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Trying to follow the suggestion by Vince, below is a QGIS expression approach.
We need to find out (1) the center of this ellipse as point O, (2) semi-major axis length x which is the half of the total distance the elephant has moved during the time T (... as you see the distance A -> B' -> B is the same as O -> B' -> O). And (3) the semi-minor ...
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