Theoretical Research And Algorithm Implementation Of Gps Single-frequency Precise Point Positioning

This article systematically studied principle and technical details of single-frequency precise point positioning (SPPP), including the mathematical model, positioning error correction methods, data pre-processing and parameter estimation method.Because SPPP can only use single-frequency observation measurements, so there were four aspects, the observation model, the ionosphere delay, different code bias correction, and data pre-processing, different from dual-frequency precise point positioning (PPP). These four aspects were the difficulties of SPPP, which were also the focus of this study. Around the four aspects, the main research contents of this article were as follows:1. Single Frequency Precise Point Positioning Observation ModelIn view of the characteristic that the ionospheric delay error in carrier phase observation equation was negative to that in the pseudorange observation equation, the method, named Half Sum of Phase and Pesudorange, was used to elimination the ionospheric delay error in carrier phase observation equation. The new combination measurement, Half Sum of Phase and Pesudorange, combined with the single-frequency pseudorange observation equation was selected as the single-frequency precise point positioning observation model.2. Ionospheric Delay CorrectionThis paper discussed two methods suitable for single-frequency observation measurements to correct the ionospheric delay error: Grid Ionosphere Model (GIM) and the Klobuchar Model. As to the problem of grid point interpolation in GIM, based on the traditional four-point interpolation model and in regard of the electronic content error, the selected-point interpolation model and two kinds of weighting methods were proposed. The experiment results proved effectiveness of the new model.3. Different Code Bias CorrectionIn this paper, the mathematical model of different code bias correction was derived in detail. The correction formula of these two types of receiver namely cross-correlation and non cross-correlation were presented respectively in the thesis.4. Data Pre-ProcessingThis paper discussed two methods suitable for single-frequency observation measurements to detect the cycle slip or gross error: polynomial fitting and Doppler integration. The characteristics of these two methods were analyzed, and the data pre-processing process of using these two methods was described.5. Parameter Estimation There was a defect existed in traditional Kalman Filter, the ambiguity parameter can not converge immediately in the beginning of the filter course, as a result the initial positioning accuracy was very low. As for the problem, this paper further introduced Forward and Reverse Kalman Filter. It is difficult to determine the weight ratio of the forward and reverse filtering results. Based on the practice, a simple method to determine the weight, named Epoch-Order Weighting Method, was proposed and proved.Based on the above research, a single-frequency precise point positioning software, named SPPP-SPAN, was accomplished independently. Supported by the software SPPP-SPAN, a large number of relevant experiments were carried out and the conclusions were as follows:1. The software SPPP-SPAN can achieve centimeter-level static positioning accuracy and its dynamic positioning accuracy was closely related with the carrier mobility. Under weak mobility condition, the positioning accuracy of horizontal and elevation direction were 0.4~0.5m and 0.5~0.6m respectively, while under strong mobility conditions, the positioning accuracy of horizontal and elevation direction were 0.5~0.6m and 0.9~1.0m respectively. So it can be considered the software SPPP-SPAN can achieve decimeter-level dynamic positioning accuracy.2. Forward and Reverse Kalman Filter can effectively overcome the traditional Kalman Filtering defects that the initial positioning accuracy was very low, so it was more suitable for dynamic positioning.3. The correction accuracy of Grid Ionospheric Model was better than that of Klobuchar Model. In SPPP, it was very effective to use Grid Ionospheric Model to correct the ionospheric delay of pseudorange measurements.4. The static SPPP results using different ionospheric products shared nearly the same precision, so the differences between different ionospheric products can be ignored in static SPPP. It was proposed to use IGS ionosphere product in dynamic SPPP. It was worth mentioning that, positioning accuracy of the fast IGS ionospheric product was equivalent to that of the final product, so users can choose IGS ionosphere products flexibly according to the real-time need, not worrying about loss of precision.