Based on the analysis above, we can summarize the difference between the truncated singular value decomposition strategy and the Nonlinear Least Squares estimation strategy. First of all, SVD is a non-parametric method while NLS is parametric. As a multi-dimensional search is necessary for NLS, NLS is time consuming while SVD has much lower computational complexity. SVD does not need a priori model selection to determine the number of signals inside the specific resolution cell; the estimated power spectrum provides a possibility for model selection while NLS needs this prior knowledge even for formulating the observation equation. However, the resolution of SVD depends on the baseline range. For instance, in our simulation, only two scatterers with a separation larger than 45 meter can be distinguished. By contrast, NLS does not have resolution dependent on the baseline range from a theoretical point of view and extremely high resolution can be obtained when the SNR is very high. However, it works perfectly only with high SNR, in the case of low SNR, it works much worse than SVD. In practice, SNR=2dB would be the critical SNR for our application which is not high enough for NLS estimation. SVD has an ill-conditioning problem, thus regularization tools such as TSVD and Wiener filtering should be used. SVD can give good and stable performance with regularization. Taking all factors into account, SVD is a better choice here.
This paper proposes a method for extracting the tropospheric time delay in a single-pass using SAR images acquired in squinted geometries. The required accuracies and error sources are analysed and a satellite configuration provid- ing single-pass measurements of the tropospheric delay is proposed. Moreover, a joint topography-tropospheric delay estimation using very-high resolution SAR images is also suggested for cases where an inaccurate DEM is available. A performance of the approach with current TerraSAR-X staring spotlight like parameters is also computed.
A wide range of processing techniques, which capitalize on the mentioned advantages of those systems has been developed to extract the information available in the focused SAR images. SAR interferometry  is based on the coherence propriety of the signals, combining the phase of at least two complex images of the same scene, acquired from different sensor positions. The distance between sensors’ positions from which the scene is illuminated is represented by the perpendicular baseline. As the phase is dependent on the sensor-target distance, this method allows the measurement of path related differences with millimetre accuracy. SAR polarimetry  is based on the construction of full targets’ scattering matrix, which offers information related to their orientation and dielectric proprieties. Exploitation of polarimetric characteristics for both natural and man-made scatterers allows the extraction of quantitative and qualitative information related to their physical characteristics. SAR tomography  represents an extension of the processing techniques into the 3D space, by inclusion of a supplementary dimension, perpendicular to the range-azimuth plane of the focused SAR images: the elevation direction. It exploits the baselines diversity of a multiple acquisitions dataset, to estimate the scene’s reflectivity profile in elevation direction. This allows the possibility to separate the contributions of scatterers interfering within the same resolution cell. An automatic analysis and interpretation of data can be derived from SAR images segmentation , which separates the regions in which radar’s reflectivity is constant. Information theory related processing algorithms can be applied for SAR images classification , which marks each pixel as belonging to one general group.
A fundamental concern of the investigations was to find an appropriate stochastic model. Motivated by the assumption that correlated observations are a better approximation of reality, the use of empir- ical covariance functions has been evaluated. Their adjustment to individual interferograms turned out to be especially problematic for interferograms with distinct large-scale nonlinear atmospheric trends, which is probably the major reason for the failure of statistical validation; another one may be the neglect of algebraic correlation. In terms of results, the covariance model has only little effect on the estimates, but it significantly influences the corresponding dispersion measures, i. e., variances. How- ever, these can neither be validated nor do they have any practical relevance except for outlier tests. There has been no evidence that the performance of outlier detection can be enhanced by considering correlations between observations either. Seeing the poor benefit in relation with the considerable ef- fort of tailoring covariance functions, an orbit error estimation from uncorrelated observations appears to be an adequate compromise.
