Ratios for estimating errors in setting the angular position in matrix simulators of an electronic environment

Simplified formulas have been obtained to estimate the error in setting the angular position of the apparent center of radiation in a matrix simulator. The approximation of the error function is used for this purpose. It is shown that the well-known formula for calculating the error in simula¬ting radar reflections from point targets, when used to find the statistical characteristics of noise coordinates of distributed targets, requires simplifications. In this case, the error function can be divided into four sections, within which its approximation by polynomials of the first or second degree is allowed. At the same time, the error function has an oblique symmetry, which makes it possible to analyze only two sections, and to extend the results to four. The numerical enumeration method is used as a way to find an optimal division into sections. For the typical shapes of the main lobe of the directional pattern of the radar antenna, the coefficients of the approximating polynomials were obtained by the Nelder–Meade simplex method. It is shown that the use of approximation makes it possible to obtain analytical expressions for the moments of error in setting the angular position of the apparent radiation center. In particular, the relations for finding the mathematical expectation of an error are given.