Precise Multiple-Receiver GNSS SPP Algorithm Based on Constrained Optimization Techniques

The demand for precise outdoor location is increasing with the development of new applications such as autonomous vehicles, exploration robots, and wireless sensor networks. Global Navigation Satellite System (GNSS) is the key enabler of outdoor localization. This investigation focuses on developing new estimation techniques for GNSS positioning of a platform, where no access to a reference station or precise GNSS parameters is need. The main goal is to investigate the potential of using multiple receivers, on the same platform, to enhance positioning accuracy. We utilize a configuration of three independent GNSS receivers in the shape of an equilateral triangle mounted on the platform. This configuration offers more observation diversity, compared to co-linear configuration, while also providing advantages in the estimation process due to the symmetry. We propose constrained estimation techniques exploiting the geometrical constraints of the equilateral triangle to achieve more precise estimation. To carry out the task, we formulate the positioning problem as a constraint optimization with an objective function based on the norm of the squared error of the pseudorange observables. We first eliminate the clock biases of the receivers from the objective function by applying a series of algebraic manipulation and convex optimization techniques, then we develop a novel Riemannian steepest descent algorithm to solve the optimization problem while enforcing the geometrical constraints. We implement both the standard Least-Square Adjustment (LSA) algorithm and the proposed algorithm in MATLAB to compare their performances. Performance evaluation based on both simulation data and experiment data shows that the proposed algorithm offers a lower root-mean-squared error (RMSE) compared to the standard LSA algorithm. The difference between the algorithms' performances is more notable as the noise level increases. Experiment data analysis confirms the simulation analysis, the proposed algorithm reduced the vertices average RMSE by 0.93 m when real GPS data is processed.