doi:10.3850/978-981-08-5118-7_012

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 in, e. g., interval-mathematical extensions of the least-squares estimation procedure if the set-theoretical overestimation is avoided (Schön and Kutterer, 2005). Overestimation means that the true range of parameter values representing both a mean value and imprecision is only quantified by rough, meaningless upper bounds. If recursively formulated estimation algorithms are used for better efficiency, overestimation becomes a key problem. This is the case in state-space estimation which is relevant in real-time applications and which is essentially based on recursions. Hence, overestimation has to be analyzed thoroughly to minimize its impact on the range of the estimated parameters. This paper is based on previous work (Kutterer and Neumann, 2009) which is extended regarding the particular modeling of the interval uncertainty of the observations. Besides a naïve approach, observation imprecision models using physically meaningful influence parameters are considered; see, e.g., Schön and Kutterer (2006). The impact of possible overestimation due to the respective models is rigorously avoided. In addition, the recursion algorithm is reformulated yielding an increased efficiency. In order to illustrate and discuss the theoretical results a damped harmonic oscillation is presented as a typical recursive estimation example in Geodesy.

Keywords: Interval mathematics, Imprecision, Recursive parameter estimation, Overestimation, Least-squares, Damped harmonic oscillation.

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