Extension of the Observability Rank Condition to Time-Varying Nonlinear Autonomous Systems

The study presents an innovative approach for observability analysis in time-varying, nonlinear autonomous systems. Traditional criteria assert that state observability applies solely to nonlinear systems where the system input is not explicitly state-dependent. In contrast, this study presents a groundbreaking observability criterion that incorporates the impact of system input without increasing the dimension of the analysis. This new criterion is applied to the relative navigation system of a Mars spacecraft, resulting in an observability conclusion for monitoring a non-cooperative target using angles-only measurements. Note to Practitioners—Observability is a critical property of observation systems that guides designs and operations. This paper introduces a new method for conducting observability analysis in time-varying, nonlinear autonomous systems. Traditional criteria typically limit state observability to nonlinear systems where the system input is not explicitly state-dependent. In contrast, this study proposes an innovative observability criterion that incorporates the influence of system input without increasing the dimensionality of the analysis. This new criterion has been successfully applied to the relative navigation system of a Mars spacecraft, resulting in an observability assessment for monitoring a non-cooperative target using angles-only measurements. This work has the potential to advance the understanding and application of observability in complex autonomous systems, especially in scenarios involving dynamic changes and nonlinearities.