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Synthetic-aperture radar (SAR) is a form of radar that is used to create two-dimensional images or three-dimensional reconstructions of objects, such as landscapes.^[1] SAR uses the motion of the radar antenna over a target region to provide finer spatial resolution than conventional stationary beam-scanning radars. SAR is typically mounted on a moving platform, such as an aircraft or spacecraft, and has its origins in an advanced form of side looking airborne radar (SLAR). The distance the SAR device travels over a target during the period when the target scene is illuminated creates the large synthetic antenna aperture (the size of the antenna). Typically, the larger the aperture, the higher the image resolution will be, regardless of whether the aperture is physical (a large antenna) or synthetic (a moving antenna) – this allows SAR to create high-resolution images with comparatively small physical antennas. For a fixed antenna size and orientation, objects which are further away remain illuminated longer – therefore SAR has the property of creating larger synthetic apertures for more distant objects, which results in a consistent spatial resolution over a range of viewing distances.

To create a SAR image, successive pulses of radio waves are transmitted to "illuminate" a target scene, and the echo of each pulse is received and recorded. The pulses are transmitted and the echoes received using a single beam-forming antenna, with wavelengths of a meter down to several millimeters. As the SAR device on board the aircraft or spacecraft moves, the antenna location relative to the target changes with time. Signal processing of the successive recorded radar echoes allows the combining of the recordings from these multiple antenna positions. This process forms the synthetic antenna aperture and allows the creation of higher-resolution images than would otherwise be possible with a given physical antenna.^[2]

Motivation and applications

SAR is capable of high-resolution remote sensing, independent of flight altitude, and independent of weather, as SAR can select frequencies to avoid weather-caused signal attenuation. SAR has day and night imaging capability as illumination is provided by the SAR.^[3][4][5]

SAR images have wide applications in remote sensing and mapping of surfaces of the Earth and other planets. Applications of SAR are numerous. Examples include topography, oceanography, glaciology, geology (for example, terrain discrimination and subsurface imaging). SAR can also be used in forestry to determine forest height, biomass, and deforestation. Volcano and earthquake monitoring use differential interferometry. SAR can also be applied for monitoring civil infrastructure stability such as bridges.^[6] SAR is useful in environment monitoring such as oil spills, flooding,^[7][8] urban growth,^[9] military surveillance: including strategic policy and tactical assessment.^[5] SAR can be implemented as inverse SAR by observing a moving target over a substantial time with a stationary antenna.

Basic principle

A synthetic-aperture radar is an imaging radar mounted on a moving platform.^[10] Electromagnetic waves are transmitted sequentially, the echoes are collected and the system electronics digitizes and stores the data for subsequent processing. As transmission and reception occur at different times, they map to different small positions. The well ordered combination of the received signals builds a virtual aperture that is much longer than the physical antenna width. That is the source of the term "synthetic aperture," giving it the property of an imaging radar.^[5] The range direction is perpendicular to the flight track and perpendicular to the azimuth direction, which is also known as the along-track direction because it is in line with the position of the object within the antenna's field of view.

The 3D processing is done in two stages. The azimuth and range direction are focused for the generation of 2D (azimuth-range) high-resolution images, after which a digital elevation model (DEM)^[11][12] is used to measure the phase differences between complex images, which is determined from different look angles to recover the height information. This height information, along with the azimuth-range coordinates provided by 2-D SAR focusing, gives the third dimension, which is the elevation.^[3] The first step requires only standard processing algorithms,^[12] for the second step, additional pre-processing such as image co-registration and phase calibration is used.^[3][13]

In addition, multiple baselines can be used to extend 3D imaging to the time dimension. 4D and multi-D SAR imaging allows imaging of complex scenarios, such as urban areas, and has improved performance with respect to classical interferometric techniques such as persistent scatterer interferometry (PSI).^[14]

Algorithm

SAR algorithms model the scene as a set of point targets that do not interact with each other (the Born approximation).

While the details of various SAR algorithms differ, SAR processing in each case is the application of a matched filter to the raw data, for each pixel in the output image, where the matched filter coefficients are the response from a single isolated point target.^[15] In the early days of SAR processing, the raw data was recorded on film and the postprocessing by matched filter was implemented optically using lenses of conical, cylindrical and spherical shape. The Range-Doppler algorithm is an example of a more recent approach.

Existing spectral estimation approaches

Synthetic-aperture radar determines the 3D reflectivity from measured SAR data. It is basically a spectrum estimation, because for a specific cell of an image, the complex-value SAR measurements of the SAR image stack are a sampled version of the Fourier transform of reflectivity in elevation direction, but the Fourier transform is irregular.^[16] Thus the spectral estimation techniques are used to improve the resolution and reduce speckle compared to the results of conventional Fourier transform SAR imaging techniques.^[17]

Non-parametric methods

FFT

FFT (Fast Fourier Transform i.e., periodogram or matched filter) is one such method, which is used in majority of the spectral estimation algorithms, and there are many fast algorithms for computing the multidimensional discrete Fourier transform. Computational Kronecker-core array algebra^[18] is a popular algorithm used as new variant of FFT algorithms for the processing in multidimensional synthetic-aperture radar (SAR) systems. This algorithm uses a study of theoretical properties of input/output data indexing sets and groups of permutations.

A branch of finite multi-dimensional linear algebra is used to identify similarities and differences among various FFT algorithm variants and to create new variants. Each multidimensional DFT computation is expressed in matrix form. The multidimensional DFT matrix, in turn, is disintegrated into a set of factors, called functional primitives, which are individually identified with an underlying software/hardware computational design.^[5]

The FFT implementation is essentially a realization of the mapping of the mathematical framework through generation of the variants and executing matrix operations. The performance of this implementation may vary from machine to machine, and the objective is to identify on which machine it performs best.^[19]

Advantages

• Additive group-theoretic properties of multidimensional input/output indexing sets are used for the mathematical formulations, therefore, it is easier to identify mapping between computing structures and mathematical expressions, thus, better than conventional methods.^[20]
• The language of CKA algebra helps the application developer in understanding which are the more computational efficient FFT variants thus reducing the computational effort and improve their implementation time.^[20][21]

Disadvantages

• FFT cannot separate sinusoids close in frequency. If the periodicity of the data does not match FFT, edge effects are seen.^[19]

Capon method

The Capon spectral method, also called the minimum-variance method, is a multidimensional array-processing technique.^[22] It is a nonparametric covariance-based method, which uses an adaptive matched-filterbank approach and follows two main steps:

1. Passing the data through a 2D bandpass filter with varying center frequencies (${\displaystyle \omega _{1},\omega _{2}}$).
2. Estimating the power at (${\displaystyle \omega _{1},\omega _{2}}$) for all ${\displaystyle \omega _{1}\in 0,2\pi ),\omega _{2}\in 0,2\pi )}$ of interest from the filtered data.

The adaptive Capon bandpass filter is designed to minimize the power of the filter output, as well as pass the frequencies (${\displaystyle \omega _{1},\omega _{2}}$) without any attenuation, i.e., to satisfy, for each (${\displaystyle \omega _{1},\omega _{2}}$),

${\displaystyle \underset{h}{min}{h}_{{\mathrm{\omega <!--\; \omega \; -->}}_1,{\mathrm{\omega <!--\; \omega \; -->}}_2}^{}}$Zdroj:https://en.wikipedia.org?pojem=Synthetic_aperture_radar
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