Hierarchical Decomposition and Approximation of Sensor Data

  • Roland RittEmail author
  • Paul O’Leary
  • Christopher Josef Rothschedl
  • Ahmad Almasri
  • Matthew Harker
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


This paper addresses the issue of hierarchical approximation and decomposition of long time series emerging from the observation of physical systems. The first level of the decomposition uses spatial weighted polynomial approximation to obtain local estimates for the state vectors of a system, i.e., values and derivatives. Covariance weighted Hermite approximation is used to approximate the next hierarchy of state vectors by using value and derivative information from the previous hierarchy to improve the approximation. This is repeated until a certain rate of compression and/or smoothing is reached. For further usage, methods for interpolation between the state vectors are presented to reconstruct the signal at arbitrary points. All derivations needed for the presented approach are provided in this paper along with derivations needed for covariance propagation. Additionally, numerical tests reveal the benefits of the single steps. The proposed hierarchical method is successfully tested on synthetic data, proving the validity of the concept.


Signal decimation Hermite approximation Hermite interpolation Covariance propagation Signal reconstruction Weighted regression 



Partial funding for this work was provided by the Austrian research funding association (FFG) under the scope of the COMET program within the K2 center “IC-MPP” (contract number 859480). This programme is promoted by BMVIT, BMDW and the federal states of Styria, Upper Austria and Tyrol.


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Chair of AutomationUniversity of LeobenLeobenAustria

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