Quadratic Phase Error Research Articles

A spawning particle filter for defocused moving target detection in GNSS-based passive radar

Global Navigation Satellite System (GNSS)-based passive radar (GBPR) has been widely used in remote sensing applications. However, for moving target detection (MTD), the quadratic phase error (QPE) introduced by the non-cooperative target motion is usually difficult to be compensated, as the low power level of the GBPR echo signal renders the estimation of the Doppler rate less effective. Consequently, the moving target in GBPR image is usually defocused, which aggravates the difficulty of target detection even further. In this paper, a spawning particle filter (SPF) is proposed for defocused MTD. Firstly, the measurement model and the likelihood ratio function (LRF) of the defocused point-like target image are deduced. Then, a spawning particle set is generated for subsequent target detection, with reference to traditional particles in particle filter (PF) as their parent. After that, based on the PF estimator, the SPF algorithm and its sequential Monte Carlo (SMC) implementation are proposed with a novel amplitude estimation method to decrease the target state dimension. Finally, the effectiveness of the proposed SPF is demonstrated by numerical simulations and preliminary experimental results, showing that the target range and Doppler can be estimated accurately.

A Study of Hypersonic Vehicle-Borne SAR Imaging Under Plasma Sheath

Hypersonic vehicle-borne synthetic aperture radar (SAR) imaging has promising application prospects for remote sensing owing to the characteristics of fast response and flexible trajectory. However, a newly observed phenomenon that occurs during hypersonic flight, called the plasma sheath, seriously affects hypersonic vehicle-borne SAR imaging. Therefore, in this study, the effect of plasma sheath on hypersonic vehicle-borne SAR imaging is investigated systematically. First, a hypersonic vehicle-borne SAR signal model under plasma sheath is developed. Then, the phase shift and amplitude attenuation which are critical in the SAR signal model under plasma sheath are deduced. Moreover, the analytical formulas for the linear and quadratic phase errors are derived. Based on the developed signal model, point target response and an SAR image of an area under plasma sheath show that linear phase error will cause image shift, and quadratic phase error will lead to pulse broadening. In addition, the amplitude attenuation will make the point target response submerged in noise, and signal amplitude nonlinear distortion will result in an asymmetric distortion phenomenon. To further explore the effect of plasma sheath on hypersonic vehicle-borne SAR imaging, quantitative evaluation and analysis of SAR imaging degradation are conducted under different electron densities, carrier frequencies, and bandwidths. The evaluation results in this study will benefit the application of hypersonic vehicle-borne SAR imaging under plasma sheath, and the analytical formulas of linear and quadratic phase error provide the possibility to compensate for SAR imaging degradation under plasma sheath in the future.

Compensation for the ionospheric dispersion effect on spaceborne P-band full-polarimetric wideband SAR

ABSTRACT Spaceborne P-band full-polarimetric wideband synthetic aperture radar (SAR) will be affected by ionospheric phase dispersion and polarimetric dispersion. An improved contrast optimization autofocus (COA) method using four polarization channel data is proposed to compensate for both phase dispersion and polarimetric dispersion. The basis and steps of the method are given. Its performance is analysed by typical target simulation under clutter background and compared with traditional COA method for single channel. The residual quadratic phase error (QPE) of single channel compensated by traditional method may exceed 45° focusing threshold, while the proposed method can reduce the error to less than 10°. Due to the lack of spaceborne P-band SAR data, we simulate the effect of ionosphere on P-band SAR based on ALOS2 PALSAR2 data and verify the proposed method. The simulation result shows the proposed method is effective and superior to traditional method.

