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This paper addresses the state estimation of systems with perspective outputs. 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. Under suitable observability assumptions, the 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. These results are also extended to solve the estimation problem when the measured outputs are transmitted through a network. In that case, we assume that the measurements arrive at discrete-time instants, are time-delayed, noisy, and may not be complete. We show that the redesigned minimum-energy estimator preserves the same convergence properties. 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.