Optimum statistical estimates in conditions of ambiguity

An ambiguity problem arises if a distance is measured by observing phase shift of signals when the range of the measured distance is greater than the wavelength of the signals used. This ambiguity generally can be resolved by pumping extra information into the system. A classical estimation problem is the obtained at the expense of reduced autonomy of the estimator due to the demand for external information not inherent to the system. The interval Λ of the unambiguous estimates can be considerably extended using observations of several different wavelengths λ_i. This yields Λ as the least common multiple of all λ_i. A method of developing optimum estimation rules for this case is introduced. Optimum estimation rules for some typical cases with Gaussian observation errors are also developed