Range Walk Research Articles

Sub-CPI STAP based clutter suppression and target refocusing with airborne radar system

Under the interference of airborne radar clutter, it is a challenge for fast maneuvering target detection, because of the nonstationary echo signal involved within the long coherent processing interval (CPI). To tackle this issue, a robust clutter suppression and small maneuvering target detection method is proposed in airborne radar system, which is referred to as the sub-CPI space-time adaptive processing (STAP) based refocusing. For robust clutter suppression, the whole CPI is divided into a series of equal-length and overlapped sub-CPIs with the sliding window technique. In each sub-CPI, the STAP algorithm is adopted for robust clutter suppression, in which the consistent covariance matrix estimation is derived to guarantee the linear phase response within the whole CPI. However, as endo-clutter weak target is considered, the signal-to-clutter-plus-noise ratio (SCNR) after sub-CPI STAP still cannot meet the performance requirement. Thus, the target refocusing is applied for further SCNR improvement based on the semi-searching mechanism. However, the range walking (RW) and Doppler frequency migration problems defocus the energy of fast maneuvering target over range and Doppler frequency dimensions, respectively. To circumvent such problems, Keystone transform is utilized to correct the RW, followed by the Lv's distribution to achieve target refocusing. Numerical simulations and measured results with sum and difference channels validate the effectiveness of the proposed method.

SAR Ground Maneuvering Targets Imaging and Motion Parameters Estimation Based on the Adaptive Polynomial Fourier Transform

This letter proposes a new method for focusing ground maneuvering targets and estimating the motion parameters with a synthetic aperture radar (SAR) system. In this method, the Hough transform is applied to estimate the cross-track velocity from the slope of the range walk (RW) trajectory, and the RW and Doppler centroid shift are compensated. The second-order Keystone transform is performed to correct the additional range curve caused by the along-track velocity and cross-track acceleration. Then, we adopt the adaptive polynomial Fourier transform to estimate the second- and third-order Doppler parameters from a 1-D parameter interval, and the corresponding motion parameters are calculated. Finally, the moving target is well focused after the motion parameters compensation because the second- and third-order Doppler parameters are efficiently eliminated. Both the simulated and real data processing results are presented to demonstrate the validity of the proposed algorithm.

Autofocus Methods for Moving Target Imaging in Synthetic Aperture Radar

To use moving target signatures in synthetic aperture radar (SAR) for classification and identification, it is desirable to obtain a well-focused image from the blurred moving target signature. While a substantial amount of research has been done on solving the constant chirp rate defocusing of a moving target, this often leaves significant blurring in the moving target signature of a real target. This work aims at improving previous work on autofocus, specifically considering higher order motion terms, including those due to range walk and small rotations. Additionally, we aim to reduce the reliance on bright well-separated point scatterers. We apply SAR autofocus methods normally used for full imagery to moving targets: minimum entropy and phased gradient autofocus, and include recent innovations that allow these methods to handle range walk. Finally, we add a novel range-varying autofocus stage. We use SAR imagery of a truthed moving pickup truck collected with the MIT Airborne Radar Testbed (ARTB) to compare autofocus algorithms.

Hybrid SAR-ISAR Image Formation via Joint FrFT-WVD Processing for BFSAR Ship Target High-Resolution Imaging

Bistatic forward-looking synthetic aperture radar (BFSAR) is a kind of bistatic SAR system that can image forward-looking terrain in the flight direction of the receiver. Current literature and reports about BFSAR mainly concentrate on the stationary scene and ground-moving target imaging. Unlike stationary and ground-moving targets, the translational and rotational movements of ship targets usually lead to complicated range cell migration (RCM) and Doppler frequency migration (DFM). Moreover, the characteristics of RCM and DFM for different scattering points of the ship target are significantly different, i.e., the characteristics of the RCM and DFM are 2-D spatial variation, ultimately leading to severe defocusing of ship target in the SAR image. To solve these problems, a kind of hybrid SAR-ISAR imaging formation is proposed for BFSAR ship target imaging. First, to solve the problem of the Doppler ambiguity caused by the forward-looking mode of the receiver, an efficient ambiguity estimation method based on the minimum entropy criterion is presented. Then, keystone transform and range alignment processing can be applied to correct the spatial variant range walk and higher order RCM, respectively. Moreover, in order to obtain a high-resolution and well-focused image after translational compensation, a new method based on the fractional Fourier transform (FrFT) and the Wigner–Ville distribution (WVD) is proposed, where FrFT is applied to separate the multiple main scattering points in each range cell, and WVD is applied to obtain the high-resolution time–frequency distribution of each scattering point. Compared with the conventional ISAR range-Doppler (RD) algorithm and time–frequency estimation-based imaging methods, this method not only has no cross terms but also has high processing accuracy and better antinoise performance.

