  Baryon Acoustic Oscillation (BAO) observations offer a robust method for
measuring cosmological expansion. However, the BAO signal in a sample of
galaxies can be diluted and shifted by interlopers - galaxies that have been
assigned the wrong redshifts. Because of the slitless spectroscopic method
adopted by the Roman and Euclid space telescopes, the galaxy samples resulting
from single line detections will have relatively high fractions of interloper
galaxies. Interlopers with a small displacement between true and false redshift
have the strongest effect on the measured clustering. In order to model the BAO
signal, the fraction of such interlopers and their clustering need to be
accurately known. We introduce a new method to self-calibrate these quantities
by shifting the contaminated sample towards or away from us along the line of
sight by the interloper offset, and measuring the cross-correlations between
these shifted samples. The contributions from the different components are
shifted in scale in this cross-correlation compared to the auto-correlation of
the contaminated sample, enabling the decomposition and extraction of the
component terms. We demonstrate the application of the method using numerical
simulations and show that an unbiased BAO measurement can be extracted. Unlike
previous attempts to model the effects of contaminants, self-calibration allows
us to make fewer assumptions about the form of the contaminants such as their
bias.
