Using the statistical theory of optimization of radio engineering systems the optimal method of coherent radar imaging of surfaces in airborne synthetic aperture radar with planar antenna arrays is developed. This method summarizes several modes of terrain observation and it is fully consistent with current trends in the development of cognitive radars with the possibilities of radiation pattern restructuring in space and adaptive reception of reflected signals. Possible modifications of the obtained optimal method for the operation of high-precision airborne radars with a wide swath are presented. The idea is to create a theoretical basis and lay the foundations for its practical application in solving a wide range of issues of statistical optimization of methods and algorithms for optimal spatiotemporal signal processing in cognitive radar systems for the formation of both high-precision and global radar images. To implement the idea, the article highlights the concept of statistical optimization of spatio-temporal processing of electromagnetic fields in on-board cognitive radar systems, which will be based on the synthesis and analysis of methods, algorithms and structures of radar devices for coherent imaging, the study of limiting errors in restoring the spatial distribution of the complex scattering coefficient, the synthesis of optimal feedback for receiver and transmitter adaptations in accordance with a priori information about the parameters of the objects of study, the area of observation and the existing sources of interference. Objective is to develop the theory and fundamentals of the technical implementation of airborne radar systems for the formation of high-precision radar images in an extended field of view from aerospace carriers. Tasks. To reach the objective it is necessary to solve following tasks:– formalize mathematical models of spatiotemporal stochastic radio signals and develop likelihood functional for observation equations in which the useful signal, receiver internal noise and interference radiation of anthropogenic objects are random processes;– to synthesize algorithms for optimal processing of spatio-temporal stochastic signals in multi-channel radar systems located on aerospace-based mobile platforms;- in accordance with the synthesized methods, to substantiate the block diagrams of their implementation;– obtain analytical expressions for the potential characteristics of the quality of radar imaging and determine the class of probing signals and space scanning methods necessary to perform various tasks of radar surveillance;‒ to confirm some of the theoretical results by simulation methods, in which to reveal the features of the technical implementation of aerospace remote sensing radar systems.

The production of parts and (or) finished products in electronics, mechanical engineering and other industries is inextricably linked with the control of the accuracy and cleanliness of the processed surfaces. Currently existing meters of parameters of statistically uneven surfaces, both contact and non-contact have some disadvantages, as well as limitations due to methods and design features of measurement. Speckle interferometric methods for measuring parameters of statistically uneven surfaces make it possible to get away from some disadvantages inherent in existing methods and measurements. The use of methods of statistical radio engineering, methods of optimization of statistical solutions and estimates of parameters of predictive distributions for optimal radio engineering system synthesis is promising for the analysis and processing optical-electronic coherent laser space-time signals (speckle images) form with the laser radiation scattered by statistically uneven surfaces. This work synthesizes the optimal algorithm and structure for analyzing the parameters of statistically-temporal surfaces based on spatio-temporal processing of optical speckle interference signals and images using modern methods of optimal synthesis of radio engineering and coherent optoelectronic systems. In this work, an algorithm for processing optical signals scattered by statistically uneven surfaces is synthesized and investigated for problems of optimal estimation of parameters and statistical characteristics of statistically uneven surfaces. A block diagram of the optical contactless device for evaluating the parameters of statistically uneven surfaces is proposed. The limiting errors of estimation parameters of statistically uneven surfaces and the optimal installation angles of the emitters and the optical receiver are investigated. Equations are obtained for estimating the root-mean-square height of the ridges and the correlation radius of small-scale statistically uneven surfaces in the approximation of small perturbations. The proposed method for evaluating the parameters of statistically uneven surfaces allows to increase the accuracy of measurements, to conduct a non-contact assessment of the parameters - even statistically uneven surfaces that have geometric surface irregularities or located in hard-to-reach places, for example, grooves, holes, as well as products of cylindrical, spherical and other shapes.

The subject of the manuscript is the algorithms for radar imaging. This research develops imaging methods and algorithms for wideband and ultrawideband active aperture synthesis systems with antenna arrays and stochastic probing signals. The use of antenna arrays makes it possible to obtain radar images without the need to move radar or antenna system in space. The use of wideband and ultra-wideband stochastic probing signals is justified by their narrow autocorrelation functions. This increased the resolution of the obtained images. The main idea of the proposed algorithms is to filter the original wideband signal into several narrowband processes. Furthermore, only the central frequencies of each narrowband signal were processed. This approach allows us to use the classical widespread methods of aperture synthesis for the case of a wideband signal. Usually, they are applicable only for narrowband signals that satisfy the condition of a quasi-monochromatic approximation. This significantly reduces the overall computational complexity of the imaging algorithm, which simplifies its further practical implementation on the existing radioelement base. Because of the simulation, a primary radar image has been obtained and the overall performance of the proposed approach to processing wideband signals has been confirmed. An increase in the quality of the obtained image when using a multiple of frequency ranges is shown. An experimental study of the effect of processing a wideband signal only at its centre frequency instead of the entire frequency band is conducted. During the experiment, the correlation functions of the signals received by two spaced receivers were obtained. As a result, the Van Cittert-Zernike theorem has been experimentally confirmed. It allows signal processing only at its centre frequency instead of the entire frequency band. Simultaneously, the prospect of expanding the bandwidth of the probing signal is indicated. It, in the presence of a wideband element base and devices for high-speed signal processing, will further increase the imaging resolution of a radar system.