GNSS unmodeled error processing based on the resilient mathematical model compensation in high-precision GNSS positioning

Global Navigation Satellite System (GNSS) plays an increasingly important role in all walks of life. In order to meet the demands of different users, it is crucial to establish corresponding correct mathematical models, especially in the field of precise positioning and navigation. However, due to the spatiotemporal complexity of and limited knowledge on GNSS errors, some residual errors would inevitably remain even after being corrected with differencing and linear combination, empirical model correction, and traditional parameterization. These residual observation errors are referred to as unmodeled errors. In fact, the unmodeled errors have adverse impacts on high-precision GNSS positioning. However, most existing studies mainly focus on handling the part of systematic errors that can be adequately modeled and then simply ignore the part of unmodeled errors that may actually exist. To make a breakthrough in the precision and reliability of GNSS applications currently, this study focuses on the theory and method for processing the GNSS unmodeled errors based on the mathematical model compensation, including resilient functional model adjustment and resilient stochastic model optimization. Specifically, according to the significance and properties of unmodeled errors, the unmodeled-error-ignored model, unmodeled-error-corrected model, unmodeled-error-fixed model, unmodeled-error-float model, and unmodeled-error-weighted model are proposed, where the approaches of significance testing, geometry-free/based/fixed models, hemispherical/hierarchy maps, composite stochastic model, multi-epoch partial parameterization, and inequality and equality constraints are adopted. Ultimately, an unmodeled error processing flow that can adaptively adjust as the external conditions change is proposed, then one can obtain high-precision GNSS positioning solutions.