The spaceborne inverse synthetic aperture radar (ISAR) has attracted significant attention due to its extensive observation range and imaging performance. However, the complex motion between spaceborne platform and the air target leads to complex signal modulation. The scattering anisotropy and occlusion lead to the scattering points missing problem. These problems pose a serious challenge to the traditional ISAR imaging algorithms. Aiming at the above problems, this paper proposes a joint intra-frame and inter-frame imaging algorithm based on spaceborne ISAR. In this algorithm, we divide the long coherent processing interval into several sub-apertures using the narrow-band tracking data, and each-order terms of the signal within sub-aperture is derived in detail. Then, the intra-frame algorithm based on the parametric minimized image entropy search is proposed to correct the spatial-variant phase errors caused by the complex relative motion. As to the well-focused images from different views and the rotation parameters obtained in sub-apertures, the inter-frame algorithm based on wavelet transform can perform image registration and image fusion to obtain more detailed target feature information and more complete target structure. In simulated and real-measured data experiments, the effectiveness and superiority of the proposed algorithm are validated.
The paper presents a full-exchange streaming adaptive processor architecture with nested parallel sampling covariance matrix estimation and adaptive weight computation, to achieve polarization-space-time adaptive processing (P-STAP), adaptive digital beamforming (ADBF) and multiple side-lobe canceller (MSLC) within a configurable computational framework. An effective method for real-time numerical calculation is proposed by reducing truncation errors, ensuring robust convergence, and low time complexity through the lower-diagnoal-lower transpose (LDLT) right multiplication iterative (LDLT-RMI) method. To fully implement P-STAP for high-intensity interference clutter adaptive robust suppression, a series of intellectual property (IP) cores are designed for high-order, high-condition symmetric positive definite matrix inversion. The adaptive processor can operate on a frame-structured data flow, accommodating various space-time-frequency-polarization multi-domain combinations, which supports 8 to 100 channels with a dynamic range of up to 80 dB. Even the interferences reach a high intensity of 65 dB, the adaptive processor can still work stably.
In this paper, we propose evaluation approaches for the spatial target localization precision based on the observation matrix conditional number. Three evaluation approaches for the spatial target localization precision are derived including relative condition numbers, absolute condition numbers, and volume condition numbers by properties of vectors and matrix norms. The theoretical analysis shows that the proposed methods are the upper certainty bound of the magnification of measurement error. Meanwhile, the proposed methods are able to account for variations of localization accuracy by exploiting geometric variations in the composition between the target and measurement stations. Finally, the proposed methods perform better, compared with the traditional evaluation methods. This is of great significance for the accuracy evaluation of high-precision measuring equipment, optimization of workstation layout and geometric configuration. Simulation experiments corroborate the effectiveness of the proposed methods.
In environments with complex electromagnetic characteristics, signals from active repeater mainlobe deception jamming are closely aligned with radar emissions, significantly impairing radar functionality. This paper explores the efficacy of frequency diverse array (FDA) radar in combating active mainlobe jamming. Initially, the signal model for FDA multi-input multi-output (FDA-MIMO) radar is introduced. Building on this, a frequency offset optimization approach for FDA radar using the differential artificial bee colony (DEABC) algorithm is developed. Following this, the steepest descent linear minimum variance distortionless response beamforming algorithm is implemented in an FDA early warning radar to mitigate mainlobe jamming. Simulations are conducted to validate the effectiveness of the proposed strategies. The results from these simulations demonstrate that the methodologies can create a focused beam aimed at the target while effectively neutralizing jamming signals within the mainlobe area.
This paper proposes a space target attitude estimation method with inverse synthetic aperture radar (ISAR) images to address the challenges of difficult feature extraction, low estimation accuracy, and inefficiency in the attitude estimation of space targets. This method relies on ISAR contour projection plane alignment. Unlike traditional contour matching methods, this approach introduces an image plane alignment algorithm for different radar lines of sight (LOS). The algorithm aligns image planes from various frames, defined by their corresponding LOS and rotation axis, with those of a reference template library. This alignment resolves attitude mismatches during template matching caused by differences in image planes. The attitude estimation method first uses the Hausdorff distance as the contour matching criterion to enhance matching speed. Second, the contour projection plane alignment algorithm outputs the actual attitude for each frame. Third, the multi-solution attitude problem is addressed by combining the actual attitudes of each frame using the minimum distance method. Finally, an optimization algorithm is employed to improve estimation accuracy. This method demonstrates higher accuracy and efficiency compared to traditional approaches in scatter point imaging and electromagnetic simulation experiments.
