Title: Recursive least-squares estimation in case of interval observation data

Authors: Hansjorg Kutterer, Ingo Neumann

Addresses: Geodetic Institute, Leibniz University Hannover, Nienburger Strasse 1, D-30167 Hannover, Germany. ' Institute of Geodesy – Geodetic Laboratory, University FAF Munich, Werner-Heisenberg-Weg 39, D-85579 Neubiberg, Germany

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.

Keywords: interval mathematics; interval data; observation uncertainty; imprecision; least squares estimation; recursive estimation; recursive parameter estimation; overestimation; state-space estimation; damped harmonic oscillation; lock monitoring; reliability.

DOI: 10.1504/IJRS.2011.041178

International Journal of Reliability and Safety, 2011 Vol.5 No.3/4, pp.229 - 249

Received: 09 Jun 2010
Accepted: 24 Jan 2011

Published online: 31 Mar 2015 *

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