An Improved Kalman Filter Time Scale Algorithm Based on Forgetting Factor

Kalman filter time scale algorithm is a real-time estimation method of atomic clock state. It is of great practical value in the time-keeping laboratory. Kalman filter algorithm is an effective algorithm of optimal filtering for Gaussian process. When the observation geometry information, dynamic model and statistical information are reliable, Kalman filtering calculation performance is better. However, when there is large error in the model, Kalman filter algorithm is seriously affected by "outdated" information and often makes the filter diverge, because the error estimation of atomic clock state has deviation. In Kalman filter time scale algorithm, the state estimation may appear abnormal perturbation. The state model error should be controlled in real time. So an improved algorithm based on forgetting factor is introduced in this paper. The forgetting factor is introduced to the state prediction covariance matrix. The value of the forgetting factor is calculated in real time, the growth of covariance matrix of state prediction is controlled. The disturbance of atomic clock state estimation is reduced. The significant difference between the improved Kalman filter algorithm and the normal Kalman filter algorithm is that the former state covariance matrix is inflated to reduce the use efficiency of historical state information, so as to achieve the purpose of reusing real measurement information. Experimental results show that, compared to the standard Kalman time scale algorithm and Kalman algorithm based on predicting residuals to construct adaptive factors, the improved Kalman filter time scale algorithm based on the forgetting factor can improve the accuracy of atomic clock state estimation and improve the stability of time scale.