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

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.