A convex optimization approach to jump nonlinear systems

Abstract

We introduce a new methodology to approximate the lter density in hybrid Markovian switching systems. We relax the assumption that the mode transition process is a Markov chain and allow it to depend on the actual and unobservable state of the target. The approximation density is obtained as an expansion of gaussian densities. Such densities are selected as the solution of a convex programming problem which trades off sparsity of the solution with goodness of fit. We provide an analytical bound on the total variation distance between our approximation density and the actual filter density. A meaningful example shows that the proposed method can outperform the widely used interacting multiple model (IMM) in terms of accuracy.