A Method of Range Walk Error Correction in SiPM LiDAR with Photon Threshold Detection

A silicon photomultiplier (SiPM) LiDAR with photon threshold detection can achieve high dynamic performance. However, the number fluctuations of echo signal photons lead to the range walk error (RWE) in SiPM LIDARs. This paper derives the RWE model of SiPM LiDAR by using the LiDAR equation and statistical property of SiPM’s response. Based on the LiDAR system parameters and the echo signal intensity, which is obtained through the SiPM’s photon-number-resolving capability, the RWE is calculated through the proposed model. After that, we carry out experiments to verify its effectiveness. The result shows that the method reduces the RWE in TOF measurements using photon threshold detection from 36.57 cm to the mean deviation of 1.95 cm, with the number of detected photons fluctuating from 1.3 to 46.5.

Imaging on Underwater Moving Targets With Multistatic Synthetic Aperture Sonar

A multistatic synthetic aperture sonar (SAS) configuration, composed of an active sonar, a towed receiver and a sonobuoy, is proposed to acquire the image of a moving target and estimate its velocity vector. The range model incorporates the time delay of an acoustic pulse between its emission and backscattered from the target to the receivers. An image is acquired from the received signals at one receiver after range cell migration correction (RCMC), range walk compensation (RWC) and compression, without prior knowledge on the motion parameters of the target. Range-frequency reversal transform (RFRT) and a modified second-order Wigner-Ville distribution (SoWVD) are used to estimate the chirp rate in the range model, and Radon transform is used to estimate the Doppler centroid. The velocity vector of the moving target is accurately estimated, within 3% of error and insensitive to noise, by using the Doppler centroids derived from the signals at the three receivers. Eight different scenarios are simulated to demonstrate the efficacy of the proposed method. The shape and size of the moving target can be clearly identified in all but one case. Three state-of-the-art methods are also used to verify the accuracy of the proposed method, the effects of noise are analyzed, and autofocus algorithms are applied to enhance the acquired images in some difficult cases.

Detection and fast motion parameter estimation for target with range walk effect based on new axis rotation moving target detection

In order to address the range walk (RW) effect in the field of radar high speed target detection, the axis rotation MTD (AR-MTD) class algorithms based on long-time coherent integration, i.e., AR-MTD, improved axis rotation MTD (IAR-MTD), and modified location rotation transform (MLRT) have been proposed in recent works. However, they are faced with detection performance loss and large computational complexity. In this paper, a new axis rotation MTD (NAR-MTD) algorithm is proposed. Different from the previous AR-MTD class algorithms, NAR-MTD first selects the image center of 2-D compressed signal as the coordinate system origin, and then simplifies the axis rotation relationship to reduce the rotation error caused by the coordinate transformation and correct the RW to the initial range location. Furthermore, by exploiting the geometrical information of mismatched NAR-MTD, the adaptive AR-MTD (AAR-MTD) is proposed to realize efficient motion parameter estimation of the moving target in different SNR environments. Numerical simulations and real data process indicate that NAR-MTD has a better detection ability than that of AR-MTD class algorithms. Meanwhile, the computational efficiency of AAR-MTD is about two orders of magnitude higher than that of direct 2-D search of NAR-MTD.

Ankle contractures and functional motor decline in Duchenne muscular dystrophy

IntroductionThis prospective, correlational pilot study investigated the relationship between ankle plantar flexion contractures and motor function in boys with Duchenne muscular dystrophy in British Columbia (BC), Canada. ParticipantsAmbulatory boys with Duchenne muscular dystrophy were recruited from BC Children’s Hospital, which follows everyone with Duchenne muscular dystrophy in BC ≤ 18 years of age (n = 14). MethodsSpearman and Pearson correlation coefficients were estimated to examine the association between the degree of ankle dorsiflexion range of motion and North Star Ambulatory Assessment scores and the degree of ankle dorsiflexion range and six-minute walk test distances. ResultsOur analysis showed a moderate correlation between the degree of ankle dorsiflexion range and North Star Ambulatory Assessment scores [rho (14) = 0.50; p = 0.070] and a weak correlation between ankle dorsiflexion range of motion and six-minute walk test distances [rho (13) = 0.08; p = 0.747], however neither result was statistically significant. DiscussionAlthough a significant relationship between ankle dorsiflexion range of motion and motor function was not found, the variability of ankle dorsiflexion range suggests challenges with preventing ankle contracture. This reinforces the importance of assessing ankle range of motion in boys with Duchenne muscular dystrophy with sufficient frequency to identify a need for additional interventions.

