scholarly journals A Versatile Algorithm for Autofocusing SAR Images

2021 ◽  
Vol 24 (1) ◽  
pp. 22-33
Author(s):  
A. A. Monakov
Keyword(s):  
Image Quality ◽  
Objective Function ◽  
Direct Method ◽  
Phase Error ◽  
Quadratic Function ◽  
Radar Image ◽  
Synthetic Aperture ◽  
Objective Functions ◽  
Radar Images ◽  
Phase Errors

Introduction. Random deviations of the antenna phase centre of a synthetic aperture radar (SAR) are a source of phase errors for the received signal. These phase errors frequently cause blurring of the radar image. The image quality can be improved using various autofocus algorithms. Such algorithms estimate phase errors via optimization of an objective function, which defines the radar image quality. The image entropy and sharpness are well known examples of objective functions. The objective function extremum can be found by fast optimization methods, whose realization is a challenging computing task.Aim. To synthesize a versatile and computationally simple autofocusing algorithm allowing any objective function to used without changing its structure significantly.Materials and methods. An algorithm based on substituting the selected objective function with a simpler surrogate objective function, whose extremum can be found by a direct method, is proposed. This method has been referred as the MM optimization in scientific literature. It is proposed to use a quadratic function as a surrogate objective function.Results. The synthesized algorithm is straightforward, not requiring recursive methods for finding the optimal solution. These advantages determine the enhanced speed and stability of the proposed algorithm. Adjusting the algorithm for the selected objective function requires minimal software changes. Compared to the algorithm using a linear surrogate objective function, the proposed algorithm provides a 1.5 times decrease in the standard deviation of the phase error estimate, with an approximately 10 % decrease in the number of iterations.Conclusion. The proposed autofocusing algorithm can be used in synthetic aperture radars to compensate the arising phase errors. The algorithm is based on the MM-optimization of the quadratic surrogate objective functions for radar images. The computer simulation results confirm the efficiency of the proposed algorithm even in case of large phase errors.

scholarly journals Effect of incorrect sound velocity on synthetic aperture sonar resolution

2019 ◽  
Vol 283 ◽  
pp. 04013
Author(s):  
Xia Ji ◽  
Lisheng Zhou ◽  
Weihua Cong
Keyword(s):  
Image Quality ◽  
Sound Velocity ◽  
Velocity Gradient ◽  
Phase Error ◽  
Synthetic Aperture ◽  
Measuring Error ◽  
Detection Range ◽  
Synthetic Aperture Sonar ◽  
Velocity Error ◽  
Velocity Measuring

Synthetic aperture sonar (SAS) is an imaging technique to produce centimeter resolution over hundreds-of-meter range on the sea floor, by constructing a virtual aperture whose length automatically adjusts itself for a given focusing range. SAS is near-field acoustic imaging, and this implies that the sound velocity should be accurately estimated for well focused imaging. Otherwise there will be image quality loss. However, sound velocity in the ocean varies with space and time, and there might also be measuring error of CTD (Conductivity, Temperature, and Depth) sensor, so sound velocity error has become one of the limiting factors to improve SAS resolution further. To characterize the effect of sound velocity error quantificationally, the practice SAS resolution is mode as the convolution of ideal seafloor reflectivity function and a phase error function in frequency domain, where the phase error is caused by incorrect sound velocity. Then the SAS resolution parameterized is calculated as a function of the sound velocity measuring error, or sound velocity gradient. It is shown that SAS azimuthally (along track) resolution loss, caused by sound velocity measurement error, increases linearly with detection range. Meanwhile the loss caused by sound velocity gradient increases squarely. It is simulated by considering the synthetic aperture data collection for a particular pixel, and results show that the point scatter response will defocus when the sound velocity measuring error is up to 1% at 200m range, or the sound velocity changes up to 2% over a typical gradient at 200m range, and be worse at a longer range. Furthermore, we demonstrate the influence of sound velocity errors on SAS imagery using a sea trial data and real CTD measurements at South China Sea. We evaluate the degradation in image quality with respect to sound velocity errors by using two plastic balls and a variable seafloor scene, and results also support the accuracy of theoretical conclusions above.

scholarly journals Robust Two-Dimensional Spatial-Variant Map-Drift Algorithm for UAV SAR Autofocusing

2019 ◽  
Vol 11 (3) ◽  
pp. 340 ◽  
Author(s):  
Guanyong Wang ◽  
Man Zhang ◽  
Yan Huang ◽  
Lei Zhang ◽  
Fengfei Wang
Keyword(s):  
Cross Correlation ◽  
Phase Error ◽  
Synthetic Aperture ◽  
Two Dimensional ◽  
Spatial Variance ◽  
Phase Errors ◽  
Residual Phase ◽  
Aerial Vehicle ◽  
Sar Imagery ◽  
The One

