An Algorithm for Target Parameter Estimation Based on Fractional Fourier and Keystone Transforms

This paper proposes an algorithm for targets detection and parameters estimation, based on intra-pulse Doppler compensation. Firstly, Keystone transform is employed to correct range migration. Then, according to parameters of radar transmitting signal and sample frequency, pulse compression coefficients which can remove the effect of intra-pulse Doppler is produced, and pulse compression is finished with the pulse compression coefficients. Finally, fractional Fourier transform is used to eliminate Doppler spread and integrate energy. This algorithm eliminates the effect of intra-pulse Doppler and guarantees the successes of targets detection and parameters estimation in lower SNR. Computer simulation demonstrates the validity of the proposed algorithm.

This paper analyses the main factors affecting the estimation accuracy of linear frequency modulation (LFM) signal parameters based on fractional Fourier transform (FRFT). By simulation and comparing we can come to the conclusion that the estimation accuracy of initial frequency is improved along with the search interval decreasing while the modulation frequency slope is improved along with the sample points increasing. Based on which we can improve the estimation accuracy of LFM signal parameters according to different cases at the same computational cost. Simulation results verify the correction of the conclusion.

HighlightsWhat are the main findings?This paper presents a high-order phase compensation and parameter estimation algorithm designed for maneuvering targets, which effectively balances detection performance and computational efficiency.The proposed method achieves precise compensation of high-order range migrations without the need for exhaustive parameter search, thereby circumventing the blind speed sidelobe effect. Futhermore, the incorporation of a time-delay variable significantly improves the anti-noise capability of the approach.What is the implication of the main finding?This algorithm introduces a novel motion compensation technique to address the challenges of range migration, Doppler frequency migration, and Doppler ambiguity in detecting weak maneuvering targets. It achieves precise range migration compensation with enhanced accuracy and robustness, forming a vital preprocessing step for high-quality SAR imaging.The algorithm supports simultaneous multi-target processing and holds promising application potential in fields such as airborne radar detection, maritime moving target indication, cooperative observation by UAV formations, and other fields.This study focuses on the key challenges in detecting and estimating motion parameters of ground maneuvering targets for airborne radar sensors. The complex unknown motion states of the ground maneuvering target, including velocity, acceleration, and jerk, result in range migrations (RMs) and Doppler frequency migrations (DFMs). These effects severely degrade the long-time coherent accumulation performance of the airborne radar, thereby limiting the reliable detection and precise parameter estimation of maneuvering targets. To address this issue, a new detection and motion parameter estimation method based on the range frequency reversal transform (RFRT) and searching Lv’s distribution (SLVD), i.e., RFRT-SLVD, is proposed. Specifically, the third-order RM (TRM) and quadratic DFM (QDFM) are considered. The proposed method operates as follows: First, RMs are eliminated simultaneously via the RFRT operation, which multiplies the echo by its reversed data in the range frequency and slow-time domains, leveraging the symmetric equal-interval sampling property of the range frequency. Subsequently, a phase compensation function (PCF) related to the jerk is constructed to compensate the QDFM. Finally, the LVD is performed to remove residual DFMs and achieve effective signal energy accumulation. Additionally, the case of a fast-moving target with Doppler ambiguity is analyzed, and a method for estimating three motion parameters is provided. A key advantage of the proposed technique is its ability to directly compensate the RMs without requiring prior knowledge of the maneuvering target, while also avoiding the blind speed sidelobe (BSSL) effect. In comparison with existing algorithms, RFRT-SLVD achieves a balanced trade-off between parameter estimation performance and computational efficiency. Numerical analyses and experiments are conducted to validate the method, assessing its detection capability for ground maneuvering targets, Doppler ambiguity resolution in parameter estimation, computational complexity, and method applicability in multi-target scenarios.

According to frequency-modulated continuous-wave synthetic-aperture radar, we establish the signal model of a moving target and propose an algorithm for target parameters estimation and imaging. The key procedures of moving target imaging include velocities estimation and range migration correction. Compared with conventional methods, the effect introduced from the along-track velocity is taken into account during the range migration correction to improve the correction accuracy. Moreover, fractional Fourier transform is adopted to estimate the Doppler parameters. To summarize, the proposed method has three advantages. First, by carrying out rough and precise estimation separately, both accurate velocity estimation and better robustness are obtained. Second, this method is available for moving targets with Doppler ambiguity. Third, the third-order phase error derived from moving target is taken into account to improve the azimuth compression result. Finally, a complete flowchart of the proposed method is presented and is verified by both simulation and real data.