Statistical considerations are not the sole basis for drawing inferences. A physical appreciation of the problem, judgement and experience should also be brought into the picture. The statistical results on the rotationally averaged power spectra must be correlated with qualitative observations of the AOI. The disturbed areas in fact appear to be characterised by high-frequency speckle changes. In contrast, waste disposal sites tend to present distinct features with high radar backscatter. Furthermore, the power-law exponents β can be related to the fractal number D 2 (Pentland, 1984). As comprehensively described by Sun et al. (2006), fractal geometry represents a valuable tool for characterising complex shapes and land surface patterns in remote sensing images. As such, the value of D 2 is intimately linked to a notion of “complexity” or “roughness” of an image (Pentland, 1984). It is beyond the scope of this research to discuss the potentials and limitations of the various fractal dimension estimation methodologies. The reader is referred to Mandelbrot (1977, 1982) for a more complete discussion of fractal geometry and to Peitgen and Saupe (1998) for an introduction to fractal analysis of images. In the context of this research it is important to recognise that the mean values of β for the two groups lead to a fractal dimension, D 2 , equal to 3.29 and 2.95 for the disturbed areas and landfill sites respectively. Turcotte (1997) explains that the first fractal value corresponds to “white noise” while the second value represents self-affine images in which the scale variability in the two dimensions is different. This latter property can consequently be linked to a certain level of anisotropy.
acquisitions with high revisit frequency are free for common use and allow unprecedented opportunities for the observation of ocean processes and natural features. However, the nature of S1 C-Band imagery for moving targets under relatively coarse resolution imposes a limit for imaging of ocean waves: only long wave structures with wavelengths longer than ca. 120 m can be clearly seen in the IW images; shorter waves or waves with amplitude above ca. 5 m under strong winds are imaged as clutter. To return the correct wave height for the whole range of sea state conditions, the traditional method of considering image spectra was extended by the implementation of image features analysis using a Grey Level Co-occurrence Matrix (GLCM).
The relativistic phase and time offsets from this paper are not only of high importance for DEM generation with a formation flying SAR cross-track interferometer. Formations with multiple satellites have also been suggested for a wide range of further remote sensing applications, ranging from along-track interferometry for moving object and ocean current measurements over sparse aperture ambiguity suppression and super resolution for enhanced high-resolution wide-swath SAR imaging up to single-pass SAR tomographyfor vertical struc- ture measurements –. Due consideration of relativistic effects from varying along-track baselines is again of essential importance for these advanced bistatic and multistatic SAR systems to avoid mutual range and phase offsets between the received SAR signals. The phase accuracy requirements for the combination of the different receiver signals are typically in the order of 1° or a few degrees. For comparison, an along-track baseline of 100 m causes in an X-band system a relativistic phase shift in the order of several tens of degrees. Future multistatic SAR satellite missions should therefore take into account relativistic effects in the design of the radar synchronization system and/or the SAR processor to avoid a possible performance loss.
Several approaches have been developed in the lit- erature in order to extract the different contributions of interest through different advanced filtering schemes. The first step in these approaches is the selection of the image pixels with enough quality to be used in the esti- mation process, being the most commonly approaches the ones based on the amplitude dispersion, i.e., the so- called permanent scatterers (PS) technique , , or on the interferometric coherence –. A PS appears in the image as a pixel showing a stable amplitude behav- ior in time and usually corresponds to point-like targets such as buildings or rocks, while distributed scatterers are discarded. On the other hand, the selection using the coherence further includes distributed scatterers that remain coherent in time, e.g., surfaces, hence increas- ing the potential number of candidate pixels. Neverthe- less, the coherence estimation implies a resolution loss in opposition to the PS technique, which works at full FIgure 15. (a) Estimated subsidence over Mexico City obtained with two TerraSAR-X images acquired with a 6-month difference (overlay of reflectivity and phase). Low coherence areas have been masked out. (b) Mean deformation velocity estimated over Mexico City using the PS technique. (c) Zoom over the city of the refined DEM retrieved as an additional product to the deformation velocity, where the individual buildings can be observed. The size of the PSs has been enlarged for visualization purposes. The scene size is approximately 8 km 8 km. # Radar illumination from the right.
