Likelihood Scouting via Map Inversion for a Posterior-Sampled Particle Filter

An exploit of the sequential importance sampling (SIS) algorithm using differential algebra techniques is derived to develop an efficient particle filter. The filter creates an original kind of particles, called scout particles, that bring information from the measurement noise onto the state prior probability density function. Thanks to the creation of high-order polynomial maps and their inversions, the scouting of the measurements helps the SIS algorithm identify the region of the prior more affected by the likelihood distribution. The result of the technique is two different versions of the proposed scout particle filter (SPF), which identifies and delimits the region where the true posterior probability has high density in the SIS algorithm. Four different numerical applications show the benefits of the methodology both in terms of accuracy and efficiency, where the SPF is compared to other particle filters, with a particular focus on target tracking and orbit determination problems.