Feedback Particle Filter
Overview
Feedback particle filter (FPF) is a Monte Carlo algorithm that is used to approximate the solution of a stochastic (nonlinear) filtering problem. In contrast to conventional particle filters, the Bayesian update step in the FPF is implemented via a mean-field type feedback control law. A very good summary of FPF appears in the IEEE Control Systems Magazine (CSM) article (August 2021 issue) article. The article situates the development of the FPF within the framework of optimal transportation theory.
The FPF algorithm was introduced by our group at the turn of the decade (beginning in 2010). The algorithm represents a modern extension of the Kalman filter, a viewpoint stressed in the review paper. From a historical perspective, the FPF is a part of a broader class of exact and approximate interacting particle algorithms, specifically, the ensemble Kalman filter (EnKF), which is widely used for data assimilation in weather prediction and other types of geophysical applications.
Presentations
"Feedback Particle Filter and its Applications to Neuroscience." Cognition & Control seminar at the University of Florida, November 2012.
Slides from the invited lecture at the Sequential Monte Carlo workshop, Uppsala University, Sweden, August 30, 2017.
Slides from the invited lecture at the Institute for Systems Research at the University of Maryland, College Park, May 2, 2015.
Awards and Honors
Paper ''Multivariable Feedback Particle Filter'' with graduate student, Tao Yang, finalist for the Best Student Paper Award at the IEEE Conference on Decision and Control, Hawaii, December 2012
"Feedback Particle Filter and its Applications to Neuroscience." Plenary lecture at the 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems, Santa Barbara, September 16, 2012.
Publications
Taghvaei, A. and P. G. Mehta, “Optimal Transportation Methods in Filtering: The Feedback Particle Filter”, IEEE Control Systems Magazine, 41:4, 34-49, August 2021.
Taghvaei, A. and P. G. Mehta, “An Optimal Transport Formulation of the Ensemble Kalman Filter,” IEEE Transactions on Automatic Control, 66:7, 3052-3067, July 2021.
Taghvaei, A., P. G. Mehta, and S. P. Meyn, “Diffusion Map-based Algorithm for Gain Function Approximation in the Feedback Particle Filter,” SIAM Journal of Uncertainty Quantification, 8:3, 1090-1117, August 2020.
Zhang, C., A. Taghvaei, and P. G. Mehta, Feedback Particle Filter for Riemannian Manifolds and Matrix Lie Groups, IEEE Transactions on Automatic Control, 63:8, 2465-2480, August 2018.
Taghvaei, A., J de Wiljes, P. G. Mehta, and S. Reich, Kalman Filter and its Modern Extensions for the Continuous-time Nonlinear Filtering Problem, ASME Journal of Dynamic Systems, Measurement, and Control, 140(3), 030904, March 2018.
Yang, T. and P. G. Mehta, Probabilistic Data Association-Feedback Particle Filter for Multiple Target Tracking Applications, ASME Journal of Dynamic Systems, Measurement, and Control, 140(3), 030905, March 2018.
Yang, T., R. Laugesen, P. G. Mehta, and S. P. Meyn, Multivariable Feedback Particle Filter, Automatica, 71, 10-23, September 2016.
Laugesen, R., P. G. Mehta, S. P. Meyn, M. Ragnisky, Poisson’s Equation in Nonlinear Filtering, SIAM Journal of Optimization and Control, 53:1, 501-525, January 2015.
Yang, T., P. G. Mehta and S. P. Meyn. Feedback Particle Filter for a Continuous-time Markov Chain, IEEE Transactions on Automatic Control, 61:2, 556-561, January 2016.
Yang, T., P. G. Mehta, and S. P. Meyn, Feedback Particle Filter, IEEE Transactions on Automatic Control, 58:10, 2465-2480, October 2013.
Acknowledgements
Financial support from the Air Force Office of Scientific Research (AFOSR) grant FA9550-09-1-0190 and the National Science Foundation (NSF) grant EECS 09-25534 is gratefully acknowledged.