Long-time Coherent Integration Research Articles

Long-Time Coherent Integration for the Spatial-Based Bistatic Radar Based on Dual-Scale Decomposition and Conditioned CPF

This paper addresses the problem of weak maneuvering target detection in the space-based bistatic radar system through long-time coherent integration (LTCI). The space-based bistatic radar is vulnerable to the high-order range migration (RM) and Doppler frequency migration (DFM), since the target, the receiver and the transmitter all can play fast movement independently. To correct high- order RM and DFM, this usually involves joint high-dimensional parameter searching, incurring a large computational burden. In our previous work, a dual-scale (DS) decomposition of motion parameters was proposed, in which the optimal GRFT is conditionally decoupled into two cascade procedures called the modified generalized inverse Fourier transform (GIFT) and generalized Fourier transform (GFT), resulting in the DS-GRFT detector. However, even if the DS-GRFT detector preserves the superior performance and dramatically decreases the complexity, high-dimensional searching is still required. In this paper, by analyzing the structure of the DS-GRFT detector, we further designed a conditioned cubic phase function (CCPF) tailored to the range–slow-time signal after GIFT, breaking the joint high-dimensional searching into independent one-dimensional searching. Then, by connecting the proposed CCPF with the GIFT, we achieved a new LTCI detector called the DS-GIFT-CCPF detector, which obtained a significant computational cost reduction with acceptable performance loss, as demonstrated in numerical experiments.

Long-Time Coherent Integration Based on Reconstructed Spectrum for Weak Target Detection Using Pulse-Doppler Radar

Long-Time Coherent Integration Based on Reconstructed Spectrum for Weak Target Detection Using Pulse-Doppler Radar

Efficient Long-Time Coherent Integration and Detection Algorithm for Radar High-Speed Target Based on the Azimuth Resampling Technology

Efficient Long-Time Coherent Integration and Detection Algorithm for Radar High-Speed Target Based on the Azimuth Resampling Technology

Weak and High Maneuvering UAV Detection via Long-time Coherent Integration based on KT-BCS-LSM Method

Weak and High Maneuvering UAV Detection via Long-time Coherent Integration based on KT-BCS-LSM Method

Long-time adaptive coherent detection of small targets in sea clutter by fast inversion algorithm of block tridiagonal speckle covariance matrices

Low-velocity small target detection in maritime surveillance radars is always a challenging task. Low signal-to-clutter ratio requires long-time coherent integration to obtain enough gain of target returns. However, long-time coherent integration encounters insufficient secondary data due to the spatial inhomogeneity of sea clutter. In this paper, considering the decorrelation time of speckle component of sea clutter short up to a dozen of milliseconds, the spherical invariant random vector (SIRV) model with block tridiagonal speckle covariance matrix and the inverse Gamma distributed texture is proposed to model sea clutter sequences in several tenths of a second. In this model, a long-time adaptive generalized likelihood ratio test with linear threshold detector (GLRT-LTD) is constructed. Owing to the block tridiagonal structure of speckle covariance matrices, the adaptive detection requires much less reference cells for speckle covariance matrix estimation and much lower computational cost for its inversion. The proposed detector is verified by an X-band high-resolution island-based radar data with an unmanned aerial vehicle (UAV) as test target. The experimental result shows that it obtains competitive detection performance in comparison with the state-of-the-art detectors.

Radar fast long-time coherent integration via TR-SKT and robust sparse FRFT

Long-time coherent integration (LTCI) is an effective way for radar maneuvering target detection, but it faces the problem of a large number of search parameters and large amount of calculation. Realizing the simultaneous compensation of the range and Doppler migrations in complex clutter background, and at the same time improving the calculation efficiency has become an urgent problem to be solved. The sparse transformation theory is introduced to LTCI in this paper, and a non-parametric searching sparse LTCI (SLTCI) based maneuvering target detection method is proposed. This method performs time reversal (TR) and second-order Keystone transform (SKT) in the range frequency & slow-time data to complete high-order range walk compensation, and achieves the coherent integration of maneuvering target across range and Doppler units via the robust sparse fractional Fourier transform (RSFRFT). It can compensate for the nonlinear range migration caused by highorder motion. S-band and X-band radar data measured in sea clutter background are used to verify the detection performance of the proposed method, which can achieve better detection performance of maneuvering targets with less computational burden compared with several popular integration methods.

