Current phase error estimation approaches, such as the signal subspace comparison (SSC) method and the orthogonal subspace (OS) method, neglect the effect of noise. Consequently, their estimation accuracy deteriorates under low signal-to-noise ratio (SNR) conditions. In contrast, the adaptive weighted least squares (AWLS) method accounts for noise. Its accuracy, however, deteriorates under highly nonuniform sampling conditions. Although the maximum normalized image sharpness (MNIS) algorithm achieves high estimation accuracy, it suffers from high computational complexity. To address these limitations, novel phase error estimation methods based on weighted subspace fitting are proposed. The proposed methods explicitly account for noise by constructing two weighted fitting models between the subspace and the steering vector, from which phase errors are estimated via optimal solutions. Depending on the employed subspace, the proposed methods are classified as weighted signal subspace fitting (WSSF) and weighted noise subspace fitting (WNSF). Simulations and airborne experiments verify the accuracy and robustness of the proposed methods.

In azimuth multichannel synthetic aperture radar (AMC-SAR) systems, channel phase errors can induce ghost targets. The estimation of signal parameters by the rotational invariance technique (ESPRIT) assumes that the principal signal subspace corresponds to the steering vector at zero Doppler frequency. However, this assumption is frequently violated in practice, resulting in performance degradation. To address this issue, a robust ESPRIT (RESPRIT) algorithm is proposed, which integrates initial ESPRIT-based phase error estimation with residual phase error correction through image contrast maximization. Both simulation and real airborne data experiments demonstrate the effectiveness and robustness of the proposed method.

This article proposes a configuration for a multiple input-multiple output (MIMO) along-track interferometry (ATI) synthetic aperture radar (SAR) satellite system designed for measuring ocean surface velocity vectors. The satellite system consists of a main satellite and at least two secondary satellites. The main satellite is equipped with dual antennas for transmitting and receiving echoes, while the secondary satellites are equipped with single antennas for receiving echoes. Based on the configuration, we explore key issues related to MIMO ATI SAR for measuring ocean surface velocity vectors to form a comprehensive solution. The issues include the current measurement principle, methods for assessing velocity vector accuracy, optimal baseline determination, carrier frequency selection, echo separation methods, and sources of phase error. The corresponding methods are derived in this article to address the challenges posed by the geometry of bistatic observations in beam steering and digital beamforming (DBF) processing. In addition, a system parameter design method based on optimizing ocean surface velocity measurement accuracy is proposed, eliminating the need for repeated trade-offs on individual parameters. Finally, the article presents an example of a high-precision wide-swath ocean surface velocity vector measurement system based on the configuration. This system achieves an ocean surface velocity accuracy of 3 cm/s, a swath coverage of 200 km, and a product resolution of$1\times 1$km2 in wind speeds above 3 m/s.

Multichannel parameter estimation is a key technology for azimuth multichannel terrain observation by progressive scans synthetic aperture radar (MC TOPS SAR) systems. Normally, for the traditional multichannel parameter estimation algorithms, the mismatch parameters are concluded as phase error, baseline error, and Doppler centroid. The beam rotation speed error is ignored. However, for MC TOPS SAR, beam rotation speed error will degrade the reconstruction performance of the Doppler spectrum. Moreover, only part of the mismatch parameters can be estimated for the traditional algorithms. To address those problems, a joint parameters estimation algorithm for TOPS SAR based on spatial time cross correlation coefficient (STCCC) is proposed. Combined with phase wrapping and the least-squares method (LSM), the algorithm is capable of realizing a joint parameters estimation of channel consistency error, azimuth baseline error, Doppler centroid frequency, and beam rotation speed estimation without iteration. The real data processing result shows that the method can effectively realize MC TOPS SAR data error estimation.

