Rubidium atomic clock error modeling and forecasting based on parameter constrained Kalman filter

The accuracy and stability of the receiver clock is particularly important to improve the performance of satellite navigation and positioning. High-precision atomic clocks can help reduce the minimum number of visible satellites required for GNSS positioning and automatic integrity monitoring. Especially for the Radio Determination Satellite Service (RDSS) system, it is difficult to meet the requirements of some high-dynamic applications for the reason it works with active round trip ranging. If the atomic clock in the receiver can maintain high precision in a long time, it can help RDSS system to realize the real-time positioning in passive way for dynamic applications. Most receiver clock error is big enough compared with the other ranging error sources. It always changes quickly and is not easy to predict for its random characters during its power on period, even Rubidium Atomic Clock. In this paper, time and frequency error of the rubidium atomic clock of the user receiver are analyzed by using the GNSS satellite ranging measurement. A linear exponential model suitable for Rubidium Atomic receiver clock error was put forward according to the actual data analysis. In order to have a more accurate clock error prediction, a Kalman filter method based on parameter constrains was proposed for modelling the clock error in the beginning of receiver power on and clock error prediction in later time. Experiments were done on one satellite receiver with Rubidium Atomic Clock using BD1 RDSS satellite signal. The results show that this method can greatly improve the prediction accuracy of Rubidium Atomic Clock error.