Multichannel signals have the characteristics of information diversity and information consistency. To better explore and utilize the affinity relationship within multichannel signals, a new graph learning technique based on low rank tensor approximation is proposed for multichannel monitoring signal processing and utilization. Firstly, the affinity relationship of multichannel signals can be acquired based on the clustering results of each channel signal. Wherein an affinity tensor is constructed to integrate the diverse and consistent information of the clustering information among multichannel signals. Secondly, a low-rank tensor optimization model is built and the joint affinity matrix is optimized with the assistance of the strong confidence affinity matrix. Through solving the optimization model, the fused affinity relationship graph of multichannel signals can be obtained. Finally, the multichannel fused clustering results can be acquired though the updated joint affinity relationship graph. The multichannel signal utilization examples in health state assessment with public datasets and microwave detection with actual echoes verify the advantages and effectiveness of the proposed method.
Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar has gained considerable research attention due to its ability to effectively counter active repeater deception jamming in complex electromagnetic environments. The effectiveness of interference suppression by FDA-MIMO is limited by the inherent range-angle coupling issue in the FDA beampattern. Existing literature primarily focuses on control methods for FDA-MIMO radar beam direction under the assumption of static beampatterns, with insufficient exploration of techniques for managing nonstationary beam directions. To address this gap, this paper initially introduces the FDA-MIMO signal model and the calculation formula for the FDA-MIMO array output using the minimum variance distortionless response (MVDR) beamformer. Building on this, the problem of determining the optimal frequency offset for the FDA is rephrased as a convex optimization problem, which is then resolved using the cuckoo search (CS) algorithm. Simulations confirm the effectiveness of the proposed approach, showing that the frequency offsets obtained through the CS algorithm can create a dot-shaped beam direction at the target location while effectively suppressing interference signals within the mainlobe.
To address the issue of incorrect fusion results caused by conflicting evidence due to inaccurate evidence and incomplete recognition frameworks in radar airborne target tactical intention recognition, a spatiotemporal evidence fusion algorithm is proposed. To resolve the conflict evidence fusion problem caused by inaccurate evidence, the algorithm performs discounting of evidence from both spatial and temporal dimensions. Spatial discounting is influenced by both inter-evidence inconsistency and intra-evidence inconsistency, while temporal discounting is determined by time intervals and information entropy. For the problem of conflicting evidence fusion due to an incomplete recognition framework, an open recognition architecture based on dynamic composite focal elements is proposed. This approach allocates some conflicting information to temporary composite focal elements, avoiding excessive basic probability assignment (BPA) of the empty set after fusion, which can lead to deviations from the actual fusion results. Simulation experiments comparing various methods indicate that the proposed method can effectively improve target intention recognition accuracy and demonstrates good stability.
Despite the superior advantages of specific emitter identification in extracting emitter features from in-phase and quadrature (I/Q) signals, challenges persist due to signal-type confusion and background noise interference. To address those limitations, this paper proposes a multi-channel contrast prediction coding and complex-valued residuals network (MCPC-MCVResNet) framework. This model employs contrast prediction techniques to directly extract discriminative features from electromagnetic signal sequences, effectively capturing both amplitude and phase information within I/Q data. A core innovation of this approach is the sphere space softmax (SS-softmax) loss, which optimizes intra-class clustering density of while establishing well-defined boundaries between distinct emitters. The SS-softmax mechanism significantly enhances the model’s capacity to discern subtle variations among radiation emitters. Experimental results demonstrate superior identification accuracy, rapid convergence, and exceptional robustness in low signal-to-noise ratio environments.
