单状态变量和两级Kalman滤波器时间尺度算法

One-state and twice Kalman filter time scale algorithms

本文首先提出一种单状态变量Kalman滤波器时间尺度算法;推导了算法的权重和预测值的解析表达式;在该解析表达式的基础上,引入虚拟Kalman采样间隔;理论分析和仿真实验都证明:通过选取不同的虚拟Kalman采样间隔,可以使时间尺度在任何指定的平滑时间的频率稳定度达到最优.在此基础上,提出了一种两级Kalman滤波器时间尺度算法;详细描述了算法原理;算法生成的时间尺度只含有频率随机游走噪声(RWFM),不含有频率白噪声(WFM);算法相当于按照RWFM的强度进行加权;生成的时间尺度的中短期频率稳定度更高.

We first propose a one-state Kalman filter time scale algorithm, and derive the analytical expressions of the weights and the predictions. Based on the analytical expressions, we introduce the virtual Kalman sampling time. The theoretical analyses and the simulations both validate that we can optimize the frequency stability on any one of the certain observation intervals of the time scale by means of choosing a certain virtual Kalman sampling time. Then, based on this algorithm, we propose a twice Kalman filter time scale algorithm, and describe the principle of the algorithm. The forming time scale only involves walk random frequency modulation noise （RWFM）, and does not involve white frequency modulation noise （WFM）. The weights are in inverse proportion to the intense of RWFM. The short-term and middle-term frequency stability of the time scale is higher.