Computationally efficient angles-only tracking with particle flow filters

Particle filters represent the current state of the art in nonlinear, non-Gaussian filtering. They are easy to implement and have been applied in numerous domains. That being said, particle filters can be impractical for problems with state dimensions greater than four, if some other problem specific efficiencies can't be identified. This "curse of dimensionality" makes particle filters a computationally burdensome approach, and the associated re-sampling makes parallel processing difficult. In the past several years an alternative to particle filters dubbed particle flows has emerged as a (potentially) much more efficient method to solving non-linear, non-Gaussian problems. Particle flow filtering (unlike particle filtering) is a deterministic approach, however, its implementation entails solving an under-determined system of partial differential equations which has infinitely many potential solutions. In this work we apply the filters to angles-only target motion analysis problems in order to quantify the (if any) computational gains over standard particle filtering approaches. In particular we focus on the simplest form of particle flow filter, known as the exact particle flow filter. This form assumes a Gaussian prior and likelihood function of the unknown target states and is then linearized as is standard practice for extended Kalman filters. We implement both particle filters and particle flows and perform numerous numerical experiments for comparison.