Long-Time Coherent Integration for Marine Targets Based on Segmented Compensation

Long-time coherent integration is an effective method for dim target detection from heavy sea clutter. To detect dim targets, a novel long-time coherent integration method based on segmented compensation is proposed in this paper. The method models the complex motion of a marine target as the combination of multi-stage uniformly accelerated motions. According to the difference of energy distribution in Doppler frequency domain, this method can suppress sea clutter and detect the regions of interest (ROIs). Using time–frequency domain energy analysis, the potential target can be extracted. After estimating the parameters and segmentation, for the potential targets, the phase compensation factor can be used to eliminate the Doppler frequency modulation caused by the complex motion. Finally, for the compensated signal, long-time coherent integration is performed to realize the target detection and discrimination under low signal-to-clutter ratio. To verify the effectiveness of the proposed method, we apply simulation data and measured CSIR data in the experiments. The results show that the proposed method can integrate the energy of target more effectively than MTD and RFrFT, and the novel method has better detection performance for complex moving targets under low signal-to-clutter ratio situation.

An Hybrid Integration Method-Based Track-before-Detect for High-Speed and High-Maneuvering Targets in Ubiquitous Radar

Due to the limited transmission gain of ubiquitous radar systems, it has become necessary to use a long-time coherent integration method for range-Doppler (RD) analysis. However, when the target exhibits high-speed and high-maneuver capabilities, it introduces challenges, such as range migration (RM), Doppler frequency migration (DFM), and velocity ambiguity (VA) in the RD domain, thus posing significant difficulties in target detection and tracking. Moreover, the presence of VA further complicates the problem. To address these complexities while maintaining integration efficiency, this study proposes a hybrid integration approach. First, methods called Keystone-transform (KT) and matched filtering processing (MFP) are proposed for compensating for range migration (RM) and velocity ambiguity (VA) in Radar Detection (RD) images. The KT approach is employed to compensate for RM, followed by the generation of matched filters with varying ambiguity numbers. Subsequently, MFP enables the production of multiple RD images covering different but contiguous Doppler frequency ranges. These RD images can be compiled into an extended RD (ERD) image that exhibits an expanded Doppler frequency range. Second, an improved particle-filter (IPF) algorithm is raised to perform incoherent integration among ERD images and to achieve track-before-detect (TBD) for a target. In the IPF, the target state vector is augmented with ambiguous numbers, which are estimated via maximum posterior probability estimation. Then, to compensate for the DFM, a line spread model (LSM) is proposed instead of the point spread model (PSM) used in traditional PF. To evaluate the efficacy of the proposed method, a radar simulator is devised, encompassing comprehensive radar signal processing. The findings demonstrate that the proposed approach achieves a harmonious equilibrium between integration efficiency and computational complexity when it comes to detecting and tracking high-speed and high-maneuvering targets with intricate maneuvers. Furthermore, the algorithm’s effectiveness is authenticated by exploiting ubiquitous radar data.

