引用本文: 宋会杰, 董绍武, 王燕平, 安卫, 侯娟. 基于渐消因子的改进Kalman滤波时间尺度估计算法[J]. 武汉大学学报 ( 信息科学版), 2019, 44(8): 1205-1211, 1219.
SONG Huijie, DONG Shaowu, WANG Yanping, AN Wei, HOU Juan. An Improved Kalman Filter Time Scale Algorithm Based on Forgetting Factor[J]. Geomatics and Information Science of Wuhan University, 2019, 44(8): 1205-1211, 1219.
 Citation: SONG Huijie, DONG Shaowu, WANG Yanping, AN Wei, HOU Juan. An Improved Kalman Filter Time Scale Algorithm Based on Forgetting Factor[J]. Geomatics and Information Science of Wuhan University, 2019, 44(8): 1205-1211, 1219.

## An Improved Kalman Filter Time Scale Algorithm Based on Forgetting Factor

• 摘要: Kalman滤波时间尺度算法是一种实时的原子钟状态估计方法，在守时实验室具有重要实用价值。由于原子钟状态模型误差估计存在偏差，Kalman滤波时间尺度算法中状态估计可能出现相应异常扰动，应当对状态模型误差进行实时控制。对此，引入基于渐消因子的改进Kalman滤波时间尺度算法。对状态预测协方差矩阵引入渐消因子，利用统计量实时计算渐消因子的量值，控制状态预测协方差阵的增长，降低了原子钟状态估计的扰动。实验结果表明，相比于标准Kalman滤波时间尺度算法和基于预测残差构造自适应因子的Kalman滤波算法，基于渐消因子的改进Kalman滤波时间尺度算法能够提高原子钟状态估计的准确度，改进时间尺度的稳定度。

Abstract: 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 However, when there is large error in the model, Kalman filter algorithm is seriously affected by "outdated" information and often makes the filter diverge, because the error estimation of atomic clock state has deviation.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.

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