BeiDou-Based Passive Radar Vessel Target Detection: Method and Experiment via Long-Time Optimized Integration

The BeiDou navigation satellite system shows its potential for passive radar vessel target detection owing to its global-scale coverage. However, the restrained power budget from BeiDou satellite hampers the detection performance. To solve this limitation, this paper proposes a long-time optimized integration method to obtain an adequate signal-to-noise ratio (SNR). During the long observation time, the range migration, intricate Doppler migration, and noncoherence characteristic bring challenges to the integration processing. In this paper, first, the keystone transform is applied to correct the range walk. Then, considering the noncoherence of the entire echo, the hybrid integration strategy is adopted. To remove the Doppler migration and correct the residual range migration, the long-time integration is modeled as an optimization problem. Finally, the particle swarm optimization (PSO) algorithm is applied to solve the optimization problem, after which the target echo over the long observation time is well concentrated, providing a reliable detection performance for the BeiDou-based passive radar. Its effectiveness is shown by the simulated and experimental results.

An innovative approach to solve the carsharing demand-supply imbalance problem under demand uncertainty

This paper studies the demand-supply imbalance problem for one-way carsharing systems under a combination of pricing strategy, relocations and access trips considering stochastic demand. A novel concept of a virtual zone is utilized to capture vehicle relocation range and client walking or biking distance constraints in one-way carsharing systems. The vehicle imbalance problem is further addressed by combining a long-term pricing strategy and real-time vehicle relocations in a two-stage stochastic programming model. In the first stage, the tactical decisions including fleet size and trip price are optimized, while anticipating the operational costs from the second stage. The second stage optimizes operational decisions under uncertain demand including vehicle relocations conditional on the tactical decisions in stage one. The model aims to maximize the profit of a carsharing company considering the fleet costs calculated in stage one and the expected operational costs and revenue obtained in stage two. A dedicated gradient search algorithm is developed to solve the two-stage stochastic programming and results are compared to a genetic algorithm and an iterated local search algorithm. The proposed model and corresponding solution approach are applied to a large-scale network with 50 zones and over 1000 vehicles in Suzhou, China. The application allows us to attain additional operational insight. Results suggest that increased prices for high demand stations during peak hours reduce demand while maintaining profitability of the system. It is also found that the real-time vehicle relocations and flexibility of clients to pick up vehicles at farther stations can increase demand service rate by as much as 10%.

High Speed Maneuvering Platform Squint TOPS SAR Imaging Based on Local Polar Coordinate and Angular Division

This paper proposes an imaging algorithm for synthetic aperture radar (SAR) mounted on a high-speed maneuvering platform with squint terrain observation by progressive scan mode. To overcome the mismatch between range model and the signal after range walk correction, the range history is calculated in local polar format. The Doppler ambiguity is resolved by nonlinear derotation and zero-padding. The recovered signal is divided into several blocks in Doppler according to the angular division. Keystone transform is used to remove the space-variant range cell migration (RCM) components. Thus, the residual RCM terms can be compensated by a unified phase function. Frequency domain perturbation terms are introduced to correct the space-variant Doppler chirp rate term. The focusing parameters are calculated according to the scene center of each angular block and the signal of each block can be processed in parallel. The image of each block is focused in range-Doppler domain. After the geometric correction, the final focused image can be obtained by directly combined the images of all angular blocks. Simulated SAR data has verified the effectiveness of the proposed algorithm.