Multi-buoy sonar systems achieve target localization by receiving broadband Linear Frequency Modulation signals emitted from the transmitter. Accurate estimations of the parameters of Linear Frequency Modulation signals significantly enhance the localization accuracy. Linear Frequency Modulation signals can be focused into the fractional domain through Fractional Fourier Transform, but this increases the computational complexity. In marine environments, the low signal-to-noise ratio and multipath effects degrade the parameter estimation accuracy further. To address these issues, this paper proposes a fast estimation algorithm based on the Fractional Fourier Transform and a Gradient Subtraction-Average-Based Optimizer. This algorithm leverages the impulsive characteristics of Linear Frequency Modulation signals after Fractional Fourier Transform transformation, using the Fractional Fourier Transform as the fitness function. The Gradient Subtraction-Average-Based Optimizer algorithm includes three enhancement strategies: chaotic mapping initialization, a Golden Sine Algorithm, and an adaptive t-distribution variational operator. The simulation results demonstrate that the Gradient Subtraction-Average-Based Optimizer algorithm improves the issues of low diversity in the search agents, imbalanced global and local search capabilities, and susceptibility to local optima. A comparative analysis and statistical testing confirm that under a low signal-to-noise ratio and multipath effect conditions, the Gradient Subtraction-Average-Based Optimizer algorithm not only ensures real-time parameter estimation but also improves the estimation accuracy. The results of the parameter estimation provide reliable data support for subsequent target localization.

Conventionally, a single-channel synthetic aperture radar (SC-SAR) system can hardly detect weak moving targets simply. In this paper, a time-Doppler chirp-varying (TDCV) filter is proposed for ground moving target indication and parameter estimation with the airborne SC-SAR system. The proposed method is easy to implement and mainly includes three steps. First, a traditional 2-D frequency range-Doppler algorithm is used to generate an original image. Second, the second-order range cell migration (RCM) phase term is partly compensated in the range frequency and azimuth time domain, and the rest of second-order RCM phase term is compensated in 2-D frequency domain. The whole processing, which is referred to as the TDCV approach, is employed to acquire a new TDCV image. Third, compared the original image with the new image, the clutter scatterers are nearly motionless while the moving targets are translated along the range direction due to their nonzero radial velocities. After the cancellation between two normalized images, the clutter background would be significantly suppressed since the two images generated by the same data. As a result, the moving targets can be indicated and the range difference of the moving target between two images can be exploited to estimate their radial velocities. The results obtained by applying the proposed method into a set of real SAR data are consistent with the analysis presented in this paper.

This study presents a comparative analysis of various optimization algorithms—Differential Evolution (DE), Particle Swarm Optimization (PSO), Arithmetic Optimization Algorithm (AOA), and Hippopotamus Optimization Algorithm (HOA)—for parameter identification in photovoltaic (PV) models. By utilizing RTC France solar cell data, we demonstrate that accurate parameter estimation is crucial for enhancing the efficiency of PV systems, ultimately supporting sustainable energy solutions. Our results indicate that DE achieves the lowest root mean square error (RMSE) of 0.0001 for the double-diode model (DDM), outperforming other methods in terms of accuracy and convergence speed. Both the HOA and PSO also show competitive RMSE values, underscoring their effectiveness in optimizing parameters for PV models. This research not only contributes to improved PV model precision but also aids in the broader effort to advance renewable energy technologies, thereby fostering a more sustainable future.

Data-driven adaptive chirp mode decomposition with application to machine fault diagnosis under non-stationary conditions

With the use of batteries increases, the complexity of battery management systems (BMSs) also rises. Thus, assessing the functionality of BMSs and performance of the BMS hardware is of utmost importance. Testing with embedded boards at an early stage of BMS development is a pragmatic approach for developing a BMS because it is cost- and time-efficient and considers hardware performance. In this study, we tested and analyzed the real-time state-of-charge (SOC) estimation using a test platform with limited CPU performance as well as memory resources of the embedded board. We collected battery data on a single-cell basis using a first-order RC equivalent circuit and achieved an accuracy of 95% compared to the measured data obtained using actual battery tests. The SOC estimation method applies the extended Kalman filter (EKF) and unscented Kalman filter (UKF). The experiment was performed on the real-time test platform, with 1%, 2%, and 5% noise in the measurement data. The algorithm complexity and hardware implementation were evaluated in terms of the resources used and processing speed. Although the EKF is cost-effective, its error rate increases by 5% with noise interference. The UKF exhibits high accuracy and noise robustness; however, it has a high resource occupancy.

