Rao-Blackwellized particle smoothing for mixed linear/nonlinear state-space model with asynchronously dependent noise processes

For the mixed linear/nonlinear state-space model (ML/NLSSM) with asynchronously dependent noise processes (ADNP), this paper aims at designing Rao-Blackwellized particle smoothing (RBPS) algorithms via the sequential Monte Carlo sampling method to solve its fixed-interval smoothing problem. Asynchronous dependency leads to the current measurement depending not only on the current state, but also on the one-step previous state. This subtle feature makes the use of conditionally linear substructures in the ML/NLSSM complicated and thus brings a technical difficulty to the design of RBPS algorithms. In this paper, we first employ a noise de-correlation technique to covert the ML/NLSSM with ADNP into the one without noise dependency. Then for the converted ML/NLSSM, we propose a particle smoothing algorithm called the basic Rao-Blackwellized backward simulation (RBBSi) for the nonlinear substate. To further alleviate the computational complexity of the basic RBBSi, two improved versions of the basic RBBSi are developed via the Metropolis-Hastings sampling. For the (conditionally) linear substate, two analytical smoothing algorithms are provided by virtue of the forward-backward smoothing formula and the two-filter smoothing formula. By integrating the proposed algorithms, a unified implementation framework enveloping six RBPS algorithms is obtained. Finally, two target tracking examples demonstrate the effectiveness and superiority of the proposed RBPS algorithms.