Phase Compensation Function Research Articles

A coherent integration method of an active sonar for maneuvering turning target detection.

The detection probability of underwater weak targets using active sonar is low, and inter-pulse coherent integration can improve the signal-to-noise ratio of echoes. When a target executes a maneuvering turn, complex range and Doppler frequency migrations occur during the coherent integration time that decrease the coherent integration gain. Most existing integration methods simplify the target motion to a finite-order polynomial model but fail to integrate a maneuvering turning target (MTT) due to model mismatch. Hence, this study proposes an underwater MTT integration method based on the modified Radon-Fourier transform. The proposed method constructs a theoretically accurate motion model for the MTT and a phase compensation function to compensate for the Doppler frequency migration. Furthermore, it yields a well-focused integration peak in the range-velocity and offset angle-turn rate dimensions and accurately estimates the target motion parameters. Moreover, the proposed method is suitable for targets with radial and oblique uniform motions. The effectiveness of the proposed method is demonstrated through simulations and a lake test. The proposed method demonstrates good integration performance, with an integration gain approximately 4-7 dB higher than that of traditional methods when using 30 integration pulses.

Integration and Detection of a Moving Target with Multiple Beams Based on Multi-Scale Sliding Windowed Phase Difference and Spatial Projection

Due to the fast scanning speed of the current phased-array radar and the moving characteristics of the target, the moving target usually spans multiple beams during coherent integration time, which results in severe performance loss for target focusing and parameter estimation because of the unknown entry/departure beam time within the coherent period. To solve this issue, a novel focusing and detection method based on the multi-beam phase compensation function (MBPCF), multi-scale sliding windowed phase difference (MSWPD), and spatial projection are proposed in this paper. The proposed method mainly includes the following three steps. First, the geometric and signal models of multiple beam integration with observed moving targets are accurately established where the range migration (RM), Doppler frequency migration (DFM), and beam migration (BM) are analyzed. Based on that, the BM is eliminated by the MBPCF, the second-order keystone transform (SOKT) is utilized to mitigate the RM, and then, a new MSWPD operation is developed to estimate the target’s entry/departure beam time, which realizes well-focusing output within the beam. After that, by dividing the radar detection area, the spatial projection (SP) method is adopted to obtain multiple-beams joint integration, and thus, improved detection performance can be obtained. Numerical experiments are carried out to evaluate the performance of the proposed method. The results show that the proposed method could achieve superior focusing and detection performances.

Underwater weak moving target detection method based on wideband Multi-pulse coherent integration

When active sonar detects a weak moving target in a noisy background, coherent integration can be used to improve the signal-to-noise ratio of echo. The active sonar often transmits wideband signals and the target velocity ambiguity often occurs, in this case, the conventional coherent integration method makes the echo energy disperse and coherent integration gain decrease due to non-constant ambiguity factors in the bandwidth. To solve this problem, an underwater weak moving target detection method using multi-pulse coherent integration based on the wideband keystone transform is proposed. To compensate the non-constant ambiguity factors, a phase compensation function is constructed by replacing a single ambiguity factor with a set of ambiguity factors in the wideband keystone transform. After the proposed method, a well-focused image can be obtained in the delay-Doppler domain, and the coherent integration peak is detected to estimate delay and Doppler of the weak moving target. Simulations and lake test results verify the effectiveness of the proposed method, and show that the coherent integration gain with the proposed method is ca. 7–8 dB higher than that with the conventional method. The simulation results of integrating thirty pulses show that when the detection probability is greater than 0.7, the root-mean-square error of delay estimation of the proposed method is about 1/8 of that of the conventional method, and the root-mean-square error of Doppler estimation is about 1/3 of that of the conventional method, indicating that the proposed method has better parameter estimation accuracy.

