H∞ Estimation of Continuous-Time Systems with Implicit Outputs from Discrete Noisy Time-Delayed Measurements

We address the state estimation of a class of continuous-time systems with implicit outputs, whose measurements arrive at discrete-time instants, are time-delayed, noisy, and may not be complete. The estimation problem is formulated in the deterministic H∞ filtering setting by computing the value of the state that minimizes the induced L2-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. The estimation of position and attitude of an autonomous robotic vehicle using measurements from an inertial measurement unit (IMU) and a monocular charged-coupled-device (CCD) camera attached to the vehicle illustrates these results. In the context of this application, the robust H∞ estimator can deal directly with the usual problems associated with vision systems such as noise, latency and intermittency of observations. We present and discuss several simulation results that demonstrate and validate the good performance and applicability of the proposed estimator.