Iterative State Estimation in Non-linear Dynamical Systems Using Approximate Expectation Propagation
Abstract: Bayesian inference in non-linear dynamical systems seeks to find good posterior approximations of a latent state given a sequence of observations. Gaussian filters and smoothers, including the (extended/unscented) Kalman filter/smoother, which are commonly used in engineering applications, yield Gaussian posteriors on the latent state. While they are computationally efficient, they are often criticised for their crude approximation of the posterior state distribution. In this paper, we address this criticism by proposing a message passing scheme for iterative state estimation in non-linear dynamical systems, which yields more informative (Gaussian) posteriors on the latent states. Our message passing scheme is based on expectation propagation (EP). We prove that classical Rauch--Tung--Striebel (RTS) smoothers, such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS), are special cases of our message passing scheme. Running the message passing scheme more than once can lead to significant improvements of the classical RTS smoothers, so that more informative state estimates can be obtained. We address potential convergence issues of EP by generalising our state estimation framework to damped updates and the consideration of general $\alpha$-divergences.
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: - Replaced the bearings-only tracking experiment with a bearings-only turning target tracking experiment (section 5.2). We only report the ablation study with respect to power since ablation with respect to damping was not interesting.
- Additional experiments (section 5.3). We investigated the ablation with respect to the dimensions in the Lorenz 96 experiment as requested by reviewer JrZp.
- Minor fixes across the document based on suggestions in reviews.
- Updated plots.
- Clarification statement in caption for Table 1
** Update (19/05/2022) **
- Added the results for the IEKS baseline in all experiments and modified the text accordingly.
- Included a results table for the UNGM experiment.
** Update (20/05/2022) **
- Included the definitions of RMSE and NLL in the appendix.
- Included a remark about inference in online settings.
- Minor fixes to plots in Fig 1 and Fig 3. In particular, changed the xlabel from 'Iterations' -> 'EP Iterations'.
Video: https://www.youtube.com/watch?v=FrTY04gXErY
Code: https://github.com/sanket-kamthe/EPyStateEstimator
Assigned Action Editor: ~Thang_D_Bui1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 40
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