State estimation for continuous-time systems with perspective outputs from discrete noisy time-delayed measurements

This paper addresses the state estimation of continuous-time systems with perspective outputs, whose measurements arrive at discrete-time instants, are time-delayed, noisy, and may not. be complete. Resorting to dynamic programming, we derive a minimum-energy estimator which produces an estimate of the state that is "most compatible" with the dynamics, in the sense that it requires the least amount of noise energy to explain the measured outputs. The state-estimator has the desired property that, under suitable observabillity assumptions, the estimate converges asymptotically to the true value of the state in the absence of noise and disturbance. In the presence of noise, the estimate remains bounded away from the true value of the state. We apply these results to the estimation of position and orientation for a mobile robot that uses a monocular charged-coupled-device (CCD) camera mounted on-board to observe the apparent motion of stationary points. In the context of our application, the estimator can deal directly with the usual problems associated with vision systems such as noise, latency and intermittency of observations. Experimental results are presented and discussed.