Observability and sensitivity analysis of lightcurve measurement models for use in space situational awareness

Abstract

ABSTRACTThis paper deals with the observability and sensitivity analysis of the lightcurve measurement for use in the estimation of instantaneous pose (orientation) and shape geometry. Since several reflectance models exist that are typically used in obtaining a synthetic lightcurve measurement, they are compared to assess the observability or/and ‘sensitivity’ to determine the ‘best model’ for use. These measurement models are nonlinear with implicit and non-trivial dependency on the states; a numerical Jacobian as well as an unscented Kalman filter derived observation matrix are synthesized for each choice of the measurement model and compared. As the linearization is about an attitude (orientation) trajectory, distinct cases are considered to elaborate the results. For the cases evaluated here, it is shown that the attitude and shape/size can indeed be estimated from the lightcurve, but this is also dependent upon the initial conditions (subsequent attitude trajectory). Linear observability analysis of a discretized system is also performed with respect to the attitude states and shape/size parameters using the singular value decomposition of the observability matrix synthesized for a batch of measurements. The results are summarized for various initial conditions of the resident space object's attitude and angular velocity states.