TY - JOUR

T1 - Recursive least-squares estimation in case of interval observation data

AU - Kutterer, Hansjörg

AU - Neumann, Ingo

PY - 2011/7/11

Y1 - 2011/7/11

N2 - 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 settheoretical 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.

AB - 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 settheoretical 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.

KW - Damped harmonic oscillation

KW - Imprecision

KW - Interval data

KW - Interval mathematics

KW - Least-squares estimation

KW - Observation uncertainty

KW - Overestimation

KW - Recursive estimation

KW - Recursive parameter estimation

KW - State-space estimation

UR - http://www.scopus.com/inward/record.url?scp=79960221840&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79960221840

VL - 5

SP - 229

EP - 249

JO - International Journal of Reliability and Safety

JF - International Journal of Reliability and Safety

SN - 1479-389X

IS - 3-4

ER -