Student's t-Filters for Noise Scale Estimation

Filip Tronarp, Toni Karvonen, Simo Särkkä

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3 Citations (Scopus)
223 Downloads (Pure)


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.

Original languageEnglish
Article number8606947
Pages (from-to)352-356
Number of pages5
JournalIEEE Signal Processing Letters
Issue number2
Publication statusPublished - 1 Feb 2019
MoE publication typeA1 Journal article-refereed


  • Kalman
  • Kalman filtering
  • Variances
  • model mis-specification
  • noise covariance estimation
  • student's t-filtering

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