Ground Based Navigation of Spacecraft in Lunar Transfer Trajectory, with Application to Chandrayaan-2

Abstract

Navigation plays a major role in space missions. For a cislunar space mission, such as Chandrayaan-2, deep space radar, inertial navigation system and optical navigation system are used to determine the position and velocity of the spacecraft.

In the present work, a mathematical model of Chandrayaan-2 motion is developed which includes J2 effect of the Earth and the Moon, solar gravitational perturbation and solar radiation pressure. Based on this model a nominal lunar transfer trajectory is simulated. Models for ground-based measurements (azimuth, elevation, range and range rate) are described. Time delays due to finite speed of electromagnetic waves are considered in the measurement. Effects of tropospheric and ionospheric refraction on measurements are incorporated in the simulation. Tropospheric errors are corrected using Saastamoinen zenith range correction model and ionospheric range errors are corrected using dual-frequency measurements. MATLAB codes are developed to simulate the observations from four ground station facilities, viz. Indian Deep Space Network, (IDSN) Byalalu, Karnataka, India as well as Deep Space Communication Complex, Goldstone, California, USA, Deep Space Communication Complex, Madrid, Spain and Deep Space Communication Complex, Canberra, Australia.

The polar measurements are used in Extended Kalman Filter (EKF) algorithm to estimate position and velocity of Chandrayaan-2 in the inertial Cartesian frame. To compensate for the time delay in measurements, the states are propagated till the time corresponding to the delayed measurements and then updated. These updated states are then propagated further till the current time to obtain the current estimates. This technique results in 11.79 km of range uncertainty (1σ) and 6.93 m/s of speed uncertainty (1σ) at the time of arrival at the insertion point to the lunar parking orbit of Chandrayaan-2.