Robust filtering for deterministic systems with implicit outputs

This paper addresses the state estimation of a class of continuous-time-affine systems with implicit outputs. We formulate the problem in the deterministic H∞H∞ filtering setting by computing the value of the state that minimizes the induced L2L2-gain from disturbances and noise to estimation error, while remaining compatible with the past observations. To avoid weighting the distant past as much as the present, a forgetting factor is also introduced. We show that, under appropriate observability assumptions, the optimal estimate converges globally asymptotically to the true value of the state in the absence of noise and disturbance. In the presence of noise, the estimate converges to a neighborhood of the true value of the state. We apply these results to the estimation of position and attitude of an autonomous vehicle using measurements from an inertial measurement unit (IMU) and a monocular charged-coupled-device (CCD) camera attached to the vehicle.