Passive Tone Detection for Moving Targets Based on Long-Time Coherent Integration

The detection of sinusoidal signals embedded in noise is an important topic in passive sonar signal processing. The performance of existing tone detection techniques is limited by the Doppler frequency shift, which is caused by the relative motion between moving targets and the receiver. In this study, an algorithm based on long-time coherent integration is proposed to achieve robust tonal signal detection under the influence of a Doppler frequency shift. First, the received narrowband signals radiated by moving targets are split into multiple segments through a window-length constraint. The results obtained by applying a discrete Fourier transform (DFT) to the data segments are modeled as a polynomial phase signal in the frequency domain. Then, the polynomial Radon-polynomial Fourier transform (PRPFT) is applied to simultaneously compensate the time-variant frequency drift and phase difference. To avoid the gain loss due to the discretization of the phase difference compensation in PRPFT, a phase compensation factor searching algorithm is proposed. The simulation results show that the proposed algorithm can provide higher frequency resolution and higher coherent integration gain even in the case of a severe Doppler shift. Furthermore, the results of sea trials demonstrate that the proposed method can perfectly achieve coherent integration for signals with a duration of several hundred seconds under different experimental conditions.

Long-time coherent integration algorithm for high-speed maneuvering target detection

Detection of high-speed maneuvering targets along with motion parameters estimation (MPE) are some of the challenging problems for modern radar systems. Such targets usually induce linear range migration (LRM), quadratic range migration (QRM), and Doppler frequency migration (DFM) problems in signal processing, resulting in severe performance degradation, especially when long time integration is needed for weak target detection. We propose an algorithm for coherent integration and MPE by combining the techniques of generalized dechirp (GD) and new axis rotation moving target detection (NAR-MTD), i.e., the GD-NAR-MTD algorithm, to solve the above problems. Specifically, the GD and NAR approaches can not only correct LRM, QRM, and DFM simultaneously with reduced rotation error in coordinate system transformation but also can abate the computational burden via frequency-domain implementation with rounding and complex addressing operations avoided, so the target’s echo energies can be well accumulated by MTD finally. Both simulation and practical radar experiments are conducted to validate the proposed algorithm. At the same time, the results by the other six typical algorithms are compared for demonstrating the superior performance of the proposed algorithm on detection and MPE. In addition, the equivalence between the practical radar experiment and the simulation experiment is analyzed by comparing the induced RMs and DFMs, which shows that the scaled equivalent experiment is persuasive in algorithm validation.

Motion Parameters Estimation and HRRP Reconstruction of Maneuvering Weak Target for Wideband Radar Based on SKT-ELVD

Compared with narrowband radars, the high-resolution range profile (HRRP) acquired by wideband radars contain abundant target information that is useful for detection and recognition. However, more and more threatening targets are of low observability and high maneuverability. Therefore, reconstructing HRRPs of maneuvering weak targets from low signal-to-noise ratio (SNR) echoes is a significant but challenging problem. To estimate motion parameters and reconstruct high-SNR HRRP, this paper proposes a long-time coherent integration (LTCI) algorithm based on subband keystone transform (SKT) and extended Lv's distribution (ELVD). In this paper, the range-spread target (RST) assumption is applied in the LTCI processing. Moreover, the proposed SKT-ELVD operations have excellent performance on range migration (RM) correction and integration gain. The proposed algorithm can be of effectiveness in lower SNR conditions, since more energy of target's echo can be accumulated. Theoretical results are initially supported by sufficient simulation examples. Finally, the validity of the proposed algorithm is confirmed by experimental data.

Segmented Radon Fourier Transform for Long-Time Coherent Radars

Coherent pulse integration is a well-known technique for effective target detection with increased output signal-to-noise ratio (SNR). Radon fourier transform (RFT) uses long-time coherent integration technique for improved target detection in a 3-dimensional search but increases the parameters search time. This paper presents a new approach of Segmented Radon Fourier Transform (SRFT) for fast detection of high speed targets without significantly degrading the detection performance. SRFT divides the received echo data matrix into an arbitrary number of segments along the slow time dimension of the data matrix. Each segment is a complete independent data matrix which can proceed independently and in parallel fashion. This paper implements a complete pipeline of radar receiver with SRFT to validate its integration in a radar signal processor. Experiments show that the parameters search time of SRFT is reduced by N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> times when compared with RFT, where N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> is the number of segments. There is a negligible degradation of 0.035dB in SNR when compared with standard RFT for 120 pulses. The difference is further reduced as the number of pulses are increased.

