Based on the batch expectation–maximization (EM) and recursive least-squares algorithms, we develop a new recursive variance components estimation (Recursive-VCE) algorithm that applies a Kalman filter and validates it by a simulated kinematic precise point positioning (PPP) experiment and a PPP test on real-world data. The Recursive-VCE algorithm processes the observations in an epoch-by-epoch or a group-by-group manner. Once new observations are obtained, it updates the estimates of the variance components in a recursive way or on the fly. Therefore, it does not require significant computing resources to store sufficiently large training datasets. The resulting algorithm is simple and able to be easily adapted to determine time-varying behaviours and is shown to converge faster than the batch EM algorithm because the EM algorithm updates the parameters only once after dealing with all the data. Hence, it is a good complement to other batch VCE methods, and its application in real-time data processing is promising.

基于批量期望最大化（EM）和递归最小二乘算法，我们开发了一种新的递归方差分量估计（Recursive-VCE）算法，该算法应用卡尔曼滤波器并通过模拟运动学精确点定位（PPP）实验对其进行了验证以及对真实数据的PPP测试。递归-VCE算法以逐个时期或逐个分组的方式处理观察结果。一旦获得新的观测值，它将以递归方式或即时更新方差分量的估计值。因此，它不需要大量的计算资源来存储足够大的训练数据集。所得算法简单易行，可确定时变行为，并且收敛速度比批处理EM算法快，因为EM算法在处理所有数据后仅更新一次参数。因此，它是对其他批处理VCE方法的良好补充，其在实时数据处理中的应用前景广阔。