Time-magnified photon counting with 550-fs resolution

Time-correlated single-photon counting (TCSPC) is an enabling technology for applications such as low-light fluorescence lifetime microscopy and photon counting time-of-flight (ToF) 3D imaging. However, state-of-the-art TCSPC single-photon timing resolution (SPTR) is limited to 3–100 ps by single-photon detectors. Here, we experimentally demonstrate a time-magnified TCSPC (TM-TCSPC) that achieves an ultrashort SPTR of 550 fs with an off-the-shelf single-photon detector. The TM-TCSPC can resolve ultrashort pulses with a 130-fs pulse width difference at a 22-fs accuracy. When applied to photon counting ToF 3D imaging, the TM-TCSPC greatly suppresses the range walk error that limits all photon counting ToF 3D imaging systems by 99.2% and thus provides high depth accuracy and precision of 26 µm and 3 µm, respectively.

Toward snapshot correction of 3D flash LiDAR imagers

We present methods enabling rapid non-uniformity and range walk error correction of 3D flash LiDAR imagers that exhibit electronic crosstalk caused by simultaneously triggering too many detectors. This additional electronic crosstalk is referred to as simultaneous ranging crosstalk noise (SRCN). Using a method in which the 3D flash LiDAR imager views a checkerboard target downrange, the SRCN is largely mitigated. Additionally, processing techniques for computing the non-uniformity correction (NUC) and range walk error correction are described; these include an in-situ thermally compensated dark-frame non-uniformity correction, image processing and filtering techniques for the creation of a photo-response non-uniformity correction, and characterization and correction of the range walk error using data collected across the full focal plane array without the need for sampling or windowing. These methods result in the ability to correct noisy test validation data to a range precision of 8.04 cm and a range accuracy of 1.73 cm and to improve the signal-to-noise ratio of the intensity return by 15 to 49 dB. Visualization of a 3D scene corrected by this process is additionally presented.

A novel hypersonic vehicle-borne multichannel SAR-GMTI scheme based on adaptive sum and difference beams within eigenspace

This paper investigates a novel ground moving target indication (GMTI) scheme for a hypersonic vehicle-borne multichannel synthetic aperture radar (MC-SAR) system with Doppler ambiguity. First, after the range compression and azimuth chirp Fourier transform (CFT), by applying the eigenspace-based adaptive sum and difference beams (EASDB) on the coarse-focused images, the high-precision cross-track velocity (CTV) can be retrieved. Then, utilizing the high-precision CTV to construct an accurate moving target steering vector to extract the moving target energy. With the proposed CFT-two-step method, we have avoided cumbersome CTV search, and simplified the process of range walk correction, resulting in lower computational complexity. Compared to the CFT-center and CFT-two-step methods, the proposed scheme obtains the accurate two-dimension motion parameters of a moving target, and has better performance and robustness in the detection, focusing, and location, preserving the moving target envelope and achieving higher signal-to-clutter-and-noise ratio (SCNR). Finally, using the processing results of simulation and real measured MC-SAR data, we verify the effectiveness and feasibility of our proposed scheme.

Effects of Movement for High Time-Bandwidths in Batched Pulse Compression Range-Doppler Radar.

Radar detection and track building performance is an essential part of a radar system. A high realized coherent integration gain often contributes to an improved performance. This is essential to the successful detection and tracking of weak moving targets. However, the actual movement within the coherent processing interval can introduce range walk effects. The processing will then result in range and Doppler frequency resolutions that become finer than a single moving point scatterer’s spread over range and—often not considered—over Doppler frequency. In particular for a wide instantaneous bandwidth, the impact on the achievable integration gain can become severe already for a constant effective velocity. Therefore, high desired integration gains as required in passive radar are not easily achieved against relatively fast moving targets. The main intent of this article is to present the movement effects on a classical range-Doppler analysis to give an insight on the achievable performance and to quantify otherwise appearing degradations. Interestingly, a classical analysis of experimental datasets evaluated from a DVB-T based passive radar measurement campaign even resolved the fluctuation of a target response within the instantaneously processed bandwidth. The findings strengthen the need for advanced processing methods that can at least partly address individual implications of fast moving targets in real-time applications properly.

Multi-Frame Integration Method for Radar Detection of Weak Moving Target

In this paper, we consider the multi-frame integration (including intra-frame integration and inter-frame integration) problem for the detection of weak moving targets, where range walk effect (RWE) occurs within the integration time. A novel integration method is proposed to achieve the accumulation of a target's multi-frame radar echoes. More specifically, the proposed integration method contains two main steps, where the modified Radon Fourier transform (RFT) is firstly used to realize the intra-frame coherent integration for every frame of echo signals. After that, the RFT-domain integration algorithm is presented to achieve the inter-frame coherent integration based on the characteristics of RFT outputs, during which the accumulation of target energy distributed in multiple frames could be realized. The explicit expressions and analysis for various performance measures of the proposed method, such as integration output response, probability of detection, input-output signal-to-noise ratio (SNR), and blind speed sidelobe (BSSL) response are derived and given. Simulation experiments are given to demonstrate the effectiveness of the proposed method.

