This paper studies a variational formulation of the image matching problem. We consider a scenario in which a canonical representative image T is to be carried via a smooth change of variable into an image which is intended to provide a good fit to the observed data. The images are all defined on a compact set G ae IR 3 . The changes of variable are determined as solutions of the nonlinear Eulerian transport equation dj(s; x) ds = v(j(s; x); s); j(ø ; x) = x; (0:1) with the location j(0; x) in the canonical image carried to the location x in the deformed image. The variational problem then takes the form arg min v kvk 2 + Z G jT ffi j(0; x) \Gamma D(x)j 2 dx ; (0:2) where kvk is an appropriate norm on the velocity field v(\Delta; \Delta), and the second term attempts to enforce fidelity to the data. In this paper we derive conditions under which the variational problem described above is well posed. The key issue is the choice of the norm. Conditions are formulated u...

We present necessary and sufficient conditions for the existence of worst case controllers and estimators for nonlinear systems. These are also called H1 suboptimal controllers and estimators. We consider affine and more general nonlinear systems, both time varying and autonomous over finite, semi-infinite and infinite intervals. In particular, we give necessary and sufficient conditions for the solvability of a standard H1 suboptimal control problem by measurement feedback that involve the solvability of a pair of partial differential equations of the Hamilton-Jacobi type. The first is the one associated with the problem of H1 suboptimal control by state feedback that has appeared previously in the work of several authors. The second is a new Hamilton-Jacobi equation associated with H1 suboptimal estimation. Key words: nonlinear H1 control, nonlinear H1 estimation, nonlinear worst case control, nonlinear worst case estimation AMS Subject Classifications: 93C10, 49A40 1 Introductio...

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 re-designed 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 onboard 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.

deterministic interpretation of the Kalman #ltering formulas is given, using theprinc#RB of least squares estimation. The observed signal and the to-be-estimated signal are modeled as being generated as outputs of a #nite-dimensional linear system driven by an input disturbanc, Postulating that the observed signal is generated by the inputdisturbanc that has minimal least squares norm leads to a method ofcqB#B#;q an estimate of the to-be-estimated output. The derivation of the resulting #lter iscqBNBN out in ac;BNPq,VL self-c,VLLVPq way. The analogous approac to least squares cuares is alsodiscPILRq c 2003 Elsevier B.V. All rights reserved.

This paper addresses the pose estimation problem for autonomous vehicles that use a monocular charged-coupled-device (CCD) camera mounted onboard that observes the apparent motion of stationary points. We formulate the problem in the framework of state estimation of a state-affine system with multiple perspective outputs. Resorting to dynamic programming, we derive a minimumenergy 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. In our formulation we take directly into account that the measurements arrive at discrete-time instants, are time-delayed, and may not be complete. In this way, we can deal with usual problems in vision systems such as noise as well as latency and intermittency of observations. The convergence of the proposed observer system is analyzed and simulations results are presented and discussed.

We consider the nonlinear filtering problem dz = f(z)dt + fidw, dy = h(z)dt + fidu, and obtain linq-oElogq'(z,t) =-W (z, t) for unnormalised conditional densities q'(z, t) using PDE methods. Here, W(z,t) is the value function for a deterministic optimal control problem arising in Mortensen's deterministic estimation, and is the unique viscosity solution of a Hamilton-Jacobi-Bellman equation.

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 observability 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 chargedcoupled-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.

This paper addresses the problem of nonlinear filter design to estimate the relative position and attitude of an autonomous vehicle with respect to a desired coordinate system defined by visual landmarks using measurements from an inertial measurement unit (IMU) and a monocular charged-coupled-device (CCD) camera mounted on-board. We formulate the problem in the framework of state estimation of a state-affine system with implicit outputs. Resorting to dynamic programming, we derive a H∞ estimator which produces an estimate of the state that is compatible with the dynamics and ensures a prescribed bound γ on the discounted induced L2-gain from disturbances and noise to estimation error. In our formulation we take directly into account that the measurements arrive at discrete-time instants, are time-delayed, and may not be complete. In this way, we can deal with usual problems in vision systems such as noise as well as latency and intermittency of observations. The convergence of the proposed observer system is analyzed and simulations results are presented and discussed.