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Nonlinear filter design using Fokker-Planck propagator in Kronecker tensor format

: Demissie, B.; Khan, M.A.; Govaers, F.

Institute of Electrical and Electronics Engineers -IEEE-; International Society of Information Fusion -ISIF-; IEEE Aerospace and Electronic Systems Society -AESS-:
19th International Conference on Information Fusion, FUSION 2016. Proceedings : Heidelberg, 5-8 July 2016
Piscataway, NJ: IEEE, 2016
ISBN: 978-0-9964-5274-8
ISBN: 978-1-5090-2012-6
8 S.
International Conference on Information Fusion (FUSION) <19, 2016, Heidelberg>
Fraunhofer FKIE ()

We consider the general continuous-discrete nonlinear filtering problem. In particular, the prediction step involving the numerical solution of the Fokker-Planck equation for the time evolution of the state probability density is known to be a challenging problem as it suffers from the curse of dimensionality. In this contribution a novel approach based on Kronecker tensor decomposition of the matrix exponential of the Fokker-Planck operator is presented. This approach allows solving high dimensional filtering problems while enlarging considerably the time propagation step size compared with finite-difference time stepping methods. We show results from simulations for a passive tracking example involving a four dimensional state vector and compare with other tensor decomposition based approaches.