Synthetic aperture radar (SAR) sometimes needs to be imaged with small time bandwidth product (TBP) for fast observation. As a real-time image algorithm, back-projection algorithm (BPA) is efficient for fast observation. However, compared with the frequency-domain algorithm, the influence of small TBP (STBP) on BPA has not been fully discussed. Thus, the performance of the original BPA on STBP SAR imaging is analyzed and an improved BPA for STBP imaging is proposed in this letter. Theoretical analysis indicates that STBP will cause the point spread function (PSF) distortion and azimuth spectrum ambiguity to the BPA imaging result. To deal with those problems, two parameters of the original BPA are modified in the improved BPA. The accumulating azimuth angle (AAA) is optimized first to calibrate the PSF distortion. Then, based on the azimuth-ambiguity-to-signal ratio (AASR), a BPA meshing criterion related to TBP is proposed to diminish azimuth spectrum ambiguity. The simulation and real data results demonstrate that the improved BPA is effective on undistorted PSF recovering and unambiguity spectrum maintaining, even when the TBP is down to 4.

To obtain digital elevation model (DEM) data through spaceborne interferometric synthetic aperture radar (InSAR) technology, the solution of nonlinear InSAR geolocation equations is one of the most important steps. On one hand, Newton iterative method is time-consuming to solve the equations. On the other hand, the conventional closed-form solution for low earth orbit (LEO) bistatic InSAR system is not suitable for the novel InSAR configuration of geostationary (GEO) transmitter with LEO receivers because of the significant geometry difference. To address these issues, this letter analyzes the bistatic GEO-LEO geometry in detail and exploits the bistatic InSAR equations to propose a GEO-LEO fast location method (GFLM), which obtains the effective closed-form solution for the novel system. Compared with the general Newton iterative method, the GFLM significantly improves the efficiency of geolocation for the bistatic GEO-LEO InSAR system with high precision. Moreover, the geolocation accuracy of the novel system under realistic parameters uncertainties is introduced. Finally, we carry out simulation experiments to verify the effectiveness and superiority of GFLM.

Combined with terrain observation by progressive scans (TOPS) synthetic aperture radar (SAR), near-nadir SAR (N-SAR) system has great potential for the surface water and ocean topography (SWOT) observation. However, one practical problem of the airborne N-SAR is the non-ideal attitude angle caused by the environment. Normally, the influence of attitude angle error can be considered as a constant squint angle of the system. However, in fact, for the near-nadir SAR system with TOPS SAR mode, the attitude angle error will cause a non-ideal 2-dimensional space-variant Doppler centroid for the receiving data and cause the traditional imaging algorithm failure. To deal with such problems, an imaging algorithm with attitude angle estimation for the near-nadir TOPS SAR system is proposed in this paper. Firstly, the influence of attitude angle error and the signal properties are analyzed. Secondly, based on the analysis, an attitude angle estimate algorithm (AAE), utilizing the nonlinear least square method (NLSM) and minimum entropy criterion, is proposed. Then, based on the estimated altitude angle, without data blocking, a full data imaging algorithm (FDA) is proposed. Its main idea is to obtain an un-ambiguous azimuth spectrum and design an appropriate range-variant azimuth filter through frequency chirp scaling (FCS). The numerical simulations and real data processing demonstrate that the proposed algorithm has good performance on attitude angle error estimation and well-focused image obtaining.

Combined with Terrain Observation by Progressive Scans (TOPS) Synthetic Aperture Radar (SAR), Near-nadir Interferometry SAR (NInSAR) has great potential on the Surface Water and Ocean Topography (SWOT) observation. One practical problem is that the Doppler center of airborne NInSAR varies along range and its bandwidth is greater than pulse repeat frequency (PRF) due to the affection of yaw angle error. Traditional imaging algorithms divide the data into several range blocks so that the range variation of Doppler center is ignorable. However, the drawback is that the size and the overlap of the blocks are hard to design. In this paper, an improved image algorithm without range block is proposed. The main procedure is to obtain unambiguous azimuth spectrum and design appropriate range varied azimuth filter through frequency chirp scaling algorithm. The good performance of the proposed algorithm is demonstrated through point target simulation and real data.

