In real world situations, most often the estimated 2D positions from the videos are effected by a noise.

I have a set of consecutive 2D positions for moving objects in 2D space. Part of this data (1000 observations) were annotated that the object is stationary (standing still). I would like to use this data (1000 observations) to define a threshold r around the zero. So, for example, if the change in the position of the object between two consecutive observations <= r; the object consider to be stationary.

In my current approach, I first calculate the absolute differences between each consecutive observations (or positions). Then, I calculated the following measures: mean, median, maximum, minimum, and the standard deviations of the absolute differences. Note that the absolute differences are not normally distributed.

My first question, what is the best way to define r ?
Second, can I use r = standard deviation (STD) of the differences?


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