Narrowband and wideband waveforms are usually adopted simultaneously during the observation of micro-motion space targets by inverse synthetic aperture radar (ISAR), which can collect rich multimodal information in the time-Doppler, time-range, and range-instantaneous-Doppler domains. In order to exploit the electromagnetic scattering, shape, structure, and motion characteristics, this article proposes an attention-augmented cross-modal feature fusion recognition network, namely ACM-FR Net. Firstly, the ACM-FR Net adopts convolution neural network (CNN) to extract initial feature vectors from joint time-frequency (JTF) image, high resolution range profiles (HRRPs), and range-instantaneous-Doppler (RID) image, respectively. Then, it transforms the feature vectors of the three modalities into feature sequences. Finally, it achieves interactive feature fusion by implementing attention-augmented cross-modal feature fusion. In the four-category micro-motion space targets recognition experiments, the proposed ACM-FR Net has demonstrated high accuracy and noise robustness.

Noise-robust color edge detector using gradient matrix and anisotropic Gaussian directional derivative matrix

The application of the fractional Fourier transform (FrFT) for the formation and analysis of acoustic holograms created by a moving linear frequency-modulated (LFM) source in a shallow-water waveguide is considered. A holographic method is proposed for constructing an interferogram of the LFM signal of a source and converting it into a Fourier hologram based on FrFT in conditions of high noise. The holographic method based on FrFT ensures the formation of localized focal areas arising from mode interference, even with high-intensity noise interference. The effectiveness of the holographic method based on FrFT is analyzed using numerical experiments in the frequency range of 100-150 Hz. The results demonstrate the high noise immunity of the method for locating the source in realistic shallow water conditions with high noise.

Power allocation and measurement matrix design for block CS-based distributed MIMO radars

ABSTRACTThe problem of estimating the direction of arrival (DoA) of multiple far-field moving targets, producing broad-banded chirp signals, in both active and passive mode of operation is addressed. As the chirp signal, commonly used in both radar and sonar systems is better processed in fractional Fourier domain, the detection is done using fractional Fourier transform (FrFT) in the proposed work. Subsequently, the DoA estimation is achieved using both conventional and subspace methods. Even though FrFT beam-forming method has been studied in the past, its performance in respect of varying signal-to-noise ratios (SNRs) and multiple target detection has not been extensively analyzed yet. The results of simulation experiments reported in the present work show that FrFT enjoys better estimation accuracy over the conventional frequency domain beam-forming for chirp signals using Fourier transform (FT), in terms of computational efficiency, accuracy and resolution with low SNR, limited snapshots and sensors, and spatially coherent/multi-path signals. The performance metrics used for the study are (i) root mean square error, (ii) 3-dB beam width and (iii) CPU time for accuracy, resolution and computation time, respectively. It is seen from computer simulations that MUSIC outperforms other DoA estimation techniques from the performance curves for both active and passive systems.

Inverse synthetic aperture radar (ISAR) imaging is one of the important high- resolution radar applications for moving target detection and identification. The radial velocity, radial acceleration, and acceleration rate of maneuvering targets can cause range cell migration and Doppler variation in the received signals, which will degrade the imaging quality. Therefore, these parameters should be estimated and compensated before imaging. In low signal-to-noise ratio (SNR) conditions, the conventional motion parameter estimation and compensation algorithms for maneuvering targets do not work properly. To effectively detect and identify the maneuvering targets in low SNR conditions, a new radar imaging algorithm is proposed. The major contributions are as follows: 1) a novel algorithm for envelope migration correction is proposed with adjacent cross correlation function; 2) the target's motion parameters are estimated with the operations of Keystone transform and time-frequency transform to the adjacent cross correlation; 3) a theoretical analysis of the impact of motion parameters on the envelope migration is made, then cross-range phase estimation with the adjacent cross function is presented; 4) based on the estimated motion parameters of targets, a new algorithm for high-resolution ISAR imaging is developed.