The particle filter associated with the Markov process X k = ( X k , Y k ) given the partial observations Y 0 = y 0 , ⋯ ⋯ , Y k = y k , is defined in terms of particles evolving in R d x + d y with a likelihood function given with some obvious abusive notation by p ( Y k | X k ) . These probabilistic techniques are closely related to Approximate Bayesian Computation (ABC). In the context of particle filters, these ABC particle filtering techniques were introduced in 1998 by P. Del Moral, J. Jacod and P. Protter. They were further developed by P. Del Moral, A. Doucet and A. Jasra.