VI. C ONCLUSIONS AND FUTURE WORK
In this paper we briefly discussed the Geosynchronous SAR mission concepts and the available land clutter literature; as a consequence we identified the need for a new clutter model in order to complete the performance estimation method. This method allows the estimation of the performance of a SAR system on a real landscape and in realistic weather conditions. Preliminary results assuming a triangular (Fig. 6) and a rectangular (Fig. 7) clutter shape show the influence of the clutter shape. In particular, it is worth noting that over a certain mean windspeed, around 5 meters per second, the clutter is pushed outside the image and thus we have an increase of the Signal to Clutter Ratio. The orbit assumed in Fig. 6 and Fig. 7 and is the typical one of the GeoSTARe  mission concept. Further work is needed to complete the short vegetation clutter model. The incoherent power model requires finding the two parameters (α and K) that are related. Actually there is only one independent parameter.
In this paper the different remote sensing data are combined to collect the underwater topography in costal areas worldwide. In spite of the fact that the worldwide bathymetry should already be known, and there are no “blank spots” on global maps, at least for 1 nautical miles resolution data sets (e.g. global topography by NOAA, ETOPO 1-Minute Global Relief, NOAA) the local depth variation e.g. sand bank, bars and reefs on the one hand and temporal morphodynamical development of seabed structures on the other hand can be significant in littoral zones. E.g. in the German Bight (North Sea), the soft seabed topography can changes relatively fast due to storms so that the official charts can be quite out of date.
In Europe, one of the first published GEO SAR concepts was by Prati et al.  in 1998. They described a bistatic passive radar reusing L-band broadcast signals. Such a system could achieve 120-m spatial resolution using an antenna with a diame- ter 4.8 m. The orbit inclination is small (satellite motion of only 25 km from the geostationary position is assumed). However, a long integration time of up to 8 h is required to form a satisfac- tory image. Imaging effects of clutter and partially stable tar- gets, as well as measuring the atmospheric phase screen (APS) are noted. Research on other GEO SAR concepts (mainly con- ventional monostatic) has continued with contributions from Cranfield –, Milan –, and Barcelona ,  in particular. These recent studies have made significant contribu- tions in the areas of system design and APS estimation/phase compensation. For the low inclination orbits and modest an- tenna sizes, which these authors have assumed, integration times are relatively long, and thus, atmospheric phase com- pensation is needed. There has been particular interest again in applications for short repeat period interferometry related to geohazards.
of uniform quantizers not suitable for typical spaceborne SAR systems. In this scenario, adaptive quantization is mandatory to overcome the high dynamic variability of the signal. Block Adaptive Quantization (BAQ) is a quantization scheme which allows to efficiently compress SAR raw data and it is nowadays widely used as quantization standard for spaceborne SAR systems . By exploiting the input signal statistics, a raw data block is quantized independently from the others, making possible the quantization deci- sion levels to be adapted to its specific dynamic. This quantization scheme is known as Max-Lloyd quantizer, adapting the quantization boundary to the normal statistics of the input signal . This method allows for high performance in quantization, meaning that it is possible to encode more information using less memory. The compression pro- cess can be carried out both in time domain and in frequency domain. The first allows a better signal to quantization noise ratio, but it is not optimized for the compression of the spectral envelope in range and azimuth direction. Even though the second technique has higher performance, operating in frequency domain implies high complexity in hard- ware . BAQ is usually implemented as a cartesian quantizer, meaning that the two components of the complex raw signal (I and Q) are treated separately, since the assump- tion of statistical independence between In-phase and Quadrature components holds (see (20)). Polar BAQ  has also been investigated leading to no significant gain in terms of performance. As an example, both the TerraSAR-X and TanDEM-X satellites from DLR  employ cartesian BAQ for on-board raw data compression. For TerraSAR-X and TanDEM-X, the input raw signal is clipped (V clip = ±127.5) and then quantized at 8
the sparse reconstruction process in tomography with syntheticapertureradar. Two hyperparameter-free approaches are introduced into the framework of SL1MMER (Scale-down by L1 norm Minimization, Model selection, and Estimation Reconstruction). By means of numerical simulations, we evaluate their performance regarding mean and standard deviation of elevation estimates, as well as detection rate. Preliminary results with real data are also provided.
