The initial results about optimum the random walk process noise rate for GNSS tropospheric delay estimation

Abstract: Unlike ionosphere, troposphere is nondispersive and delays cannot be determined from observations of signals at different radio frequencies. In GNSS data processing, station height, receiver clock error and tropospheric delay are highly correlated to each other, especially in kinematic situations. Although zenith hydrostatic delay can be provided with sufficient accuracy, zenith wet delay, which is more spatially and temporally varying than hydrostatic component, has to be carefully processed. Usually, temporal dependence of tropospheric delays at zenith is modeled as a random walk process with a solely given process noise rate σ_rw in GNSS processing. The usually used σ_rw is a constant throughout whole process session and is in range of 3~10 mm per sqrt hour. This setting is generally appropriate for desirable GNSS positioning estimation in normal conditions. However, modeling zenith tropospheric delay by using a constant σ_rw in whole session will be unsatisfactory in cases of special weather conditions, e.g., the shower case. The σ_rw is a measure of magnitude of typical variation of zenith path delay or its residual after calibration in a given time. Values of σ_rw that are too large could weaken strength for geodetic estimation, while values that are too small may introduce systematic errors, since a strong constraint for tropospheric unknowns is imposed to stabilize the system. The random walk model for wet delay must be constrained approximately to "correct" value to obtain optimum parameters estimates. Assuming temporal change of tropospheric delay at an arbitrary station can be described by random walk model, the process noise levels were calculated by some scholars. They employed water vapor radiometric, surface meteorological measurements and numerical weather model data set for optimum selection of σ_rw. In general, although a lot of efforts have made to optimize post-processing and/or real-time GNSS tropospheric delay estimation, stochastic modeling of zenith wet delay remains insufficiently investigated, especially for kinematic applications. Since temporal variation of zenith wet delay depends on water vapor content in atmosphere, it seems to be reasonable that constraints should be geographically and/or time dependent. In this work, we first investigate sensitivity of both station coordinates and zenith wet delay estimators on different σ_rw values, and then try to propose to take benefit from post-processed static or kinematic estimated tropospheric delay to obtain the optimum σ_rw. The general objective is that if zenith tropospheric delays are of different variation characteristic, e.g., relatively stable or rapid changing, then a varying σ_rw, e.g., small or large value, could be employed, which should be more theoretically feasible compared with a invariant σ_rw. The initial results show that the new method can efficiently obtain epoch-wise σ_rw values at different stations. Compared to results from conventional constant σ_rw value, time-varying noise rate can improve precision of PPP solutions. We note that this first results represent performance view at several selected stations, more works should be done to draw global or even long-term conclusions.

This work is supported by National Natural Science Foundation of China (42304010), Youth Foundation of Changzhou Institute of Technology (YN21046).