Joint elimination method of scale effect and range migration/Doppler migration for hypersonic maneuvering target under large time-bandwidth product condition

Under the large time-bandwidth product condition, the detection of hypersonic maneuvering target usually confronts two main issues: the scale effect (SE) and range migration (RM)/Doppler migration (DM). To address these issues, this paper considers the intrapulse and interpulse motions simultaneously to establish the echo model of hypersonic target with acceleration firstly. Then, the matched filtering-scaled modified location rotation transform (MF-SMLRT) method is proposed to jointly eliminate the SE and RM/DM, which are realized by searching target’s rotation angle, initial range cell and acceleration. The proposed method shows better pulse compression (PC), integration and detection performance than the conventional narrow-band long-time coherent integration (CI) methods and existed CI methods applicable to large time-bandwidth products (LTBP) condition. Finally, simulated results are given to certify the validity of the proposed method.

Motion parameters estimation of manoeuvring weak target with multiple motion stages based on range symmetry transform and short‐time fractional Fourier transform

AbstractWith the advancement of manoeuvrability and the increasement of coherent processing interval (CPI), the observed target might be of multiple motion stages. Therefore, most existing long‐time coherent integration (LTCI) algorithms based on the assumption of single‐motion stage is not proper any more. To address this problem, this letter proposes an effective motion parameters estimation algorithm, which is the key step of LTCI, for the manoeuvring weak target with multiple motion stages based on range symmetry transform and short‐time fractional Fourier transform (RST‐STFrFT). The effectiveness of the proposed algorithm is verified by signal‐level simulations.

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.

Subaperture Keystone Transform Matched Filtering Algorithm and Its Application for Air Moving Target Detection in an SBEWR System

Long-time coherent integration is an effective approach to improve detection performance for weak air moving targets (AMTs). The range position variation and azimuth Doppler variation will easily exceed range gate and Doppler resolution in a long observation time, resulting in severe performance degradation, especially for high maneuverability target. Besides, the high detection performance and low computational complexity ability are, most of times, the contradiction requirements by using the existing long-time coherent integration algorithms. To overcome above constraints, a novel subaperture Keystone transform matched filtering (SAKTMF) method is developed in this paper based on the conventional hybrid integration algorithm, which can realize coherent integration both within the subaperture and among subapertures, effectively improving the detection performance of a weak moving target. Furthermore, the proposed SAKTMF is applied for weak AMT detection in space-borne early warning radar (SBEWR), which considers serious extended clutter, range migration, and Doppler migration problems simultaneously. Simulation experiments processing results show that the proposed method can provide improved detection performance compared with the conventional hybrid integration methods.

High Maneuvering Target Long-time Coherent Integration and Motion Parameters Estimation Based on Bayesian Compressive Sensing

This paper intends to address the long-time coherent integration (LTCI) of high maneuvering targets in low signal-to-noise (SNR) environments with high computational efficiency and accuracy. The high-order motion parameters estimation, considering the acceleration and jerk, is modeled as the under-estimated linear regression and the complex-field Bayesian compressive sensing (BCS) algorithm is introduced to resolve the sparse recovery. To correct the high-order range migration (RM) and reduce the order of Doppler frequency migration (DFM), the adjacent cross correlation (ACCF) is applied. An effective method based on non-coherent integration is proposed to extract the self-term from ACCF result. Further, with the proper design of sensing matrix, the acceleration and jerk motion parameters are estimated by sparse reconstruction based on the complex-field BCS. Compared with the traditional methods based on time-frequency transform, like Lv's distribution (LVD), the proposed BCS algorithm is free from the interference of cross-terms and maintains the super-resolution ability, which provides better performance in parameters estimation and multi-targets discrimination. Finally, the numerical experiments validate the advantages of the proposed method in motion parameters estimation, super-resolution ability and computational efficiency.