Subsequent to the first demonstration of SAR tomography [Pasq 95,Home 96,Reig 00], several extensions and alternatives have been put forward in order to attain low side- lobe and ambiguity levels with a reduced number of irregular passes. The use of adap- tive spectral estimators was introduced in [Gini 02,Lomb 03,Lomb 09a,Lomb 09b] and further developed in [Saue 11, Frey 11a] (see also [Frey 11b]). In addition, subspace- based spectral estimators, such as the multiple signal classification (MUSIC) algorithm, have been recently employed [Guil 05, Nann 09, Frey 11a, Frey 11b, Huan 12, Lomb 13]. In [Forn 03], the authors formulated the tomographic inversion under the framework of linear inverse problems, thus exploiting the truncated singular-value decomposi- tion (TSVD). Also, a maximum a posteriori estimator was developed in [Zhu 10b]. Other publications have addressed irregular geometries by means of interpolation techniques (see, for example, [Lomb 08a, dAle 12]). Alternatively, an extension of SAR interferometry [Baml 98] from a parametric perspective was proposed in [Teba 10a]. In a nutshell, this last work employs covariance matching estimation techniques in order to estimate the effective scattering center of different scattering mechanisms (SMs), along with their backscattered power (see also [Lomb 98a, Cors 99, Bess 00]). Moreover, the author in [Clou 06] introduced the concept of polarization coherence tomography (PCT). Basically, the method exploits the variation of the interferomet- ric coherence with polarization to estimate ground topography and height of vege- tation layers. Then, it uses these parameters to represent a backscatter profile as a Fourier–Legendre series. Finally, sparsity-based inversion techniques were introduced in [Budi 09, Zhu 10a, Budi 11, Zhu 12, Agui 12a]. In essence, the authors applied and further developed the relatively new compressed sensing (CS) theory to achieve super- resolution imaging of vertically-sparse targets.
Other methods such as Burg’s maximum entropy,Prony, Pisarenko (Kay and Marple, 1981),Music for Doppler weather radar (Chen et al., 1995) (eigendecomposition-based methods) , noise compensated autoregressive(AR) method (based on white noise and priori knowledge of its variance)(Kay, 1980), linear prediction (LP) which is regarded as a generalized PP efficient at high SNR (larger than 20dB),minimum-norm (MN, based on eigendecom- position of LP equation useful at lower SNR versus LP, however; not reliable at SNR lower than 10dB)(Banjanin et al., 1993),vector and poly-pulse pair estimation (taking higher-order lags of autocorrelation in mean velocity esti- mation versus one-lag PP processor)(Mahapatra and Zrnic, 1983; Lee, 2000) which is supposed to compensate for the bias error due to assumption of nar- row and symmetrical shape of Doppler spectrum,and maximization of the periodogram(spectral method based on FFT)(Mahapatra and Zrnic, 1983), are all considered to be under some other priori assumptions on modeling of weather signal or noise such as AR process of some desired order (all-pole assumption),white gaussian noise or some specific colored noise ,e.g. noise of AR process of some pre-assumed order.
