 10%. Once the ambiguity was fixed, both models achieved a similar positioning accuracy.