  Continuous center-of-mass position measurements performed on an interacting
harmonically trapped Bose-gas are considered. Using both semi-analytical
mean-field approach and completely quantum numerical technique based on
positive P-representation, it is demonstrated that the atomic delocalization
due to the measurement back action is smaller for a strongly interacting gas.
The numerically calculated second-order correlation functions demonstrate
appearance of atomic bunching as a result of the center-of-mass measurement.
Though being rather small the bunching is present also for strongly interacting
gas which is in contrast with the case of unperturbed gas. The performed
analysis allows to speculate that for relatively strong interactions the size
of atomic cloud determined with a single snapshot measurement can become
smaller than the ground-state cloud size.
