Extreme Probabilistic Characteristics of the Measurement Disambiguation in Multiscale Phase-Measuring Systems

Abstract

We determine the upper limit on the correct measurement disambiguation probability in multiscale phase-measuring systems in which all scales are ambiguous. The measured value is estimated by the maximum likelihood method from the total of measured phase differences supplemented by an algorithm for rejecting (erasing) measurement results with anomalously large errors. Errors that exceed one-half of the main lobe of the likelihood function are considered anormalously large. The results are obtained by the methods of linear algebra with a geometric interpretation of the measurement disambiguation process in the space of total phase differences. The method was applied to phase direction finders, but can easily be adapted to other types of multiscale phase radio systems.