Target Tracking using a Particle Filter Based on the Projection Method

We present a new particle filter (PF) algorithm, which uses a mathematical tool known as Galerkin´s projection method to generate the proposal distribution. By definition, Galerkin´s method is a numerical approach to approximate the solution of a partial differential equation. By leveraging this method with L² theory and the FFT, this new proposal is fundamentally different to various local linearization or Kalman filter based proposals. We apply this algorithm to a bearings-only tracking problem. As shown in the theory and indicated by our simulations, this proposal renders more support from the true posterior distribution, thereby significantly enhances the estimation accuracy compared to standard bootstrap filters. In addition, because of this improved proposal distribution, the new particle filter can achieve a given level of performance with less sample size.