Analytical Solution for Positioning Based on Iridium NEXT SOPs TOA/FDOA

The low Earth orbit (LEO) satellite signals of opportunity (SOPs), with their strong antijamming capabilities, can fulfill the positioning requirements of users in global navigation satellite system (GNSS)-denied environments. Traditional LEO satellite SOPs positioning methods typically employ numerical techniques to solve nonlinear equations. However, such methods are sensitive to initial conditions, and under the circumstances of significant initial errors, the positioning results may converge slowly or even diverge. In this article, a two-step weighted least squares (TSWLSs) analytical solution method is proposed based on Iridium NEXT SOPs. This method utilizes Iridium NEXT satellite pseudorange and pseudorange-rate measurements, eliminating the need for prior knowledge about the receiver's position and directly estimating the receiver's position. Theoretical derivations and simulation results demonstrate that the proposed method, under the assumption of Gaussian measurement noise, achieves the Cramer-Rao lower bound (CRLB) based on the pseudorange/pseudorange-rate positioning model. A practical evaluation is conducted by comparing the traditional Iridium NEXT pseudorange-rate single-point positioning method with the proposed method. Experimental results indicate that the proposed method reduces convergence time by 78.7% and improves positioning accuracy by 34.1%, while also eliminating the need for initial position information.