Autofocus has attracted wide attention for unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) systems, because autofocus process is crucial and difficult when the phase error is spatially dependent on both range and azimuth directions. In this paper, a novel two-dimensional spatial-variant map-drift algorithm (2D-SVMDA) is developed to provide robust autofocusing performance for UAV SAR imagery. This proposed algorithm combines two enhanced map-drift kernels. On the one hand, based on the azimuth-dependent phase correction, a novel azimuth-variant map-drift algorithm (AVMDA) is established to model the residual phase error as a linear function in the azimuth direction. Then the model coefficients are efficiently estimated by a quadratic Newton optimization with modified maximum cross-correlation. On the other hand, by concatenating the existing range-dependent map-drift algorithm (RDMDA) and the proposed AVMDA in this paper, a phase autofocus procedure of 2D-SVMDA is finally established. The proposed 2D-SVMDA can handle spatial-variance problems induced by strong phase errors. Simulated and real measured data are employed to demonstrate that the proposed algorithm compensates both the range- and azimuth-variant phase errors effectively.

scholarly journals A Techniques to Downgrade Objective Function in Parallel Robot Kinematics Problem

2015 ◽  
Vol 4 (3) ◽  
pp. 186
Author(s):  
Trung Thanh Trang ◽  
Guang Wei Li ◽  
Long Thanh Pham
Keyword(s):  
Objective Function ◽  
Quadratic Function ◽  
Parallel Robot ◽  
Joint Space ◽  
Quadratic Functions ◽  
Robot Kinematics ◽  
Objective Functions ◽  
Quadratic Objective Function ◽  
Parallel Robot Kinematics ◽  
Alternative Configuration

Quadratic functions and quaternary functions are preferable forms solving parallel robot kinematics problems. In order to simplify and to use only one method to solve all forms of the objective functions, this article introduces prevalent techniques to downgrade mathematical model of the objective functions from quaternary function to quadratic function in parallel robot kinematics problem. By using equivalent alternative kinematic structure and additional mathematical constraints, we will change from the study of parallel robot kinematics problem with the form of quaternary objective function as the original configuration to equivalent alternative configuration in the form of quadratic objective function. The parallel robot kinematics problem based on alternative configuration with quadratic objective function is not only simpler but also helps to quickly identify the mathmatical relationships in the joint space and work space of parallel robot. Then, more accurate control solution of parallel robot kinematics problem can be identified. Moreover, by using techniques in this study, all forms of objective functions of parallel robot of any structure can be easily solved. The result from numerical simulation has been used to prove the presented approaches.

scholarly journals Analisis Karakteristik Fungsi Lagrange Dalam Menyelesaikan Permasalahan Optimasi Berkendala

2018 ◽  
Vol 1 (1) ◽  
pp. 037-043
Author(s):  
Theresia Mehwani Manik ◽  
Parapat Gultom ◽  
Esther Nababan
Keyword(s):  
Constrained Optimization ◽  
Objective Function ◽  
Lagrange Multiplier ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quadratic Function ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Objective Functions ◽  
Constrained Optimization Problems

Optimasi adalah suatu aktivitas untuk mendapatkan hasil terbaik di dalam suatu keadaan yang diberikan. Tujuan akhir dari aktivitas tersebut adalah meminimumkan usaha (effort) atau memaksimumkan manfaat (benefit) yang diinginkan. Metode pengali Lagrange merupakan metode yang digunakan untuk menangani permasalahan optimasi berkendala. Pada penelitian ini dianalisis karakteristik dari metode pengali Lagrange sehingga metode ini dapat menyelesaikan permasalahan optimasi berkendala. Metode tersebut diaplikasikan pada salah satu contoh optimasi berkendala untuk meminimumkan fungsi objektif kuadrat sehingga diperolehlah nilai minimum dari fungsi objektif kuadrat adalah -0.0403. Banyak masalah optimasi tidak dapat diselesaikan dikarenakan kendala yang membatasi fungsi objektif. Salah satu karakteristik dari metode pengali Lagrange adalah dapat mentransformasi persoalan optimasi berkendala menjadi persoalan optimasi tanpa kendala. Dengan demikian persoalan optimasi dapat diselesaikan.   Optimization is an activity to get the best results in a given situation. The ultimate goal of the activity is to minimize the effort or maximize the desired benefits. The Lagrange multiplier method is a method used to handle constrained optimization problems. This study analyzed the characteristics of the Lagrange multiplier method with the aim of solving constrained optimization problems. The method was applied to one sample of constrained optimization to minimize the objective function of squares and resulted -0.0403 as the minimum value of the objective quadratic function. Many optimization problems could not be solved due to constraints that limited objective functions. One of the characteristics of the Lagrange multiplier method was that it could transform constrained optimization problems into non-constrained ones. Thus the optimization problem could be resolved. 

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

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