Unbalanced low coherence interference microscopy

Low coherence interference microscopy (LCIM) provides high spatial phase sensitivity, i.e., speckle free and coherent noise free quantitative phase images of the test specimens. Due to low temporal coherence (TC) length of the light source, LCIM requires precise adjustment of the optical path difference (OPD) between the object and the reference arm, which is only a few micrometers. Consequently, previously demonstrated LCIM systems are implemented with the use of identical objective lenses in both the arms and also known as balanced interferometric configuration. The use of identical objective lens hinders both the use of high numerical aperture objective lens and also the swift change of the objective lens during imaging. In the present work, LCIM is implemented with non-identical objective lenses in the object and the reference arm also called unbalanced optical configuration. A range of objective lenses 10 × /0.25NA, 20 × /0.45NA and 60 × /1.2NA are employed in the object arm of the system while keeping single objective lens 10 × /0.25NA in the reference arm. To resolve the challenges associated with unbalanced configuration, advanced iterative algorithm (AIA) and principal component analysis (PCA) algorithms are integrated to recover quadratic phase error free phase images of the test specimens. The capabilities of the proposed method are exhibited on various specimens like USAF resolution, step-like test object and for the biological cells, HeLa cells. The proposed approach enables scalable magnification and resolution by simply rotating the imaging objective turret without the need of changing objective lens in the reference arm.

Parametric Azimuth-Variant Motion Compensation for Forward-Looking Multichannel SAR Imagery

Forward-looking multichannel synthetic aperture radar (FLMC-SAR) is an important tool for modern remote sensing applications, which has the capability to reconstruct the high-resolution image of the front area. However, due to the azimuth-variant characteristics of the motion errors over a long aperture, FLMC-SAR data processing is usually a challenging task, especially when involving the motion compensation (MOCO) coupled with Doppler ambiguity resolving. To accomplish an accurate MOCO for FLMC-SAR, a novel parametric azimuth-variant MOCO approach is proposed in this article. Aiming at the coupling problem of MOCO and Doppler ambiguity resolving over the full aperture, we can decouple them through the subaperture division. As a full synthetic aperture is decomposed into several subapertures, the high-order motion errors of the full aperture can be decomposed into the first-order motion errors of the subaperture. On this basis, the mismatch of the space–time spectrum caused by the motion errors can be solved by spectral estimation, yielding Doppler ambiguity resolving for each subaperture. Meanwhile, the azimuth-variant characteristic of motion errors in FLMC-SAR system is characterized by a parametric angle-dependent quadratic phase error (QPE) model. The motion parameters are estimated by a joint multichannel angle estimation-based signal quadratic decomposition method. Immediately, the MOCO for ambiguous targets with different motion errors can be processed separately to improve the imaging performance. Experimental results based on both simulated and real data demonstrate that the proposed method is suitable for FLMC-SAR system.

A Bistatic Analytical Approximation Model for Doppler Rate Estimation Error from Real-Time Spaceborne SAR Onboard Orbit Determination Data

Real-time spaceborne bistatic SAR imaging could significantly reduce the whole processing time and can enhance the spaceborne SAR mission availability. Onboard real-time SAR imaging relies on the Doppler parameters estimated from the real-time onboard orbit determination system (OODS) measurement, whose accuracy level is not comparable to the orbit ephemeris data in ground-based SAR processing. The investigation of the impact of error in real-time OODS measurements on bistatic SAR image quality is necessary, and it can help to clarify the key parameter limits of the real-time OODS. The monostatic analytical approximation model (MonoAAM) for spaceborne SAR reduces simulation complexity and processing time compared to the widely used numerical simulation method. However, due to the different configurations between spaceborne bistatic and monostatic SAR, simply applying the MonoAAM on spaceborne bistatic SAR cannot guarantee the desired result. A bistatic analytical approximation model (BiAAM) for Doppler rate estimation error from real-time OODS measurement in real-time spaceborne bistatic SAR imaging is proposed for characterizing the estimation error. Selecting quadratic phase error (QPE) as an evaluation variable, the proposed BiAAM model can provide QPE estimation results for each position of the satellite in its orbit and the maximum QPE estimation for the whole orbit, while revealing the different process of OODS measurement error transferring to QPE in spaceborne bistatic SAR. The correctness and reliability of BiAAM are evaluated by comparing the result with a Monte Carlo numerical simulation method. With the supporting result from BiAAM, the concept and early-stage development of a real-time onboard bistatic SAR imaging mission could be possibly benefited.

