Accuracy Enhancement of Multipath Navigation Using Reflected Solar Oscillation: A Geometric Perspective

The multipath navigation using time delay between the direct and reflected solar oscillation is attractive in determining the spacecraft’s position. While its navigation accuracy relies significantly on the selection of the reflected body. To address this problem, factors related to the reflected body that may affect the navigation accuracy are identified first, according to the measurement model, including the magnitude of measurement (defined as $\Delta t$ ), the distance between the spacecraft to the reflected body (defined as $| \boldsymbol {r}_{{rp}\_ t_{r}} |$ ) and that to the Sun (defined as $| \boldsymbol {r}_{{sp}\_ t_{0}} |$ ). Because the $| \boldsymbol {r}_{{rp}\_ t_{r}} |$ and $| \boldsymbol {r}_{{sp}\_ t_{0}} |$ cannot be measured directly, the $\angle SMP$ is introduced to describe the influence of them. Subsequently, the influence of $\Delta t$ and $\angle SMP$ on navigation accuracy is analyzed from the geometric perspective and simulations. The theoretical results indicate that the navigation error decreases with the reductions in $\Delta t$ and $\angle SMP$ , respectively. The simulations show that when the reflected body with the smallest $\Delta t$ and $\angle SMP$ is adopted, the navigation accuracy will be enhanced. The research provides explicit criteria for the optimal selection of reflected bodies, a key challenge unaddressed in previous research and offers valuable insights for optimizing the design of multipath navigation systems.