No abstract

Bounded-error estimation is the estimation of the parameter or state vector of a model from experimental data, under the assumption that some suitably dened errors should belong to some prior feasible sets. When the model outputs are linear in the vector to be estimated, a number of methods are available to enclose all estimates that are consistent with the data into simple sets such as ellipsoids, orthotopes or parallelotopes, thereby providing guaranteed set estimates. In the nonlinear case, the situation is much less developed and there are very few methods that produce such guaranteed estimates. In this paper, the discrete-time problem is cast into the more general framework of constraint satisfaction problems. Algorithms rather classical in the area of interval constraint propagation are extended by replacing intervals by more general subsets of real vector spaces. This makes it possible to propose a new algorithm that contracts the feasible domains for each uncertain variable optimally (i.e., no smaller domain could be obtained) and e¢ciently. The resulting methodology is illustrated on discrete-time nonlinear state estimation. The state at time k is estimated either from past measurement only or from all measurements assumed to be available from the start. Even in the causal case, prior information on the future value of the state and output vectors, due for instance to physical constraints, is readily taken into account.

Current plans call for the first Terrestrial Planet Finder mission, TPF-C, to be a monolithic space telescope with a coronagraph for achieving high contrast.The coronagraph removes the diffracted starlight allowing the nearby planet to be detected. In this paper, we present a model of the planet measurement and noise statistics. We utilize this model to develop two planet detection algorithms, one based on matched filtering of the PSF and one using Bayesian techniques. These models are used to formulate integration time estimates for a planet detection with desired small probabilities of false alarms and missed detections.Subject headings: planet finding, bayesian, hypothesis testing, completeness, TPF where E o is the electric field at the exit pupil aperture, f is the focal length of the camera, λ is the wavelength of the light, and the set S represents the exit pupil aperture, which, for an open square aperture, as an example, is given by,where D is the width of the aperture.The optical system prior to the exit pupil of the SSS consists of various reflections and correction elements all of which have a certain efficiency. If we take E i (λ) to be the uniform electric field at the entrance pupil, then E o can be written,