Fast overlapped subaperture algorithm for high-squint spotlight SAR imaging

ABSTRACT The overlapped subaperture algorithm (OSA) is popular for high-squint spotlight synthetic aperture radar (SAR) imaging due to its ability of dealing with a much larger swath than the primary polar format algorithm. However, the traditional OSA suffers from the problem of low efficiency because of the high subaperture overlapping ratio (SOR) required to get rid of spurious targets. The contribution of this study is to loosen the original SOR limit by embedding an additional spatially variant apodization (SVA) into the architecture, resulting in a new fast OSA with lighter computational load and hence higher processing efficiency. Specifically, the algorithm is modified mainly from two aspects: First, a new spatial variant quadratic phase error (QPE) filter is induced to enable effective SVA implementation; Second, a new squint subaperture stitch method is induced to accommodate the subaperture extraction with the new data format led by the new QPE filter. The proposed approach is evaluated by both the point target simulations and the real airborne SAR data in aspects of spurious target suppression, image quality and processing efficiency.

Performance Analysis of Autofocus Algorithms for Compensating Ionospheric Dispersion Effect on Spaceborne Low-Frequency SAR Focusing

Spaceborne low-frequency synthetic aperture radar with high resolution will be affected by ionospheric dispersion, which introduces a quadratic range phase error, leading to range defocusing. The dependence of the performance of contrast optimization (CO) autofocus and multilook registration (MLR) autofocus for dispersion compensation on the signal-to-clutter ratio (SCR) is analyzed. For SCR >20 dB, two autofocus algorithms have similar performances, and CO is a little better. For SCR <; 20 dB, CO, and MLR performance will be affected by initial quadratic phase error (QPE) and clutter size, respectively. When the initial QPE is less than 530°, and clutter size is at least 100 resolution cells, CO performance will be better than MLR. Taking 45° QPE as the threshold for accurate focusing, in the case of the single point object, the threshold SCR for CO to be effective is approximately between 12.5 and 18 dB, corresponding to initial QPE between 0° and 800°. For MLR, the threshold SCR is approximately between 17.5 and 18.5 dB, corresponding to clutter size between 100 and 500 resolution cells. For the case of multiple point objects, the threshold SCR values of both algorithms will decrease. Simulations based on scenes derived from PALSAR2 data demonstrate the effectiveness of the CO and MLR autofocus algorithm.

Analytical Approximation Model for Quadratic Phase Error Introduced by Orbit Determination Errors in Real-Time Spaceborne SAR Imaging

Research on real-time spaceborne synthetic aperture radar (SAR) imaging has emerged as satellite computation capability has increased and applications of SAR imaging products have expanded. The orbit determination data of a spaceborne SAR platform are essential for the SAR imaging procedure. In real-time SAR imaging, onboard orbit determination data cannot achieve a level of accuracy that is equivalent to the orbit ephemeris in ground-based SAR processing, which requires a long processing time using common ground-based SAR imaging procedures. It is important to study the influence of errors in onboard real-time orbit determination data on SAR image quality. Instead of the widely used numerical simulation method, an analytical approximation model of the quadratic phase error (QPE) introduced by orbit determination errors is proposed. The proposed model can provide approximation results at two granularities: approximations with a satellite’s true anomaly as the independent variable and approximations for all positions in the satellite’s entire orbit. The proposed analytical approximation model reduces simulation complexity, extent of calculations, and the processing time. In addition, the model reveals the core of the process by which errors are transferred to QPE calculations. A detailed comparison between the proposed method and a numerical simulation method proves the correctness and reliability of the analytical approximation model. With the help of this analytical approximation model, the technical parameter iteration procedure during the early-stage development of an onboard real-time SAR imaging mission will likely be accelerated.

