Mars's Moons-Induced Time Dispersion Analysis for Solar TDOA Navigation

The time dispersion effect affects the accuracy of solar time difference of arrival (TDOA) navigation. In this celestial autonomous navigation, Mars's moons are reflecting celestial bodies, and their shape affects the TDOA dispersion model. In the modelling process of traditional methods, the moons of Mars (Phobos and Deimos) are regarded as points, which causes the model to be inaccurate. In order to solve these problems, we simplified the Mars's moons into ellipsoids or solid diamonds, and then established a TDOA model with the nonspherical Mars's moons as reflecting celestial bodies through differential geometry and geometric optics. Finally, we analysed the time dispersion caused by the Mars's moons in theory. Theoretical analysis and experiments show that the point model error is 5·66 km, and the 3D model error is within 70 m. Thus, the 3D TDOA model established in this paper is meaningful. In addition, the Sun–Mars-moons–spacecraft angle, solar flare, three-axis length, and attitude of the Mars's moons have a great effect on the dispersion profile, while the Mars's moons-to-spacecraft distance has a small effect.