A Design of Differential-Low Earth Orbit Opportunistically Enhanced GNSS (D-LoeGNSS) Navigation Framework

Considering the problem of GNSS service interruption caused by the insufficient number of available satellites in complex environments, Low Earth Orbit (LEO) satellites can supplement GNSS effectively. To eliminate the unknown satellite clock error and the atmospheric delay error with spatial correlation in LEO observations, a Differential-Low Earth Orbit opportunistically enhancing GNSS (D-LoeGNSS) navigation framework is proposed. Firstly, because of the uncertainty of the LEO orbit, we derive the effect of the LEO orbit error on the differential measurement model. Secondly, aiming at the noise amplification and correlation in double-difference (DD), we propose a Householder-Based D-LoeGNSS (HB-DLG) algorithm, which suppresses noise by introducing an orthogonal matrix. Thirdly, in D-LoeGNSS, the typical measurement of LEO is Doppler, which is heterogeneous with the GNSS pseudorange, rendering the Dilution of Precision (DOP) evaluation method unsuitable. Given the unbiasedness of differential measurements, the Cramer Rao Lower Bound (CRLB) is derived as a metric to characterize the positioning accuracy and satellite spatial distribution. Finally, a field experiment using Orbcomm (ORB) and GPS is conducted. The experimental results show that the performance of the HB-DLG algorithm is superior to DD. Especially when the number of satellites is insufficient or the measurement redundancy is poor; the D-LoeGNSS framework has advantages of rapid convergence and high accuracy compared with a single constellation.