Space-time processing for «range – azimuth – elevation» measurements in non-cooperative systems of radars with phased array antennas

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The methods of measuring the three coordinates of an aircraft in the takeoff and landing mode on the runway of airfields based on the use of non - cooperative two-and three-position systems of radars with phased array antennas are considered. For these variants, general analytical expressions are obtained for the complex generalized correlation integral of space – time processing in the function of spatial coordinates, taking into account the individual directional pattern of phased array antennas. On the basis of two – dimensional profiles of the correlation integral modules «range – elevation» and «azimuth – elevation», examples of comparing particular variants of two-position and three-position systems of radars with their location on one straight line parallel runway are given. In conditions of large signal-to-noise ratios, power-law nonlinear transformations of the correlation integral correlation integral module are applied to reduce the level of side lobes in the two – dimensional sections «range – elevation» and «azimuth – elevation». The following results are obtained using examples. Two-dimensional diagrams of the correlation integral module «range – elevation» do not depend on the azimuth of the aircraft in the range of azimuth values β=0…10 ̊ and correctly display the angle of elevation and the range of the aircraft when 2…3 radars of a non-cooperative system are located on the straight line parallel runway. The two-dimensional diagrams of the correlation integral module «azimuth – elevation angle» have an interference structure, and the number and level of their side lobes increase with increasing azimuth of the aircraft. With azimuth β≥10 ̊, this can lead to ambiguity in the measurement of the azimuth and uncertainty in the elevation angle . One of the measures to reduce the side level of the diagrams of the correlation integral module can be the use of a power-law transformation of normalized diagrams exponentiation of degree 3...4. An increase in the number of radars from two to three when they are located on one straight line parallel to the runway led to a decrease in the side lobes level of the «range – elevation angle» and «azimuth – elevation angle» diagrams. In this case, it may be advisable to solve the problem of optimal choice of the position of the intermediate radar on the same straight line. Calculations were also carried out for an additional example of the location of the intermediate radar of a 3-position system with its removal from the base line. At the same time, there was an increase of the side lobes level in the «azimuth – elevation angle» sections, which in the future may require additional research in terms of optimizing the placement of the radars in horizontal plane for such a radar systems.