Differential Carrier Phase Positioning With System Error Corrections Based on Orbcomm Signals of Opportunity

Multiple epoch stationary positioning can be achieved using signals of opportunity (SOPs) from low-Earth-orbit (LEO) satellites when a global navigation satellite system (GNSS) is unavailable. Concurrently, the two-line element (TLE) and the simplified general perturbation 4 (SGP4) model can provide satellite positions with km-level errors for non-navigational LEO constellations. Although differential positioning can mitigate some system errors, long baselines reduce their temporal and spatial correlation, resulting in large residual system errors in differential measurements, which leads to inaccurate positioning results. First, based on the SOPs of Orbcomm, we conduct a comprehensive analysis of the effect of major system errors on the differential range residual. Second, we introduce a polynomial fitting algorithm to obtain ionospheric delay corrections (IDCs) using dual-frequency carrier phase measurements. Third, an adaptive regularized least squares (ARLSs) algorithm is proposed to estimate the satellite state and provide satellite position corrections (SPCs). Finally, differential carrier phase positioning utilizing IDC and SPC is implemented in real time. Experimental results demonstrate that the proposed algorithms can effectively smooth the variation of ionospheric delay over epochs and estimate position errors of Orbcomm satellites. Using two Orbcomm satellites, a final 3-D positioning error of less than 5 m and a 3-D positioning root mean squared error (RMSE) of 10.8 m are achieved for the long-baseline scenario. Furthermore, the proposed differential positioning algorithm shows good robustness to the age of TLE files and does not require external ionospheric correction, enhancing its practicality and real-time performance.