Particle filters with auxiliary Markov transition. Application to crossover and to multitarget tracking

In multitarget tracking, most particle approximations have the effect that new multitarget particles are obtained by discarding or replicating globally existing multitarget particles. A better design would be to produce shuffled multitarget particles in which the particle for each different target is replicated from a different existing multitarget particle. The objective of this work is to propose a solution to this problem, that is based on introducing an auxiliary Markov transition. This can be seen as an extension of independent interest of the auxiliary particle filter. Optimization of the design parameters is also addressed.