This paper addresses weak target detection problem for bistatic radar via a pseudo-spectrum (PS) based track-before- detect (TBD). Generally, PS-TBD estimates target position and velocity by means of pseudo-spectrum construction in the discrete measurement space and accurate energy accumulation in mixed coordinates. However, the grids within the polar sensing region of the receivers in the bistatic radar are not aligned. Traditional PS-TBD can not directly process these measurements. In this paper, a PS-TBD method for bistatic radar is proposed to overcome this problem. Each cell in the measurement space of the receivers is mapped to the aligned Cartesian coordinates and predicted to the integration frame according to the assumed filter velocity. A PS is formulated centered on the predicted Cartesian position. Then the samples of the pseudo-spectra are accumulated to the nearest cell around the predicted Cartesian position. The procedure of the energy integration is derived in detail. Simulation results validate the efficacy of the proposed method in terms of detection accuracy and parameter estimation.
Exact estimation of space object attitude parameters is a great challenge. The effectiveness of conventional attitude estimation approaches based on target sizes suffers a significant reduction when occlusion exists. This paper proposes an innovative approach to estimate the attitude parameters for space objects based on inverse synthetic aperture radar (ISAR) image sequences. The formulation for nonlinear size constraints (NSC) is developed by accounting for the characteristics of object size variation in ISAR image sequences. The multi-start framework for global optimization and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) based quasi-Newton iterative method are combined with and used for more accurate estimation of space object’s attitude parameters. Furthermore, the Cramer-Rao lower bound (CRLB) of attitude parameter estimates is derived. Comparative experiments demonstrate the effectiveness and robustness of the proposed method.
In the traditional radar unmanned aerial vehicle (UAV) detection process, coherent integration and micro-Doppler (m-D) parameter estimation are carried out separately. The target discrimination process needs to obtain the position information of the target, which will lose energy. In this paper, a long time integration method of radar signal based on rotating target radon Fourier transform (RTRFT) is proposed. This method modifies the distance and frequency terms in the traditional generalized radon Fourier transform (GRFT), and adds the frequency sinusoidal modulation term. Then, based on the cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter, the position of the target is detected in the high-dimensional space obtained by RTRFT. This method can combine coherent integration and micro-motion parameter estimation. Simulation experiments show that the proposed method can estimate the main translational parameters and rotational micro-motion parameters of the target while detecting the target, and the target detection performance is improved.
Electronic reconnaissance units commonly utilize an interferometer direction-finding system to measure the incoming direction of radar radiation signals. This approach enables the accurate determination of threat source locations, which is essential for devising route plans oriented toward flight path generation. When a frequency diverse array (FDA) system is adopted by ground radars, errors are introduced into the angle measurements of the passive direction finding system. To address this issue, this study starts with FDA model establishment and equiphasic surface characteristics analysis and analyzes the principles of FDA deception in identifying one-dimensional single-baseline interferometer directions. Additionally, the Cramer-Rao bounds of the signal carrier frequency estimation error and angle measurement error during the interferometer’s direction finding process are considered. The simulation results verify that the one-dimensional single-baseline interferometer direction finding system can be deceived by the FDA radar, and the FDA with a sine frequency offset exhibits the optimum deception effect.
Jamming suppression is traditionally achieved through the use of spatial filters based on array signal processing theory. In order to achieve better jamming suppression performance, many studies have applied blind source separation (BSS) to jamming suppression. BSS can achieve the separation and extraction of the individual source signals from the mixed signal received by the array. This paper proposes a perspective to recognize BSS as spatial band-pass filters (SBPFs) for jamming suppression applications. The theoretical derivation indicates that the processing of mixed signals by BSS can be perceived as the application of a set of SBPFs that gate the source signals at various angles. Simulations are performed using radar jamming suppression as an example. The simulation results suggest that BSS and SBPFs produce approximately the same effects. Simulation results are consistent with theoretical derivation results.
Accurate modeling and parameter estimation of sea clutter are fundamental for effective sea surface target detection. With the improvement of radar resolution, sea clutter exhibits a pronounced heavy-tailed characteristic, rendering traditional distribution models and parameter estimation methods less effective. To address this, this paper proposes a dual compound-Gaussian model with inverse Gaussian texture (CG-IG) distribution model and combines it with an improved Adam algorithm to introduce a method for parameter correction. This method effectively fits sea clutter with heavy-tailed characteristics. Experiments with real measured sea clutter data show that the dual CG-IG distribution model, after parameter correction, accurately describes the heavy-tailed phenomenon in sea clutter amplitude distribution, and the overall mean square error of the distribution is reduced.
