Motion Parameter Estimation Research Articles

EKF-based parameter estimation method for radar maneuvering target with unknown time information

Moving target detection (MTD) is a research hotspot in radar signal processing. Generally, the time information of non-cooperative moving targets entering and leaving a radar coverage area is unknown, which would lead to severe performance loss for target parameter estimation, detection, and imaging. Unlike our previous research work, this paper addresses the motion parameters estimation and refocusing problem for a radar maneuvering target with unknown entry and departure time. A computationally efficient method that utilizes extended Kalman filtering (EKF) for phase tracking is proposed to estimate the entry and departure times. The proposed method first performs range cell migration correction (RCMC) on the pulse compression echo signal. Then, the maneuvering target signal is modeled as a polynomial phase signal (PPS) and utilizes the EKF to construct a binary state-space equation for polynomial phase tracking. Finally, by comparing the phase tracking results of the noise cell and the signal cell, one can derive estimates for the entry/departure time and motion parameters. Compared with existing methods, the proposed method avoids multi-dimension searching on the parameter space, so it has a prominent advantage in computational complexity. Moreover, the core of the proposed method lies in tracking the polynomial phase, which is not constrained by the order of target motion, and has wider applicability in practice. Both simulated and public radar data are used to validate the effectiveness of the proposed method.

A non-parametric model of ground motion parameters for shallow crustal earthquakes in Europe

The current study focuses on deriving ground motion models (GMMs) for 21 ground motion parameters derived from data sourced from the Engineering Strong Motion (ESM) database. These parameters include Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), Peak Ground Displacement (PGD), PGV-to-PGA ratio, (V/H) PGA ratio Predominant Frequency (Fp), Central Frequency (Ω), Spectral Parameter (q), Significant Duration (TSig), Root Mean Square Acceleration (Arms), Arias Intensity (Ia), Cumulative Absolute Velocity (CAV), Characteristic Intensity (IC), Acceleration Spectrum Intensity (ASI), Velocity Spectrum Intensity (VSI), Total Energy (Eacc), Spectral Centroid (Ew), Spectral Standard Deviation (Sw), Temporal Centroid (Et), Temporal Standard Deviation (St), and Correlation between time and frequency [ρ(t,ω)]. Both horizontal and vertical components are considered in this study. The inherent random effects within ground motion regression, encompassing inter-event, inter-site, inter-locality, and inter-region variabilities, are addressed using cross-nested mixed effect regression utilizing a non-parametric GMM approach employing Artificial Neural Network (ANN). Quantitative assessment of the models involves correlation coefficients for regression through the origin and error measures like mean squared error and mean absolute error. These findings of the assessment confirm reliable estimates of Ground Motion Parameters (GMPs). A comparison of GMPs computed using the proposed model and those reported in the literature indicated model's superior performance. Furthermore, satisfactory performance of the proposed GMM in ground motion simulation for the ESM region is demonstrated.

Motion Planning for Dynamic Three-Dimensional Manipulation for Unknown Flexible Linear Object

Generally, deformable objects have large and nonlinear deformations. Because of these characteristics, recognition and estimation of their movement are difficult. Many studies have been conducted aimed at manipulating deformable objects at will. However, they have been focused on situations wherein a rope’s properties are already known from prior experiments. In our previous work, we proposed a motion planning algorithm to manipulate unknown ropes using a robot arm. Our approach considered three steps: motion generation, manipulation, and parameter estimation. By repeating these three steps, a parameterized flexible linear object model that can express the actual rope movements was estimated, and manipulation was realized. However, our previous work was limited to 2D space manipulation. In this paper, we extend our previously proposed method to address casting manipulation in a 3D space. Casting manipulation involves targeting the flexible linear object tips at the desired object. While our previous studies focused solely on two-dimensional manipulation, this work examines the applicability of the same approach in 3D space. Moreover, 3D manipulation using an unknown flexible linear object has never been reported for dynamic manipulation with flexible linear objects. In this work, we show that our proposed method can be used for 3D manipulation.

