OPTIMUM STATISTICAL ESTIMATES IN CONDITIONS OF AMBIGUITY

An ambiguity problem arises if a distance is measured by observing a phase shift of signals where the range of the measured distance is greater then the wavelength of the signals used. This ambiguity generally can be resolved by pumping extra information into the system. Then we obtain a classical estimation problem, but at the expense of reduced autonomy of the estimator due to the demand for external information not inherent to the system. The interval LAMBDA of the unambiguous estimates can also be considerably extended using observations of several different wavelengths lambda(i). This yields LAMBDA as the least common multiple of all lambda(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.