In wideband noncooperative interference cancellation, the reference signals obtained through auxiliary antennas are weighted to cancel with the interference signal. The correlation between the reference signal and the interference signal determines interference cancellation performance, while the auxiliary antenna array affects the correlation by influencing the amplitude and phase of the reference signals. This paper analyzes the effect of auxiliary antenna array on multiple performances of wideband noncooperative interference cancellation. Firstly, the array received signal model of wideband interference is established, and the weight vector coupled with the auxiliary antennas array manifold is solved by spectral analysis and eigen-subspace decomposition. Then, multiple performances which include cancellation resolution, grating null, wideband interference cancellation ratio (ICR), and convergence rate are quantitatively characterized with the auxiliary antenna array. It is obtained through analysis that the performances mutually restrict the auxiliary antenna array. Higher cancellation resolution requires larger array aperture, but when the number of auxiliary antennas is fixed, larger array aperture results in more grating nulls. When the auxiliary antennas are closer to the main antenna, the wideband ICR is improved, but the convergence rate is reduced. The conclusions are verified through simulation of one-dimensional uniform array and two-dimensional nonuniform array. The experiments of three arrays are compared, and the results conform well with simulation and support the theoretical analysis.
In this paper, we propose an improved YOLOv5-based object detection method for radar images, which have the characteristics of diffuse weak noise and imaging distortion. To mitigate the effects of noise without losing spatial information, an coordinate attention (CA) has been added to pre-extract the feature of the images, which can guarantee a better feature extraction ability. A new stochastic weighted average (SWA) method is designed to refine generalization ability of the algorithm, where the medium mean is used instead of their average value. By introducing an deformable convolution, both regular and irregular images can be proceeded. The experimental results show that the improved algorithm performs better in object detection of radar images compared with the YOLOv5 model, which confirms the effectiveness and feasibility of our model.
Nonperiodic interrupted sampling repeater jamming (ISRJ) against inverse synthetic aperture radar (ISAR) can obtain two-dimensional blanket jamming performance by joint fast and slow time domain interrupted modulation, which is obviously different from the conventional multi-false-target deception jamming. In this paper, a suppression method against this kind of novel jamming is proposed based on inter-pulse energy function and compressed sensing theory. By utilizing the discontinuous property of the jamming in slow time domain, the unjammed pulse is separated using the intra-pulse energy function difference. Based on this, the two-dimensional orthogonal matching pursuit (2D-OMP) algorithm is proposed. Further, it is proposed to reconstruct the ISAR image with the obtained unjammed pulse sequence. The validity of the proposed method is demonstrated via the Yake-42 plane data simulations.
The multifunctional integration system (MFIS) is based on a common hardware platform that controls and regulates the system’s configurable parameters through software to meet different operational requirements. Dwell scheduling is a key for the system to realize multifunction and maximize the resource utilization. In this paper, an adaptive dwell scheduling optimization model for MFIS which considers the aperture partition and joint radar communication (JRC) waveform is established. To solve the formulated optimization problem, JRC scheduling conditions are proposed, including time overlapping condition, beam direction condition and aperture condition. Meanwhile, an effective mechanism to dynamically occupy and release the aperture resource is introduced, where the time-pointer will slide to the earliest ending time of all currently scheduled tasks so that the occupied aperture resource can be released timely. Based on them, an adaptive dwell scheduling algorithm for MFIS with aperture partition and JRC waveform is put forward. Simulation results demonstrate that the proposed algorithm has better comprehensive scheduling performance than up-to-date algorithms in all considered metrics.
Low sidelobe waveform can reduce mutual masking between targets and increase the detection probability of weak targets. A low sidelobe waveform design method based on complementary amplitude coding (CAC) is proposed in this paper, which can be used to reduce the sidelobe level of multiple waveforms. First, the CAC model is constructed. Then, the waveform design problem is transformed into a nonlinear optimization problem by constructing an objective function using the two indicators of peak-to-sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR). Finally, genetic algorithm (GA) is used to solve the optimization problem to get the best CAC waveforms. Simulations and experiments are conducted to verify the effectiveness of the proposed method.
