Estimation of Linear Space-Invariant Dynamics

Helmuth Naumer, Farzad Kamalabadi

Research output: Contribution to journalArticlepeer-review


We propose a computationally efficient estimator for multi-dimensional linear space-invariant system dynamics with periodic boundary conditions that attains low mean squared error from very few temporal steps. By exploiting the inherent redundancy found in many real-world spatiotemporal systems, the estimator performance improves with the dimensionality of the system. This paper provides a detailed analysis of maximum likelihood estimation of the state transition operator in linear space-invariant systems driven by Gaussian noise. The key result of this work is that, by incorporating the space-invariance prior, the mean squared error of a estimator normalized to the number of parameters is upper bounded by N-1M-1 + O(N-1 M-2), where N is the number of spatial points, and M is the number of observed timesteps after the initial value.

Original languageEnglish (US)
Article number9272542
Pages (from-to)2154-2158
Number of pages5
JournalIEEE Signal Processing Letters
StatePublished - 2020


  • Space-invariant
  • dynamical systems
  • spatiotemporal
  • system identification

ASJC Scopus subject areas

  • Signal Processing
  • Applied Mathematics
  • Electrical and Electronic Engineering


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