Motion segmentation with event camera: [formula omitted]-patches optical flow estimation and Pairwise Markov Random Fields

This paper proposes the N-patches optical flow estimation-based motion compensation for motion segmentation using event camera. The requirement for prior knowledge of the scenario to cluster events into different motion types is addressed by the N-patches optical flow estimation. The framework of motion segmentation combines motion compensation and Pairwise Markov Random Fields, which not only realize the alignment of events in space but also enhance the spatial correlation between events. The proposed approach aims to maximize the contrast of the images of warped events. It does so by minimizing a specially designed energy function that jointly estimates motion parameters and discrete label items. The problem of selecting the optimal value for N∗ when executing N-patches optical flow estimation is discussed in Section 4.2 of the experiments. Finally, the proposed approach is evaluated in several scenes involving high-speed motion, low-light conditions, occlusions, and multiple moving objects. The experimental results show that the proposed approach achieves better segmentation performance than the event-based motion segmentation by motion compensation.

An Underwater Localization Algorithm for Airborne Moving Sound Sources Using Doppler Warping Transform

When an airborne sound source is in rapid motion, the acoustic signal detected by the underwater sensor experiences a substantial Doppler shift. This shift is intricately linked to the motion parameters of the sound source. Analyzing the Doppler shift characteristics of received acoustic signals enables not only the estimation of target motion parameters but also the localization of the airborne sound source. Currently, the predominant methods for estimating parameters of uniformly moving targets are grounded in classical approaches. In this study, the application of the Doppler warping transform, traditionally applicable to sound sources in uniform linear motion, is extended to encompass a broader spectrum of sound source trajectories. Theoretical and experimental data validate the efficacy of this transform in linearizing the Doppler shift induced by a source in curved motion. Building upon this foundation, a methodology is proposed for locating airborne acoustic sources in curved motion from underwater. Sea experimental data corroborate the method’s effectiveness in achieving underwater localization of a helicopter target during curved motion.

Speckle noise reduction on aligned consecutive ultrasound frames via deep neural network

Despite the benefits of ultrasound (US) imaging systems for medical diagnosis and treatment, US images are prone to low resolution and contrast due to US’s inherent attributes, as well as affected by speckle noise that directly influences their quality. In retrospective studies, diverse filters have been applied to minimize the effects of speckle noise and enhance the quality of US images. In this article, we propose a method of enhancing US images inspired by synthetic aperture imaging, which provides high-resolution images by adding low-resolution images and measuring the probe’s movement. Our proposed method does not involve synthetic aperture imaging but compensates for the motion effect in the temporal dimension, aligns consecutive images, and stacks aligned images to suppress speckle noise and consequently enhance the resolution of US images. We exploited deep neural network (DNN) models to estimate motion parameters between consecutive US images. In a new database of US images, we also collected the images’ position-related information implicitly measured in inertial measurement units, which was exploited as a ground truth for motion parameters between consecutive images. Compared with other image-enhancing techniques involving conventional filters and DNN modalities, our method demonstrated superiority in enhancing the quality of US images. We also found that estimating motion parameters directly influenced the success of the image-stacking process. As in ablation studies in DNNs, we additionally investigated the effect of dropping some images in the temporal dimension, which revealed that contextual differences and excessive rates of movement in successive US images weakens the image-stacking process and thus the potential enhancement of US images.

Novel motion parameter estimation and coherent integration algorithm for high maneuvering target with jerk motion

The high maneuvering target with jerk motion detection suffers from range migration (RM) and Doppler frequency migration (DFM). In this paper, the fourth order polynomial signal model is used to model the radar echo signal, and a novel high maneuvering target detection method is proposed. The RM is eliminated with Keystone transform (KT) and acceleration searching, and then the aligned echoes are extracted. With two defined symmetric autocorrelation functions (SAF) and the scaled Fourier transform, the third and fourth order motion parameters are estimated. Based on the estimated high order motion parameters, the fourth order polynomial phase signal is turned into linear frequency modulated (LFM) signal. To estimate the chirp rate of the LFM signal, a fast implementation method of second order Wigner Ville Distribution (SoWVD), named frequency domain SoWVD (FDSoWVD) is proposed. Based on the triple estimated motion parameters, the DFM is compensated and then the coherent integration can be achieved by fast Fourier transform, followed which the detection process is performed. Compared with other representative algorithms, the proposed method achieves a good balance between the computation complexity and detection ability. The effectiveness of the proposed method is verified by experiment with synthetic and raw data.

