Kriging Interpolation in Modelling Tropospheric Wet Delay

Abstract

This contribution implements the Kriging interpolation in predicting the tropospheric wet delays using global navigation satellite system networks. The predicted tropospheric delays can be used in strengthening the precise point positioning models and numerical weather prediction models. In order to evaluate the performances of the Kriging interpolation, a sparse network with 8 stations and a dense network with 19 stations from continuously operating reference stations (CORS) of the Netherlands are selected as the reference. In addition, other 15 CORS stations are selected as users, which are divided into three blocks: 5 stations located approximately in the center of the networks, 5 stations on the edge of the networks and 5 stations outside the networks. The zenith tropospheric wet delays are estimated at the network and user stations through the ionosphere-free positioning model; meanwhile, the predicted wet delays at the user stations are generated by the Kriging interpolation in the use of the tropospheric estimations at the network. The root mean square errors (RMSE) are calculated by comparing the predicted wet delays and estimated wet delays at the same user station. The results show that RMSEs of the stations inside the network are at a sub-centimeter level with an average value of 0.74 cm in the sparse network and 0.69 cm in the dense network. The stations on edge and outside the network can also achieve 1-cm level accuracy, which overcomes the limitation that accurate interpolations can only be attained inside the network. This contribution also presents an insignificant improvement of the prediction accuracy from the sparse network to the dense network over 1-year’s data processing and a seasonal effect on the tropospheric wet delay predictions.

External Tropospheric Corrections by Using Kriging Interpolation for Improving PPP-RTK Positioning Solutions

“…This is because the weights of the Kriging interpolation depend upon the distances and time variation between the unknown points and all available measurements, as well as the covariance reflected in the semivariogram. It is well known that a neutral atmosphere is stable over a small region, as supported by related studies [18,31]. Therefore, the Kriging interpolation is suitable for generating the tropospheric delay corrections because the neutral atmosphere exhibits a noticeable spatial autocorrelation.…”

Multi-GNSS-Weighted Interpolated Tropospheric Delay to Improve Long-Baseline RTK Positioning

“…These estimations can then be interpolated to the position of a user station within the network, allowing for the correction of the user measurements. A large number of field tests in previous studies have well tested and demonstrated this network-RTK approach [ 25 , 58 ].…”

“…Moreover, accurate predictions of the rover’s ZTD outside the network are mainly determined by the distance to a nearby reference station and are thus unaffected by the number of reference stations. In conclusion, Kriging interpolation depends on the distances between unknown points, all available measurements, and the covariance shown in the semivariogram [ 25 ].…”

Tropospheric Delay Parameter Estimation Strategy in BDS Precise Point Positioning

“…To this end, researchers have proposed many methods to deal with tropospheric delay, of which the following two are frequently applied in PPP: model correction method and parameter estimation method. The model correction method has been previously used to establish a mathematical model to correct tropospheric delay based on the physical characteristics of the troposphere and the functional relationship between meteorological parameters that affect its characteristics and tropospheric delay [10,11]. The model correction method can be divided into two types: one is the traditional tropospheric model based on early radio sounding observations, such as the Saastamoinen model, Hopfield model, and Black model, etc.…”