Time-Range Adaptive Focusing Method Based on APC and Iterative Adaptive Radon-Fourier Transform

In conventional radar signal processing, the cascade of pulse compression (i.e., matched filter) and Radon-Fourier transform (RFT) can extract the estimated scattering coefficient of the target in the range-velocity dimension through long-time coherent integration (i.e., long-time focusing). However, matched filter has problems such as range sidelobes. RFT belongs to a standard time-dimension matched filter, which will cause velocity sidelobes of strong targets. The range-velocity sidelobes caused by matched filter and RFT will mask other weak targets and affect the subsequent signal processing processes such as target detection and tracking. To suppress range-velocity sidelobes and achieve better range-velocity focusing, this paper proposes a time-range adaptive focusing method named APC-IARFT for short, which is based on adaptive pulse compression (APC) and newly proposed iterative adaptive Radon-Fourier transform (IARFT). In the APC-IARFT method, the radar time-range adaptive focusing consists of two steps: range-dimension adaptive focusing and long-time adaptive focusing in the velocity dimension. The APC method can realize range-dimension adaptive focusing and suppress range sidelobes of strong targets. Then, based on the minimum variance distortionless response (MVDR) formulation, the proposed IARFT method iteratively designs time-dimension adaptive filter of each range-velocity grid according to the received signal processed by APC to suppress velocity sidelobes of strong targets and achieve long-time adaptive focusing. Compared with the conventional cascade of matched filter and RFT, the cascade of matched filter and adaptive Radon-Fourier transform (ARFT), the results show that the proposed time-range adaptive focusing method (i.e., APC-IARFT) is competent for a variety of scenarios.

Weak and Maneuvering Target Detection with Long Observation Time Based on Segment Fusion for Narrowband Radar.

Detecting high-speed and maneuvering targets is challenging in early warning radar applications. Modern early warning radar has many functions such as detection, tracking, imaging, and recognition which need a high signal-to-noise ratio (SNR). Thus, long-time coherent integration is a necessary method to realize high SNR requirements. However, high-speed and maneuverable motion cause range and Doppler migration, which brings about serious coherent integration loss. Traditional integration methods usually have the drawbacks of model mismatching and high computational complexity. This paper establishes a novel long coherent processing interval (CPI) integration algorithm that detects maneuvering and weak targets which have a low reflection cross-section (RCS) and low echo SNR. The range and Doppler migration problems are solved via a layer integration by blending the association in a tracking-before-detection (TBD) technique. Compact SNR gain is achieved with a target information transmission mechanism and an updated constant false alarm ratio (CFAR) threshold. The algorithm is applicable in multiple target scenarios by considering different velocity ambiguities and maneuvers. A simulation and real-measured experiments confirm the effectiveness of the algorithm.

Radar coherent integration algorithm for detection of complexly maneuvering target with extended velocity and acceleration scopes

Excess acceleration and Doppler ambiguity produce inaccurate acceleration and radial velocity in long-time coherent integration for complexly maneuvering targets. This study proposes an algorithm based on the product-scaling periodic-modified Lv's distribution (PSPMLVD) and inverse-scaling periodic discrete Fourier transformation (ISPDFT) that solves these problems by eliminating the range migration errors. First, the periodic modified Lv's distribution (PMLVD), which extends the estimation scope of the modified Lv's distribution, is proposed to estimate the excess acceleration and precise jerk. Then, the scaling and product operations are combined with PMLVD to decouple and depress the sidelobes. Subsequently, high-order parameters are compensated for, and SPDFT is employed to extend the period of discrete Fourier transform (DFT). Finally, inverse DFT is applied to achieve coherent integration and estimate the unambiguous velocity and initial range. The algorithm is appropriate for targets following first- to third-order motions as it avoids searching for parameters and approximating models. Unlike several existing algorithms, this algorithm can achieve equilibrium between computational complexity and anti-noise detection performance. Simulation experiments and real data prove its effectiveness.