Optimal Minimum Entropy Research Articles

An Effective Space-Borne ISAR High-Resolution Imaging Approach for Satellite On-Orbit Based on Minimum Entropy Optimization

An Effective Space-Borne ISAR High-Resolution Imaging Approach for Satellite On-Orbit Based on Minimum Entropy Optimization

Noise Robust High-Speed Motion Compensation for ISAR Imaging Based on Parametric Minimum Entropy Optimization

When a target is moving at high-speed, its high-resolution range profile (HRRP) will be stretched by the high-order phase error caused by the high velocity. In this case, the inverse synthetic aperture radar (ISAR) image would be seriously blurred. To obtain a well-focused ISAR image, the phase error induced by target velocity should be compensated. This article exploits the variation continuity of a high-speed moving target’s velocity and proposes a noise-robust high-speed motion compensation algorithm for ISAR imaging. The target’s velocity within a coherent processing interval (CPI) is modeled as a high-order polynomial based on which a parametric high-speed motion compensation signal model is developed. The entropy of the ISAR image after high-speed motion compensation is treated as an evaluation metric, and a parametric minimum entropy optimization model is established to estimate the velocity and compensate it simultaneously. A gradient-based solver of this optimization is then adopted to iteratively find the optimal solution. Finally, the high-order phase error caused by the target’s high-speed motion can be iteratively compensated, and a well-focused ISAR image can be obtained. Extensive simulation experiments have verified the noise robustness and effectiveness of the proposed algorithm.

Noise-Robust Vibration Phase Compensation for Satellite ISAL Imaging by Frequency Descent Minimum Entropy Optimization

Inverse synthetic aperture ladar (ISAL) can perform high-resolution imaging for satellites. However, due to the short wavelength of the laser, satellite micro-vibration will introduce space-variant vibration phase error (SVVPE) and space-invariant vibration phase error (SIVVPE) in the echoes, which seriously blur the ISAL image. In this paper, we propose a noise-robust vibration phase compensation algorithm to accurately estimate and correct these two types of vibration phase errors by frequency descent minimum entropy optimization. Firstly, considering the characteristics of the micro-vibration of satellites, we establish a novel phase error model based on the Fourier series theory, which only contains low-frequency vibration components. The estimation of the phase errors is then translated into the estimation of the model’s Fourier coefficients, which can be achieved by a multi-dimensional minimum entropy optimization. After that, a frequency descent method (FD) is proposed to transform the multi-dimensional optimization into a group of two-dimensional optimizations so that the proposed algorithm can achieve monotonic iterative convergence. In addition, we introduce a solution space adaptive reduction operation to reduce the computational burden when solving the two-dimensional minimum entropy optimizations by the genetic algorithm (GA) to obtain the global optimal solution. Finally, experiments based on the simulated data and the real measured data confirm the effectiveness of the proposed algorithm. Compared with the traditional methods, the proposed algorithm achieves higher phase error estimation accuracy and better image quality.

Accelerating Minimum Entropy Autofocus With Stochastic Gradient for UAV SAR Imagery

Minimum entropy autofocus (MEA) has been applied in unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) imagery for its robustness in different circumstances. However, large amount of range cell samples to calculate the gradient for the minimum entropy optimization keeps its optimal convergence, which usually degrades the efficiency in real UAV SAR applications. In this letter, accelerated minimum entropy autofocus is proposed, which leverages both high computational efficiency and phase error estimation precision simultaneously. A strategy of stochastic gradient (SG) calculation is introduced in the MEA optimization with randomly selecting samples in each iteration through a probability distribution function (PDF). Experimental results with real UAV SAR data have validated the superior performance of the proposed SG-MEA algorithm.

Joint Motion Compensation and Distortion Correction for Maneuvering Target Bistatic ISAR Imaging Based on Parametric Minimum Entropy Optimization

Bistatic inverse synthetic aperture radar (Bi-ISAR) can obtain complementary information of moving targets and overcome the inherent imaging limitations of monostatic ISAR. However, the complex motion of maneuvering targets invalidates the assumption that the imaging projection plane (IPP) is constant in conventional Bi-ISAR imaging. The 2-D spatial variant phase errors would be induced. Moreover, the phase errors have a high-order form due to the time-varying bistatic angle and the high maneuvering characteristics of the target. Meanwhile, the linear geometric distortion induced by the bistatic configuration seriously challenges target identification and classification. In this paper, we propose a novel method to compensate for the 2-D spatial variant phase errors and correct the geometric distortion simultaneously for Bi-ISAR imaging based on parametric minimum entropy optimization. First, the signal mode for maneuvering target in the bistatic configuration is developed. Second, based on the developed signal model, we analyze the coupling relationship between the 2-D high-order spatial variant phase errors and the bistatic angle, and establish a parametric minimum entropy optimization model for high-order spatial variant phase errors compensation. Then, an efficient Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is adopted to obtain the optimal solution of spatial variant coefficients. Finally, with the estimated optimal parameters, the integrated processing of 2-D spatial variant phase errors compensation and distortion correction can be realized. This method can simultaneously obtain well-focused and restored Bi-ISAR images of maneuvering targets without selecting prominent scatterers. Experiments based on scattering point simulation data and electromagnetic data verify the effectiveness of the proposed method.

