Feedback Particle FilteringChristopher Kuo-LeBlancTypical chemical processes are highly nonlinear and necessitate advanced state estimation techniques for effective controller design. Many nonlinear filters have been designed for this purpose, but have design flaws for highly nonlinear systems. In the past decade, members of the particle filtering community have proposed a novel approach to particle filtering that roots out some of its key design flaws. This new particle filter is known as the feedback particle filter (FPF). The primary goal of this project is to investigate the FPF as a competitive state estimation technique. Two classic examples of nonlinear filters are the unscented Kalman filter (UKF) and the particle filter. While both are excellent options, they have design flaws for highly nonlinear systems. The UKF operates on the assumption that the posterior of the system is Gaussian, which is generally untrue for highly nonlinear systems. The particle filter is a convenient alternative as it assumes no information about the posterior distribution. The particle filter, however, suffers from a phenomenon known as particle degeneracy; which lends it to instability for unstable systems, filter divergence, and the curse of dimensionality. The FPF has a reformulated Bayesian update that alleviates particle degeneracy and provides a naturally emergent feedback structure for each individual particle. In this work we are investigating how this feedback structure influences the movement of the particle locations and the stability of the FPF. References: B. Ristic, S. Arulampalam, and N. Gordon. Beyond the Kalman filter: Particle filters fortracking applications. Artech house, 2004. F. Daum and J. Huang. article degeneracy: root cause and solution. In Signal Processing, Sensor Fusion, and Target Recognition XX, volume 8050, page 80500W. International Society for Optics and Photonics, 2011. T. Yang, P. G. Mehta, and S. P. Meyn. Feedback particle filter. IEEE transactions on Automatic control, 58(10):2465–2480, 2013. |