Vegetation canopy height inversion is a significant research content in Polarimetric Interferometry Synthetic Aperture Radar (PolInSAR) surface parameter inversion. One practical challenge is that the traditional three-stage inversion method will lead to the inaccurate inversion of vegetation canopy height in X-band because of the too concentrated distribution of polarization interference coherence coefficients (PolInCc). In this paper, an X-band PolInSAR vegetation canopy height inversion strategy is proposed based on Frequency Segmentation (FS). The FS divides the original PolInSAR images into multiple PolInSAR images called sub-images, and the sub-images are used to estimate the more near-linear PolInCc distribution of the sub-images by interferometry. Then the precise terrain phase and effective volume coherence coefficient can be obtained to invert the vegetation canopy height accurately. The validity of the proposed method is verified by N-SAR X-band real data.

Tomographic synthetic aperture radar (TomoSAR) imaging has shown great potential in the three dimensional SAR focusing in recent years. One practical challenge is that the spatial separation of the multi-pass system is always nonuniform and also the number of tracks is very limited, thus leading to the focusing results inaccurate. Conventional Tikhonov regularized method indicates a good performance against the problems above, while the drawback is that it is processed in single-look data, which may cause great estimation bias with the influence of speckle noise or the inaccurate coregistration. In this paper, a variant Tikhonov regularized method is proposed. The main procedure is to estimate a robust covariance matrix and select the SAR signal properly. Both the simulation and real data applied to this method demonstrate that the proposed method is more robust in TomoSAR focusing.

For high resolution sliding spotlight SAR (HRSS-SAR) on agile platform, its beam steering can be achieved by satellite attitude maneuver. In designing the satellite attitude, the variation of Doppler centroid and azimuth resolution should be considered, along with the illuminated scene width and shape. We proposed a feasible satellite attitude maneuver strategy for HRSS-SAR. The strategy developed the conventional sliding spotlight SAR geometry with moderate azimuth resolution. This paper conceive that the rotation center HRSS-SAR moves along azimuth time, and that the variation of Doppler center along range direction should be minimized. In the strategy, beam steering is realized by three-axes attitude maneuver, escaping from the scene bending phenomenon by one or two axes maneuver in large squint angle geometry. The effectiveness and feasibility of our strategy is validated by simulation experiments both in Satellite Tool Kit (STK) and MATLAB.

The bistatic synthetic aperture radar (BiSAR) system consists of a geosynchronous Earth orbit (GEO) illuminator and a low Earth orbit (LEO) receiver. Compared with GEO SAR, it offers great advantages of higher signal-to-noise ratio (SNR) and finer spatial resolution with lower system complexity. The concept also raises significant technical challenges. The spacecraft formation has great effect on radar performance, such as spatial resolution, the angle of two-dimensional (2-D) resolution direction and noise-equivalent sigma zero (NESZ). This paper establishes the relationship between the imaging performance and the formation parameters. Then, a novel design method of spacecraft formation is presented, identifying the principal formation design choices and constraints. Finally, simulation results are provided for typical observational tasks, to verify the effectiveness of the proposed method.

This letter presents a new approach of digital elevation model generation using circular synthetic aperture radar. The approach is composed of two steps, target separation and height estimation. In step 1, subaperture images are reshaped into vectors and stacked to build a composite matrix. The composite matrix is decomposed into a low-rank matrix and a sparse matrix based on “Semi-Soft Go Decomposition” algorithm. The targets, whose height is equal to the reference imaging height plane, are contained in the low-rank matrix, whereas the targets with other heights are contained in the sparse matrix. In step 2, the sparse matrix is further decomposed into several shifted low-rank matrices, each of which corresponds to the targets sharing one height, based on “Shifted Subspaces Tracking” algorithm. The height of the targets contained in each low-rank matrix is estimated from the shifts of the matrix's subspaces. The effectiveness of the proposed approach is investigated by the Gotcha public release data set.