the receive array height. In this system operation, a severe nonuniform sampling will not occur due to the narrow PRF range. In the case that a wide range of PRF is considered, the degree of nonuniform sampling will be significant and reach the maximum at the highest PRF. In the designed system, it is assumed that all receive channels have the identical noise figure of 3.75 dB and a system loss of 3 dB. The required peak and average power of this system are higher than those of the TerraSAR-X system (2-kW peak) in order to achieve the desired SNR over the 100-km swath width. As a rule, the sampling frequency of 275 MHz includes a 10% guard band, and then, the pulse length of 150 μs leads to 41 250 subcar- riers with the 6.67-kHz subcarrier spacing. In this example, we assume that the ICI due to instantaneous Doppler shift is compensated by the method introduced in . Regarding the undersampling for HRWS SAR imaging in the MIMO SAR, the reconstruction algorithm  recovers the original Doppler spectrum prior to the Doppler compensation. This approach has been used for frequency-modulated continuous-wave (FMCW) SAR with DBF in  and also for the very high resolution SAR data processing . Therefore, the ICI issue is not included in the performance estimation in Section VI-A. To improve the computation speed of DFT/inverse DFT, one can select a number of subcarriers that are equal to a power of two. This MIMO SAR antenna is composed of six panels in azimuth and 42 receive subarrays in elevation in each panel. The receive subarray consists of three X-band radiators in elevation and azimuth, respectively. Fig. 12 depicts the MIMO SAR antenna configuration and geometric parameters in this example design.
In this work, a functional multicopter-based SAR system for the detection of metallic tripwires was presented for the first time. It was shown that randomly orientated, vegetation- obscured tripwires can be detected by overflying the area in four different directions. Both the wire length and the vegeta- tion have a strong influence on the signal strength. However, the multi-look processing ensures reliable detection. In areas with light vegetation, this system could detect tripwires before a deminer has to enter the potentially hazardous area and thus accelerate the process of mine clearance. Currently, an area throughput of approximately 10 m 2 /s is achieved (single-look). In order to be able to operate the system in a real minefield, the focus is on automatic or ideally autonomous flight operations.
The German X-band SAR TS-X was launched successfully on 15 June 2007 from Baikonur, Kazakhstan. The satellite is in a near-polar orbit around the Earth, at an altitude of 514 km. Using its active radar antenna, TS-X is able to produce image data with a resolution down to one meter, independent of weather conditions and daylight. It has been fully operational since January 7, 2008. Main technical parameters of TS-X are briefed in Table 6.1 . The detailed information of TS-X mission, design, as well as ground segment is available in [ 16 , 17 ]. Figure 6.1 illuminates three different imaging modes of TS-X, i.e., Spotlight, Stripmap and ScanSAR modes. For both Stripmap and ScanSAR modes, the radar beam can be electronically tilted within a range of 20–45 ◦ perpendicular to the flight direction without having to move the satellite itself. For Spotlight mode, the radar beam can be further tilted to 55 ◦ . Scenes sizes and resolutions of the three imaging modes of TS-X are listed in Table 6.2 .
SAR interferometry exploits the phase measurements to infer differential range and range change in two or more SAR images of the same target area. From space, there are two ways to achieve this. The first option is to have two SAR antennas orbiting at the same time. This can be achieved by having them on the same platform, as implemented in the Shuttle Radar Topography Mission (SRTM), or by having a satellite constellation as suggested by Massonet (2001). The second option is to acquire the same scene with the same SAR antenna at two different times. This latter solution is mostly used with space-borne SAR systems and it is called repeat-pass interferometry. For this interferometric technique to be applicable, data sets must be obtained when the scene is viewed from almost the same look angle for each of the passes. Figure 2-10 illustrates a simplified interferometric imaging geometry,
As indicated previously, one of the essential character- istics of multidimensional SAR data resides in the large number of available radar observables that make a better characterization of the observed terrain possible. Conse- quently, a better classification or segmentation of the data can be achieved. In this sense, three contributions to this special issue address this topic. In the paper by L. Zhang et al., the authors focus on PolSAR data classification using Support Vector Machine techniques in which they do not directly consider PolSAR data, but rather the diﬀerent parameters derived from polarimetric incoherent decompositions. The paper shows the key role of the diﬀerent decomposition techniques when exploiting PolSAR data. In a second work, T. Zou et al. propose first a review and comparison of the diﬀerent parameters and techniques