Alignment-tolerant single-shot digital holographic microscopy based on computer-controlled telecentricity.

An alignment-tolerant telecentric digital holographic microscopy (AT-T-DHM) system based on computer-controlled telecentricity is proposed. It consists of a three-step process-optical recording, computational compensation, and retrieving processes. With a tube-lens-based two-beam interferometer, phase information of the object is recorded on the hologram, where another optical quadratic phase error (O-QPE) due to the misalignment of the tube lens happens to be added. In the computational compensation process, this phase error can be estimated, by which the O-QPE is balanced out from the recorded hologram. Then, only the phase information of the object can be retrieved from the O-QPE-compensated hologram. This computational compensation process makes the proposed system virtually operate in a telecentric imaging mode, which enables implementing a practical AT-T-DHM. Wave-optical analysis and experiments with a test object confirm the feasibility of the proposed system.

Unified Coordinate System Algorithm for Terahertz Video-SAR Image Formation

Video synthetic aperture radar (ViSAR) is a novel imaging mode where the radar system forms a sequence of SAR images while the radar platform is flying. To achieve a high frame rate, ViSAR system typically operates in the terahertz (THz) band. In this paper, the unified coordinate system algorithm (UCSA) improving on the polar format algorithm (PFA) is proposed for THz ViSAR images formation, which is based on the more accurate wavenumber domain signal model derived by second-order Taylor expansion. Considering the small synthetic angle feature of THz ViSAR, the UCSA divides two-dimensional resampling into range and azimuth resampling using the chirp z-transform to reduce the processing complexity in ViSAR imaging. Through the analysis in this paper, it can be known that THz PFA images are free from the quadratic phase errors. However, the PFA images are oriented to different directions and exist image distortion caused by linear phase errors (LPE). Through an image resampling, the UCSA corrects the LPE and rotates the images to the unified coordinate system simultaneously. The effectiveness of UCSA is validated by a ground-based experiment performed by a 0.3 THz radar system.

Focusing High-Resolution Airborne SAR with Topography Variations Using an Extended BPA Based on a Time/Frequency Rotation Principle

With the increasing requirement for resolution, the negligence of topography variations causes serious phase errors, which leads to the degradation of the focusing quality of the synthetic aperture (SAR) imagery, and geometric distortion. Hence, a precise and fast algorithm is necessary for high-resolution airborne SAR. In this paper, an extended back-projection (EBP) algorithm is proposed to compensate the phase errors caused by topography variations. Three-dimensional (3D) variation will be processed in the time-domain for high-resolution airborne SAR. Firstly, the quadratic phase error (QPE) brought by topography variations is analyzed in detail for high-resolution airborne SAR. Then, the key operation, a time-frequency rotation operation, is applied to decrease the samplings in the azimuth time-domain. Just like the time-frequency rotation of the conventional two-step approach, this key operation can compress data in an azimuth time-domain and it reduces the computational burden of the conventional back-projection algorithm, which is applied lastly in the time-domain processing. The results of the simulations validate that the proposed algorithm, including frequency-domain processing and time-domain processing can obtain good focusing performance. At the same time, it has strong practicability with a small amount of computation, compared with the conventional algorithm.

