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Recursive least-squares estimation in case of interval observation data

Author

Listed:
  • Hansjorg Kutterer
  • Ingo Neumann

Abstract

In the engineering sciences, observation uncertainty often consists of two main types: random variability due to uncontrollable external effects and imprecision due to remaining systematic errors in the data. Interval mathematics is well suited to treat this second type of uncertainty if set-theoretical overestimation is avoided. Overestimation means that the true range of parameter values is only quantified by rough, meaningless outer bounds. If recursively formulated estimation algorithms are used, overestimation becomes a key problem. This occurs in state-space estimation which is relevant in real-time applications and which is essentially based on recursions. Hence, overestimation has to be analysed thoroughly to minimise its impact. In this study, observation imprecision is referred to physically meaningful influence parameters. This allows to reformulate the recursion algorithm yielding an increased efficiency and to rigorously avoid overestimation. In order to illustrate and discuss the theoretical results, a damped harmonic oscillation and the monitoring of a lock are presented as examples.

Suggested Citation

  • Hansjorg Kutterer & Ingo Neumann, 2011. "Recursive least-squares estimation in case of interval observation data," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 5(3/4), pages 229-249.
    • Handle: RePEc:ids:ijrsaf:v:5:y:2011:i:3/4:p:229-249
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    Cited by:

    1. Ligang Sun & Hamza Alkhatib & Boris Kargoll & Vladik Kreinovich & Ingo Neumann, 2019. "Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems," Mathematics, MDPI, vol. 7(12), pages 1-22, December.

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