Interpolation of the GNSS Wet Troposphere Delay

Abstract

Troposphere delay is one of the main distance-dependent errors in Global Navigation Satellite Systems (GNSS) observations. Precise estimation of the troposphere wet delay is necessary to aid ambiguity resolution and for positioning in network Real-Time Kinematic (RTK) and Precise Point Positioning. Wet tropospheric estimates can also serve as a source of atmospheric information to facilitate weather forecasting. Interpolation of the troposphere wet delay is thus required when its estimation is interrupted for short periods or when data are processed at higher intervals from that of available data. The objective of this research is to compare the performance of several interpolation methods that can be used in order to suggest the most appropriate technique. Six interpolation models were considered. The models ranged from the easy-to-implement linear model, to the more sophisticated Kriging model. Other models considered are the cubic spline interpolation, cubic Hermite polynomial interpolation, Lagrange polynomial interpolation, and Fast Fourier transform interpolation. The performance of these methods was assessed by comparing their results with actual troposphere wet delay data collected at the station Onsala (ONSA) in Sweden. As the number of observations used to generate the interpolation process affects the determination of the model coefficients; the use of different lengths of observations was investigated. The number of missing wet delay values considered for interpolation during testing ranged from one to four in a row.Test results showed that the linear interpolation, the cubic Hermite polynomial and fast Fourier transform models produce better estimates than splines and ordinary Kriging. The Lagrange polynomials method was the poorest performer. The paper provides explanation of the interpolation results achieved by linking them with autocorrelation of the troposphere wet delays.