A. Wieser:

"Uncertainty of Motion Detection from Coordinate Differences";

Talk: MCG Stuttgart 2012, Stuttgart (invited); 2012-03-27 - 2012-03-29; in: "3rd International Conference on Machine Control & Guidance Proceedings", V. Schwieger, S. Böttinger, B. Zheng (ed.); (2012), ISBN: 9783000372957; 57 - 63.

The distance computed from measured coordinate differences is a biased estimate of the true distance. The bias exceeds the standard deviation of the coordinate differences if the true distance is short. Therefore, it is necessary to take the uncertainty of the measurements properly into account when motion is to be distinguished from static periods using estimated coordinate differences. In this contribution we focus on the stochastic properties of the coordinate differences and the vector norm. We give a suitable statistical test which allows correctly detecting motion with a chosen probability if the amount of motion exceeds a chosen minimum. We also quantify the bias of the computed distance and present the Normal distribution as a suitable approximation if the true distance exceeds the level of the standard deviations by a factor of 10 or more. This approximation may be useful in practical applications to express the amount of actual motion using confidence intervals.

Motion detection, distribution of vector norm, distance bias.

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