In this paper, a multitasking 3-layer Mars centered satellite system is proposed to meet the future demands of a long term in-place communication and navigation over Mars. The Mars satellite constellations are capable of onboard autonomous navigation via the visibility based relative measurements of the satellites in different layers which are forming a time varying diamond-shaped topological structure. The main results of this paper contain that 1) a multitasking 3-layer Mars satellite system which is composed of 19 satellites is constructed, 2) a computational method of designing a multi-layer satellite system which is cost optimal and has ISL(Inter-satellite Links) topological structure is developed, 3) an extended Kalman filter is used to estimate the positions and velocities implementing the autonomous navigation of the Mars satellite system, and, 4) the simulations of the satellite systems are performed to analyze the position and velocity estimation errors.