High-Resolution Azimuth Missing Data SAR Imaging Based on Sparse Representation Autofocusing

Due to significant electromagnetic interference, radar interruptions, and other factors, Azimuth Missing Data (AMD) may occur in Synthetic Aperture Radar (SAR) echo, resulting in severe defocusing and even false targets. An important approach to solving this problem is to utilize Compressed Sensing (CS) methods on AMD echo to reconstruct complete echo, which can be abbreviated as the AMD Imaging Algorithm (AMDIA). However, the State-of-the-Art AMDIA (SOA-AMDIA) do not consider the influence of motion phase errors, resulting in an unacceptable estimation error of the complete echo reconstruction. Therefore, in order to enhance the practical applicability of AMDIA, this article proposes an improved AMDIA using Sparse Representation Autofocusing (SRA-AMDIA). The proposed SRA-AMDIA aims to accurately focus the imaging result, even in the Phase Error AMD (PE-AMD) echo case. Firstly, a Phase-Compensation Function (PCF) based on the phase history of the scene centroid is designed. When the PCF is multiplied with the PE-AMD echo in the range-frequency domain, a coarse-focused sparse representation signal can be obtained in the range-Doppler domain. However, due to the influence of unknown PE, the sparsity of this sparse representation signal is unsatisfying, breaking the sparse constraints requirement of the CS method. Therefore, we introduced a minimum entropy autofocusing algorithm to autofocus this sparse representation signal. Next, the estimated PE is compensated for this sparse representation signal, and a more sparse representation signal is obtained. Hence, the non-PE complete echo can be reconstructed. Finally, the estimated complete echo can be used with classic imaging algorithms to obtain high-resolution imaging results under the PE-AMD condition. Simulation and real measured data have verified the effectiveness of the proposed SRA-AMDIA.

Radar Maneuvering Target Detection Based on Product Scale Zoom Discrete Chirp Fourier Transform

Long-time coherent integration works to significantly increase the detection probability for maneuvering targets. However, during the observation time, the problems that often tend to occur are range cell migration (RCM) and Doppler frequency cell migration (DFCM), due to the high velocity and acceleration of the maneuvering target, which can reduce the detection of the maneuvering targets. In this regard, we propose a new coherent integration approach, based on the product scale zoom discrete chirp Fourier transform (PSZDCFT). Specifically, by introducing the zoom operation into the modified discrete chirp Fourier transform (MDCFT), the zoom discrete chirp Fourier transform (ZDCFT) can correctly estimate the centroid frequency and chirp rate of the linear frequency-modulated signal (LFM), regardless of whether the parameters of the LFM signal are outside the estimation scopes. Then, the scale operation, combined with ZDCFT, is performed on the radar echo signal in the range frequency slow time domain, to remove the coupling. Thereafter, a product operation is executed along the range frequency to inhibit spurious peaks and reinforce the true peak. Finally, the velocity and acceleration of the target estimated from the true peak position, are used to construct a phase compensation function to eliminate the RCM and DFCM, thus achieving coherent integration. The method is a linear transform without energy loss, and is suitable for low signal-to-noise (SNR) environments. Moreover, the method can be effectively fulfilled based on the chirp-z transform (CZT), which prevents the brute-force search. Thus, the method reaches a favorable tradeoff between anti-noise performance and computational load. Intensive simulations demonstrate the effectiveness of the proposed method.

Design of Amplifier Circuit of Optical Fiber Sensor and Its Application in Cloud Computing of Mechanical Vibration Fault

