An Improved Position Determination Algorithm Based on Nonlinear Compensation for Ground-Based Positioning Systems

In the absence of GNSS or when signals from satellites are blocked in harsh environments, a ground-based positioning system can be used to estimate the position of users and receivers. Nevertheless, ground-based systems suffer dramatic nonlinear error resulting from the linearization used in typical positioning algorithms. Robust positioning algorithms that are capable of handling strong nonlinearity cases are therefore of great value. In this paper, we propose an algorithm termed promoted iterative least-squares based on nonlinear-compensation (PILSBON) to effectively alleviate the influence of nonlinear effects. This algorithm is based on the accurate expression of the nonlinear error terms in the double-differenced pseudorange measurement model. In order to eliminate the effects of nonlinearity for targeted solutions, the PILSBON uses iterative numerical estimation to compensate for nonlinear error so that the nonlinear position determination is transformed into a linear model, which can then be estimated with a linear estimation algorithm. In this paper, we analyze the properties of the PILSBON and compare it to conventional solutions. Because of its specific strategy for nonlinearity, our results show that the PILSBON improves the overall accuracy by approximately 30% compared with conventional solutions according to statistic RMSE data from over 500 experiments and positions. Moreover, by deploying a practical ground-based positioning system with six transmitters on the rooftop of our laboratory building, we demonstrate that the PILSBON algorithm can be efficiently employed in real-world experiments.