sgd4filtering
Data-driven Optimal Filtering for Linear Systems with Unknown Noise Covariances
Science Score: 44.0%
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Repository
Data-driven Optimal Filtering for Linear Systems with Unknown Noise Covariances
Basic Info
- Host: GitHub
- Owner: shahriarta
- License: apache-2.0
- Language: Jupyter Notebook
- Default Branch: main
- Size: 169 KB
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- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 0
Metadata Files
README.md
sgd4filtering
This is the repository for regenerating the simulations in the following work appeared in Neural Information Processing Systems (NeurIPS) 2023:\ "Data-driven Optimal Filtering for Linear Systems with Unknown Noise Covariances"\ by Shahriar Talebi $^{1,2} \quad$ Amirhossein Taghvaei $^{1}\quad$ Mehran Mesbahi $^{1}$\ $^{1}$ University of Washington, Seattle, WA, 98105\ $^{2}$ Harvard University, Cambridge, MA, 02138 \ emails: talebi@seas.harvard.edu $\quad$ amirtag@uw.edu $\quad$ mesbahi@uw.edu
Abstract: This paper examines learning the optimal filtering policy, known as the Kalman gain, for a linear system with unknown noise covariance matrices using noisy output data. The learning problem is formulated as a stochastic policy optimization problem, aiming to minimize the output prediction error. This formulation provides a direct bridge between data-driven optimal control and, its dual, optimal filtering. Our contributions are twofold. Firstly, we conduct a thorough convergence analysis of the stochastic gradient descent algorithm, adopted for the filtering problem, accounting for biased gradients and stability constraints. Secondly, we carefully leverage a combination of tools from linear system theory and high-dimensional statistics to derive bias-variance error bounds that scale logarithmically with problem dimension, and, in contrast to subspace methods, the length of output trajectories only affects the bias term.
Owner
- Name: Shahriar Talebi
- Login: shahriarta
- Kind: user
- Location: Seattle, WA
- Company: University of Washington
- Website: http://students.washington.edu/shahriar/
- Repositories: 2
- Profile: https://github.com/shahriarta
I’m a Ph.D. candidate at the William E. Boeing Department of Aeronautics and Astronautics supervised by Prof. M. Mesbahi.
Citation (CITATION.cff)
cff-version: 1.2.0
title: SGD for Filtering
message: >-
If you use this software, please cite it using the
metadata from this file.
type: misc
authors:
- given-names: Shahriar
name-particle: Talebi
email: talebi@seas.harvard.edu
affiliation: Harvard University
orcid: 'https://orcid.org/0000-0001-8752-2888'
- given-names: Amirhossein
name-particle: Taghvaei
email: amirtag@uw.edu
affiliation: University of Washington
- given-names: Mehran
name-particle: Mesbahi
email: Mesbahi@uw.edu
affiliation: University of Washington
version: 1.0.0
doi: shahriarta/sgd4filtering
url: https://github.com/shahriarta/sgd4filtering
note: Available at \url{https://github.com/shahriarta/sgd4filtering}
date-released: 2023-10-19