In this study, we develop a new algorithm for online variance components estimation (Online-VCE) of geodetic data based on the batch expectation-maximization (EM) algorithm and stochastic approximation theory. The Online-VCE algorithm is then applied to the Kalman filter and least-squares method and validated using simulated kinematic precise point positioning (PPP) based on the global navigation satellite system as well as real-data PPP experiments. The Online-VCE algorithm is specifically designed to monitor and establish a stochastic model in real-time or high-rate data applications. Compared to other methods, the Online-VCE is faster and can estimate the stochastic model in real time because it does not need to store all data, but simply estimates the expected result and computes the gradient of the parameters using only one or a few observations. In future, the Online-VCE algorithm can be used to develop a real-time atmospheric stochastic model for PPP applications.

在这项研究中，我们基于批量期望最大化（EM）算法和随机逼近理论，开发了一种大地数据在线方差分量估计（Online-VCE）的新算法。然后将Online-VCE算法应用于Kalman滤波和最小二乘法，并基于全球导航卫星系统以及实际数据PPP实验，使用模拟运动学精确点定位（PPP）进行了验证。Online-VCE算法专门设计用于监视和建立实时或高速率数据应用程序中的随机模型。与其他方法相比，Online-VCE速度更快并且可以实时估计随机模型，因为它不需要存储所有数据，但只需估计一个预期结果并仅使用一个或几个观察值即可计算出参数的梯度。将来，可以将Online-VCE算法用于为PPP应用开发实时大气随机模型。