Smoothed state estimation for nonlinear Markovian switching systems

The contributions of the work presented here are twofold. First we introduce a computationally efficient refinement of the unscented transformation (UT) which is applicable to nonlinear systems with a linear substructure. The resulting UT is referred to as the marginalised UT and is derived in two forms: the conventional UT marginalised form and the simplex sigma point marginalised form. The second contribution is the application of the proposed marginalised UT to smoothed state estimation in Markovian switching systems with nonlinear dynamic and measurement equations. Three algorithms for smoothing are proposed in this context. The first two algorithms are based on the well-known interacting multiple model (IMM) and hypothesis pruning techniques. The third algorithm uses maximum a posteriori (MAP) estimates of the switching parameter to generate a stochastic dynamic system within which smoothed state estimation is performed. The performances of the smoothing algorithms are analysed and compared in two scenarios involving a target which undergoes coordinated turn maneuvers.