Observability Analysis of Autonomous Navigation for Deep Space Exploration with LOS/TOA/Velocity Measurements

Autonomous navigation for a deep space probe is based on the measurements, including the Line of sight(LOS) of different celestial bodies measured by optical images, the velocity with respect to the stable stars measured by optical doppler shifts, and the distance to the solar system barycenter measured by time of arrival of X-ray pulsar sources. This paper is aimed at proposing an optimal measurement strategy by analyzing the autonomous navigation system in different scenarios with LOS/TOA/Velocity measurements in the view of observability. Piecewise constant system (PWCS) observability, and stochastic observability based on Fisher information are introduced. After established and analyzed the orbital dynamics and measurement models of LOS of planets, doppler velocity, and time of arrivals( TOA), scenarios with different measurements are constructed. Considering nonlinear and time invariant characteristics of the autonomous navigation system, the observability analysis method for PWCS is employed, and the stochastic observability based on Fisher information is also adopted to analyze the lower bound of the estimation. Via analyzing the different cases with different LOS/TOA/Velocity measurements by PWCS observability and Fisher information, this paper established the minimal conditions in which the autonomous navigation system is fully observable with enough measurements. Moreover, for some cases incompletely observable, the singularities are specified. Simulations of autonomous navigation of a Mars probe are performed to confirm the theoretical results. The observability analysis results can help the autonomous navigation system achieve better estimation.