Spaceborne bistatic synthetic aperture radar (SAR) system with an inclined geosynchronous (GEO) illuminator and a low-earth-orbit (LEO) receiver is capable of providing a vast area of surveillance and fine spatial resolution, which presents huge potentials for future earth observation. In this letter, inclined GEO-LEO azimuth multichannel SAR (MC-SAR) system for high-resolution wide-swath imaging is investigated. Starting from modeling geometry of inclined GEO-LEO bistatic MC-SAR, the signal model is analyzed in detail for the first time, and the equivalent positions of the received channels are obtained. Then, we found the spatial-variant residual phase error cannot be compensated accurately by conventional effective phase center (EPC) processing. Moreover, because of the complex bistatic configuration, the frequency-domain imaging algorithms become extremely difficult to achieve a well-focused and phase-preserved image. Meanwhile, the time-domain back-projection algorithm (BPA) faces with a technical challenge due to the nonuniform sampling in azimuth. To address these issues, a bistatic weighted BPA (BWBPA) for GEO-LEO MC-SAR is derived and presented. Without the procedure of EPC, the BWBPA can suppress azimuth ambiguities effectively and yield phase-preserved SAR images. Simulated data results show the validity of the presented method.

Phase unwrapping, a process of recovering the real phase from ambiguous one, is one of key techniques for interferometric synthetic aperture radar (InSAR) data processing. The larger interferograms make the phase unwrapping to be a more challenging task. A novel fast phase unwrapping method is proposed in this paper which is very effective in dealing with the large scale datasets. Several sub-networks consisting of residues are constructed in the method. Therefore, smaller networks make the execution more efficient using minimum cost flows(MCF) algorithm. In addition, the method takes an effective strategy to balance all the sub-networks in order to ensure a feasible solution to each sub-network. Experiment with real data demonstrates the effectiveness of the proposed method.

When combined with digital beam-forming (DBF) techniques, multichannel synthetic aperture radar (SAR) systems can achieve high-resolution and wide-swath SAR imaging. However, inevitable channel biases will degrade the performance of DBF in practice. To address this problem, a novel channel phase bias estimation algorithm is proposed in this letter. Theoretical analysis reveals that the signal of the first channel, which is considered as the reference channel, can be reconstructed from the signals of other channels, regardless of noise and signals outside the Doppler bandwidth. In the presence of phase biases, there is a reconstruction error after the cancellation by subtracting this reconstructed signal from the original signal. However, by minimizing the reconstruction error, the channel phase biases can be precisely estimated. The effectiveness of the proposed algorithm is validated by the experimental results.

Interferometric synthetic aperture radar (SAR) filtering is a crucial processing step in topography reconstruction and deformation measurement. The high-resolution interferograms over vegetation or urban areas are heterogeneous, which will violate the local stationarity assumption and make it difficult to obtain a large number of independent and identically distributed samples for interferometric noise suppression. To overcome this problem, a refined nonlocal filter is proposed in this letter. Given coherence, topography phase, and expected SAR intensity of the pixel to be filtered, the similarity distance between the central pixel and other pixels in the searching window is measured by the normalized probability density function of the interferogram. Then, the outliers whose normalized probability density is smaller than the given threshold are removed from the filtering process. Finally, both simulated and real high-resolution interferograms are used to evaluate the effectiveness of the proposed method.

In multichannel high-resolution and wide-swath (HRWS) synthetic aperture radar (SAR) systems, Doppler centroid (DC) is essential for SAR focusing. However, conventional phase-dependent DC estimators for single-channel SAR systems face many problems in multichannel HRWS SAR systems because of the azimuth undersampling of each channel and channel mismatches in phase. To estimate the baseband DC, the spatial cross-correlation coefficients (SCCCs) of multichannel HRWS SAR signals are exploited, and a novel baseband DC estimator named SCCC method is proposed in this letter. Validation of the proposed method is demonstrated with the real airborne multichannel SAR data.

Multichannel synthetic aperture radar (SAR) systems in azimuth can achieve high-resolution and wide-swath imaging. However, the quality of final SAR image can be degraded by the channel mismatch in phase which increases the energy outside the processed Doppler bandwidth (PDB). To address this problem, a calibration algorithm is proposed in this letter by minimizing the energy outside the PDB. Theoretical analysis shows that the presented method can be interpreted as an adaptively weighted least square estimation problem, where the weights are related to the signal-to-noise ratio (SNR) of the echoes from different directions. Simulation results reveal that our method outperforms the conventional methods in the case of quasi-uniform sampling, particularly at the low-SNR region.

In this paper, a comparison between four channel error estimation methods for high resolution and wide swath (HRWS) synthetic aperture radar (SAR) systems is present. Three of the methods are based on subspace theory and implemented in Doppler frequency domain, while the fourth is based on the correlation between adjacent samples and implemented in time domain. After a brief overview of the approaches, the performance of each is analyzed with respect to its computational complexity and precondition. Quantitative results are shown using the ground-based real-data.

With the combination of digital beamforming (DBF) processing, multichannel synthetic aperture radar (SAR) systems are promising in high-resolution wide-swath imaging. However, the mismatch among channels will degrade the performance of DBF. In this letter, two novel methods are proposed to estimate channel errors for multichannel SAR systems in azimuth. The first method is based on the fact that the space spanned by the signal eigenvectors is equal to that spanned by the practical steering vectors. In the second method, the channel errors are directly estimated by the antenna patterns without matrix decomposition and inversion processing. Both the theoretical analysis and experiments demonstrate the effectiveness and efficiency of these two methods.

Incorporated with digital beam-forming processing, multichannel spaceborne synthetic aperture radar (SAR) systems are able to overcome the minimum antenna area constraint and yield high resolution and wide swath (HRWS) images. This letter mainly investigates the performance of the space-time adaptive processing (STAP) approach applied to HRWS SAR imaging. The analytic expressions for the signal-to-noise ratio (SNR) scaling factor and azimuth ambiguity to signal ratio (AASR) are derived and confirmed by the simulated results. Then, the influence of channel errors on HRWS imaging is analyzed in detail.

Multibaseline phase unwrapping is a critical processing procedure of multibaseline synthetic aperture radar interferometry (InSAR). It has an advantage over single-baseline phase unwrapping in discontinuous-terrain-height estimation. In this paper, the pixels' combination information of multiple InSAR interferograms with different baseline lengths is deeply investigated, and the term ambiguity vector is proposed to represent a pixel's ambiguity number of multiple interferograms. It is also revealed that pixels with the same ambiguity vector have an exclusive pattern among them. A fast cluster-analysis (CA)-based method is proposed for multibaseline phase unwrapping. In this method, all pixels are first clustered into different groups according to their patterns, and then, information of the cluster center is used to unwrap the phases of pixels group by group. Simulation results are shown to verify the effectiveness, efficiency, and noise robustness of CA multibaseline phase-unwrapping method.

2-D phase unwrapping is an important technique in many applications. However, with the growth of image scale, how to tile and splice the image effectively has become a new challenge. In this paper, the phase unwrapping problem is abstracted as solving a large-scale system of inconsistent linear equations. With the difficulties of large-scale phase unwrapping analyzed, L(0)-norm criterion is found to have potentials in efficient image tiling and splicing. Making use of the clustering characteristic of residue distribution, a tiling strategy is proposed for L(0)-norm criterion. Unfortunately, L(0)-norm is an NP-hard problem, which is very difficult to find an exact solution in a polynomial time. In order to effectively solve this problem, equations corresponding to branch cuts of L(0)-norm in the inconsistent equation system mentioned earlier are considered as outliers, and then an outlier-detection-based phase unwrapping method is proposed. Through this method, a highly accurate approximate solution to this NP-hard problem is achieved. A set of experimental results shows that the proposed approach can avoid the inconsistency between local and global phase unwrapping solutions caused by image tiling.

A new approach is presented to estimate the fringe frequencies in interferometric synthetic aperture radar (InSAR) phase image. A first-order model is usually used for fringe frequency estimation, but in steep regions or low-correlation regions, it often fails. In this letter, a prefiltered interferogram, obtained by the slope-compensated or conventional mean filter, is divided into small patches and unwrapped separately. Subsequently, we differentiate the local-phase-unwrapping results to obtain the fringe frequencies. Furthermore, the invalid fringe frequencies are eliminated by a statistical threshold. Finally, the interferogram is filtered by compensating the estimated fringe frequencies in the averaging window of the mean filter. The proposed method can obtain continuous fringe frequency estimation, and it is not constrained by the first-order model. The effectiveness of the proposed approach is verified by the simulated and real InSAR data.

This letter deals with the problems of retrieving height and synthetic aperture radar (SAR) reflectivity of layovered terrain using multibaseline SAR interferometry (InSAR). In particular, we focus on the wideband array problem caused by practically large InSAR arrays and high-resolution SAR images, i.e., the problem of signal envelope misalignment, which is neglected in the work by Gini We propose two methods to eliminate or mitigate the effect of envelope misalignment, one called the aligning method and the other called the joint range cell processing method. In the aligning method, we align each signal envelope for each searched height of the layovered components (i.e., ground resolution cells with different altitudes) during searching procedure. The joint range cell processing method jointly processes the neighboring cells in range to estimate the parameters of layovered components so that the effect of the envelope misalignment can be mitigated. Theoretical analysis and computer simulation results show that both methods have the ability to provide accurate estimation of the heights and radar reflectivities of multiple layovered resolution cells in the presence of large envelope misalignments.

As is well known, image coregistration, interferometric phase noise suppression, and phase unwrapping are three key processing procedures of synthetic aperture radar interferometry (InSAR). The three procedures are cascaded in the conventional processing flow of InSAR. Unlike the conventional processing flow, in this paper we propose a joint processing idea to carry out image coregistration, interferometric phase noise filtering, and phase unwrapping simultaneously based on subspace projection for multibaseline InSAR systems. The joint processing method can perform the fine coregistration of all SAR images implicitly by extracting the correlation information in the neighboring pixel sets, suppress the phase noise by utilizing the orthogonality of the signal subspace and the corresponding noise subspace, and optimally estimate the unwrapped interferometric phases (or the terrain heights) by combining the pixel coherence and the baseline diversity of a multibaseline InSAR system. Simulated results are presented to verify the effectiveness of the joint processing method

We designed a grid computing model in math based on current network computing technologies. MICE is an emerging technology to provide uniform programming, task submission, and management specifications across the large scale distributed computing nodes which deployed some famous mathematical software. MICE utilizes a three-level architecture that shields users from low-level computing resource discovery and provides globe uniform view for users. We extended MathML to solve the mathematical semantic objects' expression. CSP (computing service platform) servers are adopted in MICE to provide uniform task access, transfer and management of heterogeneous distributed resources across multiple administrative domains. This architecture enables the mathematical software resources to be deployed as services on the Internet. MICE can achieve good scalability, reliability and can be flexibly deployed and configured

In this paper, we propose a new method to estimate synthetic aperture radar interferometry (InSAR) interferometric phase in the presence of large coregistration errors. The method takes advantage of the coherence information of neighboring pixel pairs to automatically coregister the SAR images and employs the projection of the joint signal subspace onto the corresponding joint noise subspace to estimate the terrain interferometric phase. The method can automatically coregister the SAR images and reduce the interferometric phase noise simultaneously. Theoretical analysis and computer simulation results show that the method can provide accurate estimate of the terrain interferometric phase (interferogram) as the coregistration error reaches one pixel. The effectiveness of the method is also verified with the real data from the Spaceborne Imaging Radar-C/X Band SAR and the European Remote Sensing 1 and 2 satellites.

Future spaceborne synthetic aperture radar (SAR) systems will be required to produce high-resolution imagery over a wide area of surveillance. However, the minimum antenna area constraint makes it a contradiction to simultaneously obtain both unambiguous wide-area and high azimuth resolution. To overcome this limitation, a technique has been suggested that combines a broad illumination source with multiple receiving channels. Then, the coherent combination of the recorded multichannel signals will allow for the unambiguous SAR mapping of a wide ground area with fine azimuth resolution. This letter first gives an overview of current research work carried out about the generation of wide-swath and high-resolution SAR images from multichannel small spaceborne SAR systems, and then a space-time adaptive processing (STAP) approach combined with conventional SAR imaging algorithms is presented, which could be of help to overcome the existing difficulties in data processing. The main idea of the approach is to use a STAP-based method to properly overcome the aliasing affect caused by the lower pulse repetition frequency and thereby retrieve the unambiguous azimuth wide (full) spectrum signal from the received signal. Following this operation, conventional SAR data processing tools can be applied to fully focus the SAR images. The performance of the approach is also discussed in this letter. The approach has the advantages of simplicity, robustness, and high efficiency.