Photoelectric detection technology has been widely used in industry, agriculture, medicine, and other fields. The signal collected by photoelectric signal detection equipment is weak and vulnerable to noise interference. Therefore, a preamplifier circuit with good performance is needed to amplify the original signal effectively. Firstly, considering that a single-mode fiber coupler is more sensitive to the length of the coupling region, a coupled optical fiber vibration sensor is designed. Secondly, the appropriate operational amplifier (Op-amp) is chosen based on the photodetector. By listing and selecting the OPA656 Op-amp produced by TI Company, the basic current and voltage conversion circuit of photoelectric detection equipment is analyzed. In addition, a basic trans-impedance circuit with a phase compensation function is proposed and the calculation method of optimal phase compensation capacitance is derived. Finally, in the process of monitoring the vibration data of equipment, cloud computing technology (fuzzy C-means clustering algorithm+MapReduce model) is used for distributed processing of mechanical vibration data. In the test, the coupled optical fiber vibration sensor designed with an amplifier circuit and moving coil vibration sensor are placed on the ship equipment at the same time, and the rubber hammer is employed to hit the surface of the ship machinery. The test results of the two sensors are the same, which proves that the optical fiber sensor designed in this study meets the requirements of vibration measurement.

Extended Polar Format Algorithm (EPFA) for High-Resolution Highly Squinted SAR

The conventional polar format algorithm (CPFA) is widely used for synthetic aperture radar (SAR) because of its simple and efficient operations. However, due to its wavefront curvature assumption, the CPFA’s depth-of-focus (DOF) is extremely small, which greatly limits the scene size, especially for high-resolution and highly squinted (HRHS) SAR. To solve this problem, an extended PFA (EPFA) is proposed in this study, re-deriving mapping functions by expanding the range history into slant- and cross-range components according to the forms of real data storage. This allows the full use of storage data, which the CPFA cannot achieve due to the large approximations introduced by the projection of echo data onto the ground. The wavefront curvature error is then analyzed and eliminated using a space-variant phase compensation function. Due to the high accuracy of expansion in the slant range plane and the space-variant correction processing, the EPFA has a larger DOF than the CPFA. The EPFA is also more suitable for undulating terrains since it avoids the projection of real data onto the ground plane performed in the CPFA. Using comparative analyses of simulated data and real-world images, the results suggest that the proposed EPFA achieves better focusing effects than the CPFA and is particularly useful for HRHS SAR.

Phase Compensation and Time-Reversal Transform for High-Order Maneuvering Target Detection

In this letter, we consider a target with high-order motion and propose two long-time coherent integration algorithms with low computational cost for target detection via phase compensation and time-reversal transform. Due to the even/odd characteristic, the coupling effect between the range frequency and slow time can be eliminated by constructing the phase compensation function and doing the time-reversal transform. In doing so, the target energy can be accumulated by inverse fast Fourier transform (IFFT) in range frequency and fast Fourier transform (FFT) in slow time. Simulations are given to demonstrate the effectiveness of the proposed algorithms. Moreover, compared with the generalized Radon–Fourier transform (GRFT) and generalized dechirp-keystone transform (GDKT), the proposed algorithms have much lower computational burden.

SAR Imaging Method for Moving Target With Azimuth Missing Data

To solve the problem of the moving target SAR imaging from an incomplete echo, we proposed a novel SAR imaging method for the moving target with the azimuth missing data (MTIm-AMD). Instead of directly reconstructing the moving target image using the sparse SAR imaging method, we estimate and reconstruct the non-cooperative moving target&#x0027;s complete echo from the azimuth incomplete echo based on its sparsity. At first, the non-cooperative moving target&#x0027;s motion parameters are estimated from the incomplete echo. Then, to ensure that the complete echo can be well reconstructed using the compressed sensing method, these parameters are exploited to design a phase compensation function. Finally, using the reconstructed data, the fine-focused moving target can be obtained via the traditional SAR imaging algorithm. The simulation and experiment data results verify the effectiveness of the proposed MTIm-AMD method and demonstrate that the moving target can be fine-imaging when the echo SNR is higher than <inline-formula><tex-math notation="LaTeX">$-$</tex-math></inline-formula>20 dB and the azimuth missing ratio (AMR) is less than 70&#x0025;. This implies that the proposed MTIm-AMD method achieves satisfactory robustness to echo SNR and can handle most AMR cases.

