Guaranteed nonlinear estimation using constraint propagation on sets
Résumé
Bounded-error estimation is the estimation of the parameter or state vector of a model from experimental data, under the assumption that some suitably de
ned 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.
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