Astrometric bias caused by inhomogeneous background

All kinds of measurements are taken against some background. The greater the signal-to-noise ratio is, the smaller error is expected in both position and magnitude of an object. If we take measurements of the objects that are slightly less than the magnitude of the background, their positions will be affected by background inhomogeneity. In the case of point sources with the Gaussian-like distribution of intensity, the symmetry is broken, and the source's position is biased. We provide an analytic solution for the bias of the Gaussian image if the neighbourhood background gradient is known or measured. The solution explains the exponential-looking degradation of the astrometric errors with respect to the magnitude and gives a way to balance the reduction by the proper weights introduced. The abstraction allows correcting the bias in the astrometry of Gaussian-like sources whatever wavelengths or instruments are used.