Optimal Transportation Particle Filter for Linear Filtering Systems With Correlated Noises

Dedicate to Professor Thomas Kailath on the occasion of his 87 Birthday. In this article, we derive an optimal transportation particle filter for linear time-varying systems with correlated noises. This method can be regarded as the extension of the feedback particle filter with an optimal transportation structure. However, the particles in our method are evolved in a deterministic way, while we need to generate random particles in a feedback particle filter. Consequently, we only need a very few particles to obtain the satisfying results, and this property is especially significant for high-dimensional problems. The error analysis of our method and the feedback particle filter has been carried out when the system is time invariant. Compared with the feedback particle filter and the ensemble Kalman filter, our method shows great efficiency in numerical experiments, including both the scalar and high-dimensional cases.