Zhang Zhetao, Li Bofeng
In global navigation satellite system (GNSS) precise positioning, some residual systematic errors inevitably exist in GNSS observations. These residual systematic errors can be regarded as the unmodeled errors that cannot be easily mitigated by traditional parameterization, modeling or other methods, mainly due to their spatiotemporal complexity. In a multi-GNSS scenario, there are enough redundant observations to reveal the unmodeled errors to a great extent, according to the behaviors of observation residuals. However, in the case of single frequency, the first-order ionospheric delays cannot be eliminated by the ionosphere-free combination in terms of two or more carrier phases with different frequencies, thus resulting in significant unmodeled effects more frequently. We therefore propose a method for real-time mitigation of the unmodeled errors in single-frequency multi-GNSS precise positioning. The proposed method has two main aspects. First, considering the estimability and property of unmodeled error parameters, the method of multi-epoch partial parameterization is proposed. Second, an iterative procedure is given, which can be applied in real time. The experiment is conducted using a four-station network of real single-frequency and combined global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations, with baseline lengths from approximately 5 to 25 km. The results show that the GPS/BDS unmodeled errors are indeed mitigated and the positioning precision is improved after using the proposed method, where the precision of the up direction can be improved by a maximum of 56.90%.