The high precision positioning can be easily achieved by using real-time kinematic (RTK) and precise point positioning (PPP) or their augmented techniques, such as network RTK (NRTK) and PPP-RTK, even if they also have their own shortfalls. A reference station and datalink are required for RTK or NRTK. Though the PPP technique can provide high accuracy position data, it needs an initialisation time of 10–30 min. The time-relative positioning method estimates the difference between positions at two epochs by means of a single receiver, which can overcome these issues within short period to some degree. The positioning error significantly increases for long-period precise positioning as consequence of the variation of various errors in GNSS (Global Navigation Satellite System) measurements over time. Furthermore, the accuracy of traditional time-relative positioning is very sensitive to the initial positioning error. In order to overcome these issues, an improved time-relative positioning algorithm is proposed in this paper. The improved time-relative positioning method employs PPP model to estimate the parameters of current epoch including position vector, float ionosphere-free (IF) ambiguities, so that these estimated float IF ambiguities are used as a constraint of the base epoch. Thus, the position of the base epoch can be estimated by means of a robust Kalman filter, so that the position of the current epoch with reference to the base epoch can be obtained by differencing the position vectors between the base epoch and the current one. The numerical results obtained during static and dynamic tests show that the proposed positioning algorithm can achieve a positioning accuracy of a few centimetres in one hour. As expected, the positioning accuracy is highly improved by combining GPS, BeiDou and Galileo as a consequence of a higher amount of used satellites and a more uniform geometrical distribution of the satellites themselves. Furthermore, the positioning accuracy achieved by using the positioning algorithm here described is not affected by the initial positioning error, because there is no approximation similar to that of the traditional time-relative positioning. The improved time-relative positioning method can be used to provide long-period high precision positioning by using a single dual-frequency (L1/L2) satellite receiver.
High precision positioning algorithm based on carrier phase and time of arrival