Most of the existing non-line-of-sight (NLOS) localization methods depend on the layout information of the scene which is difficult to be obtained in advance in the practical application scenarios. To solve the problem, an NLOS target localization method in unknown L-shaped corridor based ultra-wideband (UWB) multiple-input multiple-output (MIMO) radar is proposed in this paper. Firstly, the multipath propagation model of L-shaped corridor is established. Then, the localization process is analyzed by the propagation characteristics of diffraction and reflection. Specifically, two different back-projection imaging processes are performed on the radar echo, and the positions of focus regions in the two images are extracted to generate candidate targets. Furthermore, the distances of propagation paths corresponding to each candidate target are calculated, and then the similarity between each candidate target and the target is evaluated by employing two matching factors. The locations of the targets and the width of the corridor are determined based on the matching rules. Finally, two experiments are carried out to demonstrate that the method can effectively obtain the target positions and unknown scene information even when partial paths are lost.
To enhance direction of arrival (DOA) estimation accuracy, this paper proposes a low-cost method for calibrating far-field steering vectors of large aperture millimeter wave radar (mmWR). To this end, we first derive the steering vectors with amplitude and phase errors, assuming that mmWR works in the time-sharing mode. Then, approximate relationship between the near-field calibration steering vector and the far-field calibration steering vector is analyzed, which is used to accomplish the mapping between the two of them. Finally, simulation results verify that the proposed method can effectively improve the angle measurement accuracy of mmWR with existing amplitude and phase errors.
Accurate target angle estimation is one of the challenges for wideband radars due to the fact that target occupies multiple range bins, resulting in lower energy or signal to noise ratio in a single range bin. This paper proposes a processing technique for enhanced accuracy of target angle estimates for wideband monopulse radars. Firstly, to accumulate the energy of the received echo signals from different scatterers on a target, the phase difference between different scatterers on a target is estimated using the minimum entropy phase estimation method combining with the correlation between adjacent pulses. Then, the monopulse ratio is obtained by using the signals from the accumulated sum and difference channels. The target angle is estimated by weighting the accumulated echo energy for accuracy enhancement. Experimental results based on both numerical simulation and measured data are presented to validate the effectiveness of the proposed technique.
For target tracking and localization in bearing-only sensor network, it is an essential and significant challenge to solve the problem of plug-and-play expansion while stably enhancing the accuracy of state estimation. This paper proposes a distributed state estimation method based on two-layer factor graph. Firstly, the measurement model of the bearing-only sensor network is constructed, and by investigating the observability and the Cramer-Rao lower bound of the system model, the preconditions are analyzed. Subsequently, the location factor graph and cubature information filtering algorithm of sensor node pairs are proposed for localized estimation. Building upon this foundation, the mechanism for propagating confidence messages within the fusion factor graph is designed, and is extended to the entire sensor network to achieve global state estimation. Finally, groups of simulation experiments are conducted to compare and analyze the results, which verifies the rationality, effectiveness, and superiority of the proposed method.
Automatically recognizing radar emitters from complex electromagnetic environments is important but non-trivial. Moreover, the changing electromagnetic environment results in inconsistent signal distribution in the real world, which makes the existing approaches perform poorly for recognition tasks in different scenes. In this paper, we propose a domain generalization framework is proposed to improve the adaptability of radar emitter signal recognition in changing environments. Specifically, we propose an end-to-end denoising based domain-invariant radar emitter recognition network (DDIRNet) consisting of a denoising model and a domain invariant representation learning model (IRLM), which mutually benefit from each other. For the signal denoising model, a loss function is proposed to match the feature of the radar signals and guarantee the effectiveness of the model. For the domain invariant representation learning model, contrastive learning is introduced to learn the cross-domain feature by aligning the source and unseen domain distribution. Moreover, we design a data augmentation method that improves the diversity of signal data for training. Extensive experiments on classification have shown that DDIRNet achieves up to 6.4% improvement compared with the state-of-the-art radar emitter recognition methods. The proposed method provides a promising direction to solve the radar emitter signal recognition problem.
