MSE-impact of PPP-RTK ZTD estimation strategies

In PPP-RTK network processing, the wet component of the zenith tropospheric delay (ZTD) cannot be precisely modelled and thus remains unknown in the observation equations. For small networks, the tropospheric mapping functions of different stations to a given satellite are almost equal to each other, thereby causing a near rank-deficiency between the ZTDs and satellite clocks. The stated near rank-deficiency can be solved by estimating the wet ZTD components relatively to that of the reference receiver, while the wet ZTD component of the reference receiver is constrained to zero. However, by increasing network scale and humidity around the reference receiver, enlarged mismodelled effects could bias the network and the user solutions. To consider both the influences of the noise and the biases, the mean-squared errors (MSEs) of different network and user parameters are studied analytically employing both the ZTD estimation strategies. We conclude that for a certain set of parameters, the difference in their MSE structures using both strategies is only driven by the square of the reference wet ZTD component and the formal variance of its solution. Depending on the network scale and the humidity condition around the reference receiver, the ZTD estimation strategy that delivers more accurate solutions might be different. Simulations are performed to illustrate the conclusions made by analytical studies. We find that estimating the ZTDs relatively in large networks and humid regions (for the reference receiver) could significantly degrade the network ambiguity success rates. Using ambiguity-fixed network-derived PPP-RTK corrections, for networks with an inter-station distance within 100 km, the choices of the ZTD estimation strategy is not crucial for single-epoch ambiguity-fixed user positioning. Using ambiguity-float network corrections, for networks with inter-station distances of 100, 300 and 500 km in humid regions (for the reference receiver), the root-mean-squared errors (RMSEs) of the estimated user coordinates using relative ZTD estimation could be higher than those under the absolute case with differences up to millimetres, centimetres and decimetres, respectively.