Sensability and excitability metrics applied to navigation systems assessment

Abstract

Based on a principal components decomposition of the state covariance matrix a "practically sensable" subspace and its orthogonal complement, the "practically non-sensable" subspace, are defined. The orthogonal projection of each augmented state vector (ASV) component over the practically sensable subspace defines its sensability measure. The excitability analysis quantifies the information conveyed by the innovations regarding the ASV for any particular trajectory stretch. This is done off line using a synthetic trajectory determined from actual flight data. Linearized models, referred to the synthetic trajectory, of the state deviations and innovations are used for a principal component analysis of the innovation signals. This allows decomposing the ASV over the trajectory stretch under consideration into a practically observable subspace and its orthogonal complement the practically un- observable one. A measure of the excitability of any component of the ASV space is defined as the norm of its orthogonal projection onto the first subspace. These concepts were applied to a CONAE navigation and control experiment on board the Brazilian VS30 suborbital rocket.