Spatial-Variant SAR Range Cell Migration Correction Using Subaperture Strategy

The coupling between range and azimuth dimensions is the main obstacle for highly squinted synthetic aperture radar (SAR) data focusing. Range walk correction (RWC) processing is effective to remove the linear coupling term, but the residual high order range cell migration (RCM) parts are spatial-variant in both range and azimuth dimensions. In this paper, we propose a precise spatial-variant range cell migration correction (RCMC) method with subaperture processing. The method contains two stages. Firstly, the main component of range-variant RCM is corrected in the coarse RCMC stage. Secondly, data are derived into azimuth subapertures (SAs), an SA-image-domain RCMC is developed by interp correction, where the SA image is obtained using a modified spectrum analysis (SPECAN) algorithm by establishing the relationship between Doppler frequency and residual spatial-variant RCM. In the proposed algorithm, precise compensation of space-variant RCM is implemented by SA processing, which is designed for a better practicality in real-time processing system. Simulated and real measured data experiments are designed to validate the effectiveness of the proposed approach for highly squinted SAR imaging.

Windowed region-of-interest non-uniformity correction and range walk error correction of a 3D flash LiDAR camera

We present experimental methods and results for photo-response non-uniformity correction (PRNUC) in range for a 3D flash LiDAR camera from non-optimal static-scene calibration data. Range walk is also corrected. This method breaks up the camera’s focal plane array (FPA) into 16 × 16 windowed regions of interest that are incrementally captured and stitched together in post-processing across the entire FPA. The illumination was not uniform, thus requiring additional methods described by our paper to create an acceptable correction. We present the results from a full non-uniformity correction and range walk error correction processed for a set of independently collected validation frames; these validation frames used identical experimental conditions and the same target as was collected for the corrections. We will show that this experimental approach improves range accuracy and range precision of the corrected validation frames despite the sub-optimal conditions of the data used to compute the corrections; the single shot range precision is corrected to 33 cm, as compared to a modeled precision of 15.65 cm, while the accuracy is corrected to 252 cm. This method has implications for simplification of characterization of non-uniformity and range walk error, and its subsequent correction, in 3D flash LiDAR cameras.

Continuous pulse repetition interval variation for highly squint high-resolution spotlight SAR imaging

ABSTRACT Highly squint Synthetic Aperture Radar (SAR) is a competitive candidate for intelligence surveillance and disaster monitoring because of its capacity for multi-angle information acquisition and high spatial resolution. However, large Range Cell Migration (RCM) results in a considerably long receive window and an extremely large volume of invalid data, which burdens the computational load and severely reduces the efficiency of image processing. The existing method is designed to remove range walks using continuous Pulse Repetition Interval (PRI) variation. When a high-resolution system is required, the range curvature is apparent. This paper proposes a novel strategy to remove the RCM of a reference point accurately using continuous PRI variation for highly squint high-resolution spotlight spaceborne SAR. Additionally, the proposed strategy avoids contamination by transmit and nadir interferences. The simulation results show that the proposed method achieves improved data volume reduction performance compared with the existing method.

Long‐time coherent integration based on intra‐partition range‐Doppler processing for passive bistatic radar

The Doppler mismatch, range migration and Doppler frequency migration (DFM) correction problem for realizing the long-time coherent integration of space moving target with high-speed manoeuvring performance in passive bistatic radar is considered. A novel method based on intra-partition range-Doppler (RD) processing is proposed, where the intra-partition RD processing is first performed to achieve the pre-accumulation of target’s energy in each partition and eliminate the Doppler mismatch. Then, the generalized keystone transform is employed to correct the range curvature. After that, the residual range walk is removed with the centre frequency of the coarse Doppler filter related to the target velocity. Furthermore, matched filtering process is carried out to compensate the DFM. The advantage of the method is that it can obtain superior coherent integration and detection performance in comparison with the existing algorithms. Numerical simulations are presented to demonstrate the coherent integration and the detection performance for a high-speed target.