Parameterization of user functions in digital signal processing for obtaining angular superresolution

Abstract

Objectives. One of the most important tasks in the development of goniometric systems is improving resolution in terms of angular coordinates. This can be achieved in two ways: firstly, by increasing the aperture, which is very expensive and often technically challenging to implement; secondly, with the help of digital signal processing methods. If the recorded signal sources are located close to each other and not resolved by the Rayleigh criterion, it can be impossible to determine their number, location and reflection characteristics. The aim of the present work is to develop a digital signal processing algorithm for obtaining angular superresolution.Methods. Mathematical methods for solving inverse problems are used to overcome the Rayleigh criterion, i.e., obtain angular superresolution. These problems are unstable, since there is an infinite number of approximate solutions and false targets may occur. The search for the optimal solution is carried out by minimizing the standard deviation.Results. A description of a mathematical model for a goniometric system is presented. A signal processing algorithm is developed based on existing methods according to the principle of parameterization of user functions. Results of numerical experiments for achieving superresolution by algebraic methods are given along with an estimation of solution stability. The accuracy and correspondence of the amplitude of the obtained objects to the initial parameters are measured. The degree of excess of the Rayleigh criterion by the obtained solution is estimated.Conclusions. Algebraic methods can be used to obtain stable solutions with angular superresolution. The results obtained correctly reflect the location of objects with a minor error. Errors in the distribution of the signal amplitude are small, appearing false targets have negligible amplitude.