Algorithm for Eliminating of the Limiting Disambiguation of Measurement Made by Phase Radio Direction Finders by Sorting Out the Abnormally Large Errors

Abstract

The aim of the article is to find the upper probability limit of the measurement results to correct disambiguation in case of multi-base phase direction finders, where all bases are ambiguous. Direction finding is done using the maximum likelihood method based on a set of measured phase differences and an algorithm of rejecting (erasing) abnormally large measurement errors. The theoretical background of the article is the maximum likelihood method applied to disambiguate results of the phase measurements in multi-base measuring systems. The physical meaning of the method is that if the disambiguation process is correct, the results of angular measurements for each base are grouped around the true value of bearing. The mathematical background of the article are methods of linear algebra based on the geometric interpretation of disambiguation measurement results. We obtained formulas for calculating upper bounds for the probability correct disambiguation of measurement results, which are applicable to direction finders with linear, planar and conformal antenna arrays. The obtained theoretical relations are exemplified by a numerical calculation of error probability including the upper bounds for a specific three-base direction finder 'bad' measurement results. The calculations proved effectiveness of the proposed algorithm, which depends on the accuracy of phase measurements. The proposed algorithm is applicable not only in case of the direction finders, but also for other multi-base phase measurements. The work may be interesting for designers of direction finders in terms of achievable accuracy of measurement results even if some of the results are rejected.