Noise-robust range alignment method for inverse synthetic aperture radar based on aperture segmentation and average range profile correlation

Range alignment is an essential procedure in the translation motion compensation of inverse synthetic aperture radar imaging. Global optimization or maximum-correlation-based algorithms have been used to realize range alignment. However, it is still challenging to achieve range alignment in low signal-to-noise ratio scenarios, which are common in inverse synthetic aperture radar imaging. In this paper, a novel anti-noise range alignment approach is proposed. In this new method, the target motion is modeled as a uniformly accelerated motion during a short sub-aperture time. Minimum entropy optimization is implemented to estimate the motion parameters in each sub-aperture. These estimated parameters can be used to align the profiles of the current sub-aperture. Once the range profiles of each sub-aperture are aligned, the non-coherent accumulation gain is obtained by averaging all profiles in each sub-aperture, which can be used as valuable information. The accumulation and correlation method is applied to align the average range profiles of each sub-aperture because the former step focuses mainly on alignment within the sub-apertures. Experimental results based on simulated and real measured data demonstrate the effectiveness of the proposed algorithm in low signal-to-noise ratio scenarios.

High-Resolution ISAR Imaging with Modified Joint Range Spatial-Variant Autofocus and Azimuth Scaling.

Well-focused and accurately scaled high-resolution inverse synthetic aperture radar (ISAR) images provide a sound basis for feature extraction and target recognition. This paper proposes a novel high-resolution ISAR imaging algorithm, namely modified joint range spatial-variant autofocus and azimuth scaling algorithm (MJAAS). After motion compensation, the shift of the equivalent rotational center (ERC) of the target destroys the linear relationship between the azimuth chirp rates (ACR) of echo signals and the range coordinates of scattering points, thereby leading to the failure of azimuth scaling. Accordingly, a new joint equivalent rotational center position and effective rotational velocity (JERCP-ERV) signal model is established, serving as the basis of MJAAS. By recourse to the Davidon-Fletcher-Powell (DFP) algorithm, MJAAS can jointly estimate the ERCP and ERV by solving a minimum entropy optimization problem, so as to simultaneously achieve accurate azimuth scaling and range spatial-variant autofocus, which further improves the image focusing performance. MJAAS is not restricted by the modes of motion errors (coherent or non-coherent) and the motion compensation methods, so it can be widely applied to real data with the advantages of strong practicality and high accuracy. Extensive experimental results based on both simulated and real data are provided to corroborate the effectiveness of the proposed algorithm.

Noise-Robust Motion Compensation for Aerial Maneuvering Target ISAR Imaging by Parametric Minimum Entropy Optimization

When a target is involved in maneuvering motion, the nonuniform 3-D rotation motion will cause a continuous change of image projection plane (IPP), which would induce 2-D spatial-variant phase errors. In this case, the inverse synthetic aperture (ISAR) image would be seriously blurred when using the traditional compensation methods. On the other hand, strong noise has been always challenging the conventional methods in motion parameters estimation and phase error compensation. In this paper, we propose a noise-robust compensation method to compensate the 2-D spatial-variant phase errors of the maneuvering target via using tracking information and parametric minimum entropy optimization. First, the maneuvering signal model is developed based on a 2-D spatial-variant model and a 3-D rotation motion model. Based on the developed signal model, a parametric entropy minimum optimization is established to estimate the rotation motion parameters. A gradient-based solver of this optimization is then adopted to iteratively find the global optimum. Meanwhile, in order to increase the robustness of this optimization under low SNR, an extended Kalman filter is adopted here for coarse motion estimation via using tracking information. By treating these estimated motion parameters as initial values, we can effectively prevent this optimization from trapping into a local optimum. Finally, the 2-D spatial-variant phase error can be iteratively compensated, and a well-focused ISAR image can be obtained. The proposed method has three main contributions: 1) it is applicable in the case of changing IPP; 2) it gives the exact expression of chip parameters; and 3) it can efficiently compensate the 2-D spatial-variant phase errors under low SNR. Experiments based on the simulated data and the real measured data prove the effectiveness and robustness of the proposed method.

COMPENSATION OF PHASE ERRORS FOR COMPRESSED SENSING BASED ISAR IMAGERY USING INADEQUATE PULSES

Due to the inaccuracies in radar's measurement, autofocus including range alignment and phase compensation is always essential in inverse synthetic aperture radar (ISAR) imagery. Compressed sensing (CS) based ISAR imagery suggests that the image of target can be reconstructed from much fewer random pulses. Because the number of pulses is inadequate and the pulse intervals are nonuniform, conventional phase compensating algorithms can't work in CS imaging. In this paper, an iterative algorithm is proposed to compensate the phase errors and reconstruct high-resolution focused image from limited pulses. In each iteration, the image of target is reconstructed by CS method, and then the estimation of phase errors is updated based on the reconstructed image. By cycling these steps, well-focused image can be obtained. The smoothed � 0 algorithm is used to reconstruct the image, and the idea of minimum entropy optimization is used to estimate the phase errors. Besides, a method of extracting range bins in range profile based on amplitude information is proposed, which can reduce the computational complexity and improve the speed of convergence considerably. Both simulation and experiment results from real radar data demonstrate the effectiveness and feasibility of our method.

Parameters tuning of model free adaptive control based on minimum entropy

Dynamic linearization based model free adaptive control (MFAC) algorithm has been widely used in practical systems, in which some parameters should be tuned before it is successfully applied to process industries. Considering the random noise existing in real processes, a parameter tuning method based on minimum entropy optimization is proposed, and the feature of entropy is used to accurately describe the system uncertainty. For cases of Gaussian stochastic noise and non-Gaussian stochastic noise, an entropy recursive optimization algorithm is derived based on approximate model or identified model. The extensive simulation results show the effectiveness of the minimum entropy optimization for the partial form dynamic linearization based MFAC. The parameters tuned by the minimum entropy optimization index shows stronger stability and more robustness than these tuned by other traditional index, such as integral of the squared error (ISE) or integral of time-weighted absolute error (ITAE), when the system stochastic noise exists.