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Effect of Sensor Quality on Relative State Estimation of Formation Flying of Satellites

One of the most important challenges involved in the formation flight of satellites is that of state estimation in terms of relative and inertial estimates. In near earth spacecraft GPS measurements are commonly used to solve this problem and for deep space missions the DSN is used. The objective of this paper is to determine sensitivities of relative state estimation errors to varying sensor quality in a GPS-denied environment. This paper considers a Chief-Deputy architecture that will travel in an elliptical orbit with a perigee in Low-Earth Orbit and an apogee in Mid-Earth orbit (MEO). While in the GPS-available zone, the Chief satellite will process GPS measurements to determine its state relative to the Earth-Centered Inertial (ECI) frame. Measurements are taken of range and range-rate of the Deputy relative to the Chief throughout the orbit and processed using an Indirect, Extended Kalman Filter (EKF). The states being estimated are the position and velocity of each satellite, along with sensor biases. A Monte-Carlo simulation is developed to validate the consistency of the EKF covariance estimates. Only two satellites are considered for simplicity, though the formation can be expanded to include an arbitrary number of satellites. Following validation of the EKF, the covariance estimates are used to identify trends in relative state estimation for the two-satellite formation as a function of sensor parameters. Specifically, the sensitivity of state estimation to range and range-rate sensor quality is assessed by analyzing covariance as a function of range and range-rate bias. The resulting analysis provides a preliminary estimate of system performance, enabling the selection of system components to meet future mission requirements.