Invertible Particle Flow for Nonlinear Filtering

A key challenge when designing nonlinear filters (e.g. particle filters, sequential MCMC, etc.) in high-dimensional state spaces is the construction of a proposal distribution that is close to the target distribution. Recent advances in particle flow filters provide a promising avenue to avoid weight degeneracy in the particle filters; particles drawn from the prior distribution are migrated in the state-space to the posterior distribution by solving partial differential equations.

 

Approximations are needed in the implementation of particle flow filters; as a result the particles do not exactly match a sample drawn from the desired posterior distribution. We propose new particle filters and MCMC algorithms which incorporate deterministic particle flows into an encompassing particle filter or sequential MCMC framework. The valuable theoretical guarantees concerning particle filter or sequential MCMC still apply, but we can exploit the attractive performance of the particle flow methods. The filters we describe involve a computationally efficient weight update step, arising because the embedded particle flows we design possess an invertible mapping property. 

We constructed particle flow procedures in [1] so that the flow constitutes an invertible mapping. This allows an efficient proposal density evaluation.

 

The invertible particle flow can be incorporated into the particle filtering framework [1] or the sequential MCMC framework [2].

[1] Li, Y., and M. J. CoatesParticle Filtering with Invertible Particle Flow, Submitted.

[2] Li, Y., and M. J. CoatesSequential MCMC with Invertible Particle Flow, Submitted.

We present tracking results in a multi-target tracking scenario with a relatively large state space and highly informative measurements [1].

 

The tracking with the particle flow particle filter [1] is displayed as follows:

Faculty: Prof. Mark Coates

Ph.D. Student: Yunpeng Li

Collaborator:  Lingling Zhao (visiting scholar from Harbin Institute of Technology)

[1] Li, Y., and M. J. CoatesParticle Filtering with Invertible Particle Flow, Submitted. (Matlab codes provided.)

[2] Li, Y., and M. J. CoatesSequential MCMC with Invertible Particle Flow, Submitted.

[3] Li, Y., and M. J. Coates"Fast Particle Flow Particle Filters via Clustering", Proc. International Conference on Information Fusion, Heidelberg, Germany, 07/2016. 

[4] Zhao, L.J. WangY. Li, and M. J. Coates"Gaussian particle flow implementation of PHD filter", Proc. SPIE Conf. Signal Proc., Sensor Fusion, Target Recog., 04/2016.

[5] Li, Y.L. Zhao, and M. J. Coates"Particle flow for particle filtering", Int. Conf. Acoustics, Speech and Signal Proc. (ICASSP), Shanghai, China, 03/2016.

[6] Li, Y.L. Zhao, and M. J. Coates"Particle flow auxiliary particle filter", IEEE Int. Workshop Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Cancun, Mexico, 12/2015.