Analyzing the impact of geometric constraints on GNSS positioning accuracy using realistic stochastic model

In relative GNSS surveying, the accuracy of the vector solution is influenced by measurement conditions such as baseline length, atmospheric effects, satellite geometry, and environmental obstructions. To ensure high accuracy under challenging conditions, surveyors often apply constraints such as static positioning or control point initialization. These practices, while effective, typically rely on empirical judgment that result in longer measurement times to ensure reliability. Alternatively, integrated systems such as INS/GNSS can introduce real-time motion-based constraints that may optimize measurement time without compromising accuracy. Despite the known potential of such constraints, no comprehensive study has assessed their contribution to the GNSS vector solution using a statistically rigorous and generalizable approach. This study proposes a novel analytical framework for evaluating the contribution of geometric constraints to GNSS vector solutions, based on a closed-form mathematical formulation and a realistic stochastic model. The model enables quantification of the constraints’ effects on both accuracy (e.g., covariance of estimates) and ambiguity resolution success, across diverse measurement scenarios. Numerical simulations are conducted for common constraint types—including control point initialization, static positioning, and inertial motion—under varying measurement conditions. Results demonstrate that constraints significantly reduce solution errors and ambiguity resolution time in challenging environments, while offering minimal benefit in favorable conditions. The proposed methodology provides a robust foundation for systematic evaluation and optimization of constraint use in GNSS surveying, with practical implications for reducing field time and improving solution reliability.