Line spectrum detection and motion parameters estimation for underwater moving target

For the detection of underwater moving target with constant speed at low signal-to-noise ratio (SNR), a track-before-detect method is proposed based on motion parameters estimation and hidden Markov model (HMM). Optimization algorithm is used for the moving target motion parameter estimation with cost function obtained by energy accumulation along line spectrum tracked with 1-D Hidden Markov model in spatially filtered LOFAR spectrum. This method is suitable for detecting weak targets with fast changes in azimuth.

Comparison of methods for intravoxel incoherent motion parameter estimation in the brain from flow-compensated and non-flow-compensated diffusion-encoded data.

Joint analysis of flow-compensated (FC) and non-flow-compensated (NC) diffusion MRI (dMRI) data has been suggested for increased robustness of intravoxel incoherent motion (IVIM) parameter estimation. For this purpose, a set of methods commonly used or previously found useful for IVIM analysis of dMRI data obtained with conventional diffusion encoding were evaluated in healthy human brain. Five methods for joint IVIM analysis of FC and NC dMRI data were compared: (1) direct non-linear least squares fitting, (2) a segmented fitting algorithm with estimation of the diffusion coefficient from higher b-values of NC data, (3) a Bayesian algorithm with uniform prior distributions, (4) a Bayesian algorithm with spatial prior distributions, and (5) a deep learning-based algorithm. Methods were evaluated on brain dMRI data from healthy subjects and simulated data at multiple noise levels. Bipolar diffusion encoding gradients were used with b-values 0-200 s/mm2 and corresponding flow weighting factors 0-2.35 s/mm for NC data and by design 0 for FC data. Data were acquired twice for repeatability analysis. Measurement repeatability as well as estimation bias and variability were at similar levels or better with the Bayesian algorithm with spatial prior distributions and the deep learning-based algorithm for IVIM parameters and , and for the Bayesian algorithm only for , relative to the other methods. A Bayesian algorithm with spatial prior distributions is preferable for joint IVIM analysis of FC and NC dMRI data in the healthy human brain, but deep learning-based algorithms appear promising.

SISMIK for brain MRI: Deep-learning-based motion estimation and model-based motion correction in k-space.

MRI, a widespread non-invasive medical imaging modality, is highly sensitive to patient motion. Despite many attempts over the years, motion correction remains a difficult problem and there is no general method applicable to all situations. We propose a retrospective method for motion estimation and correction to tackle the problem of in-plane rigid-body motion, apt for classical 2D Spin-Echo scans of the brain, which are regularly used in clinical practice. Due to the sequential acquisition of k-space, motion artifacts are well localized. The method leverages the power of deep neural networks to estimate motion parameters in k-space and uses a model-based approach to restore degraded images to avoid "hallucinations". Notable advantages are its ability to estimate motion occurring in high spatial frequencies without the need of a motion-free reference. The proposed method operates on the whole k-space dynamic range and is moderately affected by the lower SNR of higher harmonics. As a proof of concept, we provide models trained using supervised learning on 600k motion simulations based on motion-free scans of 43 different subjects. Generalization performance was tested with simulations as well as in-vivo. Qualitative and quantitative evaluations are presented for motion parameter estimations and image reconstruction. Experimental results show that our approach is able to obtain good generalization performance on simulated data and in-vivo acquisitions. We provide a Python implementation at https://gitlab.unige.ch/Oscar.Dabrowski/sismik_mri/.