Efficient Ground Moving Target Imaging Method for Synthetic Aperture Radar With Target Azimuth Ambiguity

The synthetic aperture radar (SAR) image of ground moving target is easily defocused given the unknown relative motions between radar and target. In addition, the limitation of pulse repetition frequency for SAR easily induces the azimuth ambiguity (including Doppler center blur and spectrum ambiguity) of target signals, which causes the difficulty of moving target imaging. In this paper, a new efficient method for imaging and motion parameter estimation of ground moving targets with azimuth ambiguity is presented. Firstly, the time reversal process-2D scaled Fourier transform (TRP-2DSCFT) is developed to eliminate the effects of cross-track velocity and estimate the along-track velocity of target, simultaneously. Secondly, an operation based on discrete polynomial-phase transform and phase compensation function is proposed to estimate the cross-track velocity of target. Finally, a matched filter function based on estimated parameters is constructed to focus the moving targets. The well-focused result can be obtained by the presented method without the residual compensation errors. Moreover, the proposed method is computationally efficient given that the exhaustive searching steps are avoided. Additionally, the azimuth ambiguity can be effectively removed without the ambiguity number searching and pre-processing based on the prior information. The cross-terms for multiple target processing are analyzed. The effectiveness of the method is verified by both spaceborne and airborne real data results.

Efficient coherent detection of maneuvering targets based on location rotation transform and non-uniform fast Fourier transform

Long-term coherent integration can remarkably improve the ability of detection and motion parameter estimation of radar for maneuvering targets. However, the linear range migration, quadratic range migration (QRM), and Doppler frequency migration within the coherent processing interval seriously degrade the detection and estimation performance. Therefore, an efficient and noise-resistant coherent integration method based on location rotation transform (LRT) and non-uniform fast Fourier transform (NuFFT) is proposed. QRM is corrected by the second-order keystone transform. Using the relationship between the rotation angle and Doppler frequency, a novel phase compensation function is constructed. Motion parameters can be rapidly estimated by LRT and NuFFT. Compared with several representative algorithms, the proposed method achieves a nearly ideal detection performance with low computational cost. Finally, experiments based on measured radar data are conducted to verify the proposed algorithm.

Noise-Resistant Estimation Algorithm for TDOA, FDOA and Differential Doppler Rate in Passive Sensing

This paper addresses the joint time difference of arrival (TDOA), frequency difference of arrival (FDOA) and differential Doppler rate estimation problem for high-speed maneuvering targets in passive location systems, involving linear range migration (LRM), quadratic range migration (QRM) and linear Doppler frequency migration (LDFM) within observation time. A noise-resistant estimation algorithm based on second-order keystone transform (SKT) and non-uniform fast Fourier transform (NUFFT) is proposed. After QRM correction via SKT, a phase compensation function is constructed to eliminate LRM and estimate the FDOA. Then, NUFFT is used to remove LDFM and realize the joint estimation of TDOA and differential Doppler rate. Comparisons with several relatively new algorithms indicate that the proposed algorithm can obtain a good trade-off between computational cost and estimation performance. Extensive numerical examples, analysis of computational complexity and estimation performance can validate the effectiveness of the proposed method.

Fringe discretization and manufacturing analysis of a computer-generated hologram in a null test of the freeform surface.

A computer-generated hologram (CGH) is the core component for an aspheric surface test. According to fabrication demands, it is necessary to convert the designed CGH phase compensation function into the processed pattern, that is, the fringe discretization process. In this paper, we propose a new discretization method for a CGH in a test of the freeform surface, and realized the encoding of processed fringes by MATLAB software. Furthermore, we designed the experiment to verify the accuracy of the new discretization method and compared the calculation efficiency between the new algorithm and the reported algorithm. Finally, based on the testing requirement of a freeform mirror in a camera optical system, we completed the design, encoding, and fabrication of the CGH sample, and analyzed the influence of various errors on wavefront accuracy of the CGH.