Ground penetrating radar (GPR), as a fast, efficient, and non-destructive detection device, holds great potential for the detection of shallow subsurface environments, such as urban road subsurface monitoring. However, the interpretation of GPR echo images often relies on manual recognition by experienced engineers. In order to address the automatic interpretation of cavity targets in GPR echo images, a recognition-algorithm based on Gaussian mixed model-hidden Markov model (GMM-HMM) is proposed, which can recognize three dimensional (3D) underground voids automatically. First, energy detection on the echo images is performed, whereby the data is pre-processed and pre-filtered. Then, edge histogram descriptor (EHD), histogram of oriented gradient (HOG), and Log-Gabor filters are used to extract features from the images. The traditional method can only be applied to 2D images and pre-processing is required for C-scan images. Finally, the aggregated features are fed into the GMM-HMM for classification and compared with two other methods, long short-term memory (LSTM) and gate recurrent unit (GRU). By testing on a simulated dataset, an accuracy rate of 90% is obtained, demonstrating the effectiveness and efficiency of our proposed method.
Implementing an efficient real-time prognostics and health management (PHM) framework improves safety and reduces maintenance costs in complex engineering systems. However, research on PHM framework development for radar systems is limited. Furthermore, typical PHM approaches are centralized, do not scale well, and are challenging to implement. This paper proposes an integrated PHM framework for radar systems based on system structural decomposition to enhance reliability and support maintenance actions. The complexity challenge associated with implementing PHM at the system level is addressed by dividing the radar system into subsystems. Subsequently, optimal measurement point selection and sensor placement algorithms are formulated for effective data acquisition. Local modules are developed for each subsystem health assessment, fault diagnosis, and fault prediction without a centralized controller. Maintenance decisions are based on each local module’s fault diagnosis and prediction results. To further improve the effectiveness of the prognostics stage, the feasibility of integrating deep learning (DL) models is also investigated. Several experiments with different degradation patterns are performed to evaluate the effectiveness of the framework’s DL-based prognostics model. The proposed framework facilitates transitioning from traditional reactive maintenance practices to a predictive maintenance approach, thereby reducing downtime and improving the overall availability of radar systems.
This paper considers the problem of sea clutter suppression. We propose the cuttable encoder-decoder-augmentation network (CEDAN) to improve clutter suppression performance by enriching the contrast information between the target and clutter. Specifically, the plug-and-play residual U-block (ResUblock) is proposed to augment the feature representation ability of the clutter suppression model. The CEDAN first extracts and fuses the multi-scale features using the encoder and the decoder composed of the ResUblocks. Then, the fused features are processed by the contrast information augmentation module (CIAM) to enhance the diversity of target and clutter, resulting in encouraging sea clutter suppression results. In addition, we propose the result-consistency loss to further improve the suppression performance. The result-consistency loss enables CEDAN to cut some blocks of decoder and CIAM to reduce the inference time without significantly degrading the suppression performance. Experimental results on measured and simulated data show that the CEDAN outperforms state-of-the-art sea clutter suppression methods in sea clutter suppression performance and computation efficiency.
Separation and recognition of radar signals is the key function of modern radar reconnaissance, which is of great significance for electronic countermeasures and anti-countermeasures. In order to improve the ability of separating mixed signals in complex electromagnetic environment, a blind source separation algorithm based on degree of cyclostationarity (DCS) criterion is constructed in this paper. Firstly, the DCS criterion is constructed by using the cyclic spectrum theory. Then the algorithm flow of blind source separation is designed based on DCS criterion. At the same time, Givens matrix is constructed to make the blind source separation algorithm suitable for multiple signals with different cyclostationary frequencies. The feasibility of this method is further proved. The theoretical and simulation results show that the algorithm can effectively separate and recognize common multi-radar signals.
There is a growing body of research on the swarm unmanned aerial vehicle (UAV) in recent years, which has the characteristics of small, low speed, and low height as radar target. To confront the swarm UAV, the design of anti-UAV radar system based on multiple input multiple output (MIMO) is put forward, which can elevate the performance of resolution, angle accuracy, high data rate, and tracking flexibility for swarm UAV detection. Target resolution and detection are the core problem in detecting the swarm UAV. The distinct advantage of MIMO system in angular accuracy measurement is demonstrated by comparing MIMO radar with phased array radar. Since MIMO radar has better performance in resolution, swarm UAV detection still has difficulty in target detection. This paper proposes a multi-mode data fusion algorithm based on deep neural networks to improve the detection effect. Subsequently, signal processing and data processing based on the detection fusion algorithm above are designed, forming a high resolution detection loop. Several simulations are designed to illustrate the feasibility of the designed system and the proposed algorithm.
