Application of expectation–maximization algorithm to estimate random walk process noise for GNSS tropospheric delay

GNSS (Global Navigation Satellite Systems) tropospheric delay, specifically zenith wet delay (ZWD), shows clear spatial–temporal variations and is usually modeled as RWPN (random walk process noise). However, because RWPN does not take the geographical position of GNSS stations and local weather conditions into account for precise point positioning (PPP), it may lead to biased ZWD estimates. To address the scientific problem and improve ZWD estimates, we adopt the Expectation–Maximization algorithm (EM algorithm) to validate the feasibility of estimating RWPN using only GNSS measurements. Numerical experiments reveal that using only GNSS observations is capable of determining the RWPN parameter, although it could take several days to reach a stable solution if the initial guess deviates far away from the truth. It is also shown that estimating RWPN can almost always effectively improve ZWD estimates by several millimeters in contrast with traditional PPP results. If the ambiguities are fixed to their integer values correctly, the accuracy of RWPN estimates for ZWD can be greatly reduced by 2 mm / hour .