| Abstract: |
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. |