A rapid convergent positioning algorithm based on projected cancellation technique for pseudolite positioning systems

In many harsh environments where a global navigation satellite system (GNSS) is absent or satellite signals are blocked, pseudolite positioning systems (PLPSs) can provide stand-alone positioning service with high accuracy and flexible deployment of base stations. Nevertheless, since distances from users to pseudolites in PLPS are much closer than those to satellites in GNSS, PLPSs suffer severely from nonlinearity problems because linearization applied in traditional linearization-based positioning algorithms leads to errors in the mathematical model that impact the convergence of iterations and possibly significantly deviate positioning solutions from actual positions. To enhance the convergence performance of positioning algorithms under severe nonlinearity situations, we propose a projected cancellation (PC) technique that linearizes pseudoranges at the reference and user sites on a virtual site. Single-differenced pseudoranges effectively eliminate the nonlinear error terms. Therefore, the observation model is transformed into an approximately linear version, and the traditional positioning algorithms are more suitable to be employed. Based on this, we develop a fusion positioning algorithm that adaptively combines the projected cancellation technique with different linear positioning algorithms according to the severity of nonlinearity in order to achieve a positioning service with more rapid convergence and a higher convergence success rate. Both simulated and experimental results under various cases are obtained and compared with those of traditional algorithms. Numerical results show that the proposed algorithm improves the overall positioning accuracy by approximately 30% under severe nonlinearity situations without additional time cost compared with the existing algorithms. Moreover, it provides a significant reduction of about 48% in time cost, yielding equivalent accuracy as the Levenberg–Marquardt algorithm in normal applications fields. Real-world experiment results validate the applicability and superiority of the new method to solve the nonlinearity problem in practical applications.