Adaptive hybrid Kalman filter for attitude motion parameters estimation of space non-cooperative tumbling target

Attitude motion parameters estimation of the space non-cooperative tumbling target is the premise of the on-orbit target capture task. However, existing methods cannot balance the estimation accuracy and efficiency. In this paper, an adaptive hybrid Kalman filter is presented to estimate the attitude, angular velocity and inertia motion parameters of the space non-cooperative tumbling target. First, the dynamic model of the non-cooperative tumbling target is derived, and the nonlinear discrete state-space equation is obtained. Then, a hybrid Kalman filter is designed by combining the extended Kalman filter and the unscented Kalman filter. The adaptive technique is introduced to track time-varying uncertain measurement noise caused by complex space disturbances. After that, based on the first-order linearization technique, the sufficient condition for the local convergence of the proposed method is proved. Finally, the numerical simulation experiment was conducted to compare the proposed method with the adaptive extended Kalman filter and the adaptive unscented Kalman filter. The experimental results show that the estimation accuracy of the proposed method is much higher than that of the adaptive extended Kalman filter and slightly lower than that of the adaptive unscented Kalman filter, and the iteration-average Central-Processing-Unit time is 64.2% smaller than that of the adaptive unscented Kalman filter and slightly longer than that of the adaptive extended Kalman filter. The proposed method achieves a much higher accuracy with a slight loss of iteration-average Central-Processing-Unit time.

Self-supervised video distortion correction algorithm based on iterative optimization

Wide-angle video frames typically contain more information, but they also exhibit distortion that degrades the visual quality, especially at the edges. To eliminate this distortion from videos, we propose a self-supervised iterative optimization method in this paper. Specifically, we construct a motion parameter estimation model utilizing two consecutive distorted frames, where motion parameters comprise affine transform and distortion parameters. We apply the Gauss–Newton algorithm to minimize the sum-of-squares error between frames and update parameters. Treating inter-frame motion as undistort-affine-distort transformations, frame alignment is achieved by continuously adjusting transform parameters. Ultimately, frames are corrected using the converged parameters. We generated a synthetic dataset with various distortion parameters for evaluation. Experiments demonstrate superior performance versus state-of-the-art methods on synthetic and real wide-angle videos. Our algorithm also achieves higher parameter estimation accuracy without sacrificing efficiency.

Coherent Accumulation for Measuring Maneuvering Weak Targets Based on Stepped Dechirp Generalized Radon–Fourier Transform

The problem of accurately measuring the motion parameters of low radar cross-section (RCS) maneuvering targets has long been a hurdle in the radar technology landscape. Small targets, due to their elusive characteristics, are particularly difficult to detect with conventional radar systems. In this paper, we investigate the capabilities of dechirp-receiving stepped-frequency radar, a modern system using a linear frequency modulation signal for downconversion. This permits the radar to function at reduced sampling rates while maintaining the transmission of large-bandwidth signals and achieving synthetic imaging. Our primary contribution is introducing the stepped dechirp generalized Radon–Fourier transform (stepped DGRFT) algorithm. This novel approach allows the radar system to perform coherent accumulation, enhancing the accuracy of motion parameter estimates for low-RCS maneuvering targets. Results from our simulations and measured data analysis validate the effectiveness of our proposed algorithm, demonstrating its superiority over other methods.

Estimation of Target Motion Parameters from the Tonal Signals with a Single Hydrophone.

In the shallow-water waveguide environment, the tonal signals radiated by moving targets carry modal interference and Doppler shift information. The modal interference can be used to obtain the time of the closest point of approach (tCPA) and the ratio of the range at the closest point of approach to the velocity of the source (rCPA/v). However, parameters rCPA and v cannot be solved separately. When tCPA is known, the rCPA and the v of the target can be obtained theoretically by using the Doppler information. However, when the Doppler frequency shift is small or at a low signal-to-noise ratio, there will be a strong parametric coupling between rCPA and v. In order to solve the above parameter coupling problem, a target motion parameter estimation method from tonal signals with a single hydrophone is proposed in this paper. The method uses the Doppler and modal interference information carried by the tonal signals to obtain two different parametric coupling curves. Then, the parametric coupling curves can be used to estimate the two motion parameters. Simulation experiments verified the rationality of this method. The proposed method was applied to the SWellEx-96 and speedboat experiments, and the estimation errors of the motion parameters were within 10%, which shows the method is effective in its practical applications.

