The Selection of Basic Functions for a Time-Varying Model of Unmodeled Errors in Medium and Long GNSS Baselines

Abstract

Unmodeled errors play a critical role in improving the positioning accuracy of Global Navigation Satellite Systems. Few studies have addressed unmodeled errors in medium and long baselines using their time correlation, which is highly beneficial for achieving a precise and real-time solution. However, before tackling unmodeled errors, it is first necessary to determine reasonable basic functions to fit such unmodeled errors. Therefore, we study the selection of basic functions for time-varying unmodeled errors in two positioning modes: estimating atmospheric delays and using an IF combination. We choose three basic functions: polynomials, sinusoidal functions, and combinatorial functions. Fitting experiments and positioning experiments are conducted using the unmodeled error data provided by four baselines ranging from 30 to 220 km. The Root Mean Square Errors fitted by the second order are approximately 2 mm. The corresponding residuals generally converge to 3 mm in about 30 s. After correcting the observations using the fitted unmodeled errors of the second-order polynomial, the positioning results show improvements of about 40% to 80% in all directions. We conclude that the second-order polynomial is the optimal basic function in all two positioning modes.