  We consider the problem of estimating the distance, or range, between two
locations by measuring the phase of multiple sinusoidal signals transmitted
between the locations. Traditional estimators developed for optical
interferometry include the beat wavelength and excess fractions methods. More
recently, estimators based on the Chinese remainder theorem (CRT) and least
squares have appeared. Recent research suggests the least squares estimator to
be most accurate in many cases. The accuracy of all of these range estimators
depends upon the wavelengths chosen. This leads to the problem of selecting
wavelengths that maximise accuracy. Procedures for selecting wavelengths for
the beat wavelength and excess fractions methods have previously been
described, but procedures for the CRT and least squares estimators are yet to
be developed. In this paper we develop an algorithm to automatically select
wavelengths for use with the least square range estimator. The algorithm
minimises an optimisation criterion connected with the mean square error.
Interesting properties of a particular class of lattices simplify the criterion
allowing minimisation by depth first search. Monte-Carlo simulations indicate
that wavelengths that minimise the criterion can result is considerably more
accurate range estimates than wavelengths selected by ad hoc means.
