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A differential geometric approach to nonlinear filtering - the projection filter

Objective



In dealing with stochastic linear systems, predictions and estimates are computed via the Kalman filter. Generalization to non-linear systems is an important area of research. Unfortunately, the optimal filter for nonlinear systems is infinite-dimensional. Approximate filters for non-linear systems, as the extended Kalman filter, are of great practical value. A disadvantage of many filters is that they are based on heuristic considerations. A new class of filters, the projection filters, was developed by the applicant. These filters use an a priori given finite dimensional class of probability distributions and at each moment the change in distribution that is prescribed by the exact filter is projected on the linear space of changes corresponding to the chosen class of distributions. Computer simulations, existence of exponential families which simplify the filters, application to finance and theoretical analysis in case of small noise were developed by the applicant. Such results strongly motivate the prosecution of the project by mean of further simulations, further theoretical analysis and applications to financial and engineering problems.

Funding Scheme

RGI - Research grants (individual fellowships)

Coordinator

Institut National de Recherches en Informatique et en Automatique (INRIA)
Address
Campus Universitaire De Beaulieu Avenue Du Général Leclerc
35042 Rennes
France

Participants (1)

Not available
Italy