Motion estimation and system identification of a moored buoy via physics-informed neural network

This paper explores the use of physics-informed neural networks (PINNs) to estimate motion and identify system parameters of a moored buoy under three different sea states. PINNs are a deep learning architecture that incorporates physical information to provide an interpretable and physically-meaningful neural network model, making it well-suited for modeling offshore moored structures with high nonlinearity. The moored buoy is modeled as a nonlinear ordinary differential equation (ODE), and the general formulation of PINN for the system of ODEs is established. Two new metrics for motion estimation and system identification are proposed to evaluate the accuracy and efficiency of the implementation of PINN. The results demonstrate that PINN can accurately estimate motion and identify system parameters by choosing appropriate hyperparameters (HPs). This paper also investigates the effects of the number of layers, nodes, and learning rate on motion estimation and system identification to provide a benchmark for selecting optimal HPs. This study finds that hyperparameter optimization can reduce the relative error of identified parameters by up to two thousand times compared to no optimization. Motion estimation prefers large neural networks for all sea states, while at least three layers of neural networks are needed for accurate parameter identification. The paper also provides a look-up table to investigate further implementing PINN on moored floating offshore structures. Proper selection of HPs is crucial as it can incur up to three orders of magnitude PINN loss and exceedingly-high identification error. Overall, this study highlights the applicability of PINN in modeling complex offshore structures and provides insights into selecting optimal HPs for accurate and efficient estimation of motion and system parameters.

High-Speed Maneuvering Target Inverse Synthetic Aperture Radar Imaging and Motion Parameter Estimation Based on Fast Spare Bayesian Learning and Minimum Entropy

High-speed maneuvering target inverse synthetic aperture radar (ISAR) imaging is always a hot topic in signal processing. High-speed maneuvering targets often have high-order maneuvering characteristics, such as translational and rotational characteristics, which destroy the signal structure of stationary targets and make basic imaging processing methods such as range-Doppler (RD) algorithm no longer suitable. In this paper, a high-resolution imaging method for high-speed maneuvering targets is proposed, which uses the fast sparse Bayesian learning (SBL) algorithm and the minimum entropy algorithm for ISAR high-resolution imaging and motion parameter estimation, respectively. Because SBL makes full use of the characteristics of the target and the environment, it can obtain an ISAR high-resolution image of the maneuvering target. However, the high computational complexity caused by matrix inversion and some matrix operations in SBL iteration limit the practical application of SBL in ISAR imaging. In view of the special structure of the matrix required to be inverted, we propose a fast SBL algorithm, which uses a new decomposition method to obtain the decomposition formula of the inverse matrix. Based on the decomposition factors, the multiplication operation involving the inverse matrix can be quickly calculated using fast Fourier transform (FFT), which greatly improves the computational efficiency. Image entropy represents the sharpness and focusing degree of an image, and so the minimum entropy algorithm can estimate the motion parameters of maneuvering targets more accurately. We combine the minimum entropy algorithm with the fast SBL algorithm to realize phase error correction and high-resolution imaging, which has better noise sensitivity and can obtain the best focusing degree image. Finally, simulation results prove the effectiveness of this algorithm.

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.

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.

A fast and robust detection and estimation method for weak multitargets with complex motions

To address the range cell migration (RCM) and Doppler frequency migration (DFM) effects of maneuvering targets with complex motions during coherent integration times, this paper proposes a method to detect and estimate multitargets based on the full-range bandwidth reversal function (FRBRF) and scaled integrated trilinear autocorrelation function (SITAF). The FRBRF is first introduced to construct a new signal by multiplying the echo with the reversal of its own echo; after this, the range envelope of the echo is blindly aligned. Then, the SITAF is proposed to accumulate the energy of the