Joint parameter estimation method for multiple manoeuvring targets with high speed

In this study, a joint parameter estimation method is proposed to realise the long-time coherent integration and estimate the motion parameters for multiple weak manoeuvring targets with high speed and acceleration, involving the first-order range migration (FRM), second-order RM (SRM) and Doppler frequency migration. In the proposed method, the effect of the target's Doppler spectrum spanning over two neighbouring pulse repetition frequency bounds on first-order keystone transform (FKT) is first analysed and a Doppler shifting function is constructed to solve this problem. Then, FKT and the velocity ambiguity factor searching are performed to eliminate the FRM. After that, SRM is removed through the phase compensation function related to acceleration. Finally, the Lv's distribution is applied to realise the coherent integration and obtain the estimates of velocity and acceleration. The numerical experiments using both simulated and real data demonstrate that the proposed method can achieve close detection and estimation performance with much lower computational complexity, compared with the generalised radon-Fourier transform. Moreover, it can estimate the motion parameters of the targets without knowing any prior knowledge of targets and obtain good coherent integration performance in low signal-to-noise ratio scenarios.

Time–frequency method to reduce contamination by ionospheric fast frequency modulation for HF skywave radars

The unstable and time-varying property of the ionosphere causes a frequency modulation on the high frequency sky-wave radar echo signals. When the modulation period is of 10 s or smaller, it is called the fast phase-path modulation. This sort of modulation will result in the broadening, the splitting and even the overlapping of the spectra, which makes target detection and sea-state remote sensing hard. Hence, it is necessary to decontaminate the echo signals before the coherent integration process. In this study, the pseudo Wigner-Ville distribution is proposed as a means of estimating the ionospheric frequency modulation. A frequency weighting method is used to obtain the instantaneous frequency (IF) from the time–frequency distribution and an adaptive low-pass filter is introduced to purify the IF. Then, the amplitude difference between the two first-order Bragg peaks is adopted in the weighting process to obtain the phase compensation function. To improve the compensation effect, an optimising process is proposed. The simulation results show that the method can improve the quality of the spectra for the target detection and remote sensing efficiently even in the cases of a high sea-state.

Experimental study on the role of a resistor in the filter of Hall thrusters

A filter is a mainly component applied to reduce the discharge current low frequency oscillation in the range of 10–100 kHz. The only form of the filter in actual use involves RLC networks, whose design originates from the 1970s, but even now, researchers are unaware of the actual primary motivations for the resistor’s presence [S. Barral et al., AIAA Paper 2008-4632, 2008]. Therefore, the role of the resistor in the filter is experimentally studied and discussed through the analysis of control system and electric circuit theory. Experimental results and analysis indicate that the presence of a resistor makes the filter having the phase compensation function. The proper phase-angle and amplitude provided by the filter would increase or decrease the ion mobility and be helpful to balance the ion production in the discharge channel and then to decrease the fluctuation of the plasma density and lower the low frequency oscillation.

EXTENDED EXACT TRANSFER FUNCTION ALGORITHM FOR BISTATIC SAR OF TRANSLATIONAL INVARIANT CASE

This paper presents an Extended Exact Transfer Function (EETF) algorithm for Bistatic Synthetic Aperture Radar (BiSAR) imaging of a Translational Invariant (TI) case. This algorithm adopts directly the 2D transfer function of monostatic SAR (MoSAR), instead of deriving a new one, by converting the BiSAR into an equivalent MoSAR. A new azimuth phase compensation function is constructed through exploiting this equivalency. Geometry distortion correction for BiSAR imaging result is considered in the proposed algorithm. In addition, the applying condition of the algorithm is also discussed. One desirable property of the proposed algorithm is that the computing ∞ow and e-ciency are the same as ETF algorithm for MoSAR. The efiectiveness is validated by point target simulations with Tandem and forward-looking conflguration.