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Student's t-Filters for Noise Scale Estimation

Tronarp, Filip LU ; Karvonen, Toni and Sarkka, Simo (2019) In IEEE Signal Processing Letters 26(2). p.352-356
Abstract

In this letter, we analyze certain student's t-filters for linear Gaussian systems with misspecified noise covariances. It is shown that under appropriate conditions, the filter both estimates the state and re-scales the noise covariance matrices in a Kullback-Leibler optimal fashion. If the noise covariances are misscaled by a common scalar, then the re-scaling is asymptotically exact. We also compare the student's t-filter scale estimates to the maximum-likelihood estimates. Simulations demonstrating the results on the Wiener velocity model are provided.

Please use this url to cite or link to this publication:
author
; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Kalman filtering, model misspecification, noise covariance estimation, student's t-filtering
in
IEEE Signal Processing Letters
volume
26
issue
2
article number
8606947
pages
5 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85060530856
ISSN
1070-9908
DOI
10.1109/LSP.2018.2889440
language
English
LU publication?
no
id
813ac6a1-6ba1-4171-ae94-72f26db15525
date added to LUP
2023-08-20 22:45:56
date last changed
2025-10-14 11:26:57
@article{813ac6a1-6ba1-4171-ae94-72f26db15525,
  abstract     = {{<p>In this letter, we analyze certain student's t-filters for linear Gaussian systems with misspecified noise covariances. It is shown that under appropriate conditions, the filter both estimates the state and re-scales the noise covariance matrices in a Kullback-Leibler optimal fashion. If the noise covariances are misscaled by a common scalar, then the re-scaling is asymptotically exact. We also compare the student's t-filter scale estimates to the maximum-likelihood estimates. Simulations demonstrating the results on the Wiener velocity model are provided.</p>}},
  author       = {{Tronarp, Filip and Karvonen, Toni and Sarkka, Simo}},
  issn         = {{1070-9908}},
  keywords     = {{Kalman filtering; model misspecification; noise covariance estimation; student's t-filtering}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{352--356}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Signal Processing Letters}},
  title        = {{Student's t-Filters for Noise Scale Estimation}},
  url          = {{http://dx.doi.org/10.1109/LSP.2018.2889440}},
  doi          = {{10.1109/LSP.2018.2889440}},
  volume       = {{26}},
  year         = {{2019}},
}