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.

中文翻译：

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用于太阳 TDOA 导航的火星卫星诱导时间色散分析

时间色散效应影响太阳到达时差（TDOA）导航的精度。在这种天体自主导航中，火星的卫星正在反射天体，它们的形状会影响 TDOA 色散模型。在传统方法的建模过程中，将火星的卫星（火卫一和火卫二）视为点，导致模型不准确。为了解决这些问题，我们将火星卫星简化为椭球体或实心菱形，然后通过微分几何和几何光学建立以非球形火星卫星为反射天体的TDOA模型。最后，我们从理论上分析了火星卫星造成的时间离散。理论分析和实验表明，点模型误差为5·66 km，3D模型误差在70 m以内。因此，本文建立的 3D TDOA 模型是有意义的。此外，火星卫星的太阳-火星-卫星-航天器角度、太阳耀斑、三轴长度和姿态对色散剖面影响很大，而火星卫星到航天器的距离影响较小。