Fast ISAR Cross-Range Scaling Using Modified Newton Method

This paper proposes a fast and novel cross-range scaling algorithm for inverse synthetic aperture radar (ISAR) imaging. The rotational motion of the target unavoidably results in high-order phase errors that blur the ISAR image. To achieve the cross-range scaling and compensate the quadratic phase error, the rotational velocity and rotational center of the target are jointly estimated by optimizing the ISAR image quality in terms of either entropy or contrast. Since it is a two-dimensional nonlinear optimization problem, the grid search is generally computationally inefficient and inaccurate. To improve the computational efficiency, a modified Newton method is introduced by adjusting the Hessian to be positively definite to ensure the iterative optimization process in a correct direction. The proposed algorithm offers the following desirable advantageous features. First, it automatically compensates the quadratic phase errors jointly with the scaling process to improve the image quality. Second, it is a data-driven, rather than image-driven, process that does not depend on the quality of ISAR image. It also performs satisfactorily for the sparse aperture data, while most other algorithms are invalid. The modified Newton method ensures fast convergence. For example, our numerical experiments achieve a precision of $ \bf {10^{-6}}$ with less than ten iterations. Last but not least, the proposed algorithm is robust to noise because our experiments show that it is still effective when signal-to-noise ratio is as low as $-$ 10 dB.

Focusing Nonparallel-Track Bistatic SAR Data Using Extended Nonlinear Chirp Scaling Algorithm Based on a Quadratic Ellipse Model

Image formation for bistatic synthetic aperture radar data with nonparallel tracks is a challenging task due to the existence of the spatial variance of range cell migration (RCM) and azimuth frequency modulation (FM) rate. In this letter, an extended nonlinear chirp scaling (ENLCS) algorithm based on a quadratic ellipse model with two motion platform parameters is proposed for this configuration. For range processing, a method combining linear range walk correction and keystone transform is adopted to remove linear RCM completely and mitigate range–azimuth cross coupling. For azimuth focusing, a quadratic ellipse model using the two motion platform parameters is established to depict the azimuth-variant properties of the azimuth FM rate, and its accurate high-order approximation is derived as well. Investigations of the quadratic phase error show that great improvement can be made by this model. Following which, coefficients of the ENLCS are derived to accomplish the azimuth equalization. Simulation results validate the effectiveness of the algorithm proposed by this letter.

New Phase Error Corrections for PFA with Squinted SAR

The polar format algorithm, while being more efficient than backprojection for synthetic aperture radar image formation, produces images with distortion and defocus. Since these errors are caused by uncompensated phase, a correction may be applied in postprocessing. Recent work utilizes a slow-time Taylor expansion of the differential range to derive the residual quadratic phase error for broadside linear flight paths. In this letter, we extend this approach to squinted linear flight paths and present new distortion and defocus corrections.

RESEARCH ON AIRBORNE SAR IMAGING BASED ON ESC ALGORITHM

Abstract. Due to the ability of flexible, accurate, and fast obtaining abundant information, airborne SAR is significant in the field of Earth Observation and many other applications. Optimally the flight paths are straight lines, but in reality it is not the case since some portion of deviation from the ideal path is impossible to avoid. A small disturbance from the ideal line will have a major effect on the signal phase, dramatically deteriorating the quality of SAR images and data. Therefore, to get accurate echo information and radar images, it is essential to measure and compensate for nonlinear motion of antenna trajectories. By means of compensating each flying trajectory to its reference track, MOCO method corrects linear phase error and quadratic phase error caused by nonlinear antenna trajectories. Position and Orientation System (POS) data is applied to acquiring accuracy motion attitudes and spatial positions of antenna phase centre (APC). In this paper, extend chirp scaling algorithm (ECS) is used to deal with echo data of airborne SAR. An experiment is done using VV-Polarization raw data of C-band airborne SAR. The quality evaluations of compensated SAR images and uncompensated SAR images are done in the experiment. The former always performs better than the latter. After MOCO processing, azimuth ambiguity is declined, peak side lobe ratio (PSLR) effectively improves and the resolution of images is improved obviously. The result shows the validity and operability of the imaging process for airborne SAR.

Theoretical Application of Overlapped Subaperture Algorithm for Quasi-Forward-Looking Parameter-Adjusting Spotlight SAR Imaging

This letter theoretically extends and applies the overlapped subaperture algorithm (OSA) for the challenging spotlight synthetic aperture radar (SAR) imaging in a quasi-forward-looking (QFL) geometry. A parameter-adjusting framework, in which the radar parameters relate closely to the geometry, is employed to mitigate the spatial signal coupling. By innovatively fitting the phase error induced by the planar wavefront assumption directly to the wavenumbers, both the linear and quadratic phase errors, which determine the geometrical distortion and the defocusing effects, respectively, can be accurately expressed and then corrected. When compared with the parameter-adjusting polar format algorithm proposed by the authors in previous work, the OSA is superior in contributing to an expanded imaging swath. The validity of the OSA methodology is demonstrated by the simulation of a Ka-band SAR working in the QFL diving mode with an extreme 85° squint angle.

Parameter Estimation of a Ground Moving Target Using Image Sharpness Optimization.

Motion parameter estimation of a ground moving target is an important issue in synthetic aperture radar ground moving target indication (SAR-GMTI) which has significant applications for civilian and military. The SAR image of a moving target may be displaced and defocused due to the radial and along-track velocity components, respectively. The sharpness cost function presents a measure of the degree of focus of the image. In this work, a new ground moving target parameter estimation algorithm based on the sharpness optimization criterion is proposed. The relationships between the quadratic phase errors and the target’s velocity components are derived. Using two-dimensional searching of the sharpness cost function, we can obtain the velocity components of the target and the focused target image simultaneously. The proposed moving target parameter estimation method and image sharpness metrics are analyzed in detail. Finally, numerical results illustrate the effective and superior velocity estimation performance of the proposed method when compared to existing algorithms.

Scene size limits for polar format algorithm

Synthetic aperture radar (SAR) is a form of remote sensing where coherent radar echoes transmitted from a moving platform are processed to form an image of a scene, usually on the ground. There are several algorithms that have been developed with varying levels of complexity and accuracy. In applications with large scene size requirements, the choice of image formation algorithm is important. Exact imaging algorithms like the back-projection algorithm (BPA) can form large images without errors, but they are computationally expensive. Another well-known algorithm is the polar format algorithm (PFA), which is significantly faster than BPA, but it uses approximations that cause image errors in large scenes. In this paper, we evaluate the scene size limitations of the PFA in terms of image defocus. This is caused by residual quadratic phase errors that arise due to approximations in the algorithm. We derive this residual quadratic phase error using a Taylor series expansion in the slow time dimension. Then, we derive simplified expressions for image defocus for two flight paths: circular and linear. We also use the Taylor series expansion to derive accurate corrections for image distortion caused by PFA. These distortion corrections are used in conjunction with the residual quadratic phase errors to derive accurate scene size limitations that are notably different from the circular regions of focus determined in earlier works.

Cubic Phase Distortion and Irregular Degradation on SAR Imaging Due to the Ionosphere

The interest in the use of spaceborne synthetic aperture radar (SAR) for collecting earth bio/geophysical information and detecting foliage-obscured targets has been increased. However, the signals are inevitably affected by the ionosphere, particularly at very high frequency and ultrahigh frequency. Thus, it is crucial to understand the potential effects of the ionosphere on SAR systems. In this paper, three possible contributions are made to analyze these effects. First, for analyzing range resolution, in addition to linear and quadratic phase errors due to the background ionosphere, the cubic phase error is considered. The expected mean electron density inferred from the International Reference Ionosphere is used. Second, for analyzing azimuthal resolution, the effects of ionospheric irregularities are evaluated under the conditions of oblique incidence and anisotropic irregularities. The model is presented on the basis of the multiple phase screen (MPS) method. Compared with the previous model, the MPS method can give results in good agreement with both weak and strong scattering theories. Finally, based on the theory of moment equation, range resolution degradation caused by the multiple scattering is also studied in the case of anisotropic irregularities. By using the range Doppler algorithm, a number of degraded point responses due to these ionospheric effects are shown, and then, some evaluation results are listed.