Linear parametrically varying systems with brief instabilities: an application to vision/inertial navigation

This paper addresses the problem of nonlinear filter design to estimate the relative position and velocity of an unmanned air vehicle (UAV) with respect to a point on a ship using infrared (IR) vision, inertial, and air data sensors. Sufficient conditions are derived for the existence of a particular type of complementary filters with guaranteed stability and performance in the presence of so-called out-of-frame events that arise when the vision system loses its target temporarily. The results obtained build upon new developments in the theory of linear parametrically varying systems (LPVs) with brief instabilities - also reported in the paper - and provide the proper framework to deal with out-of-frame events. Field tests with a prototype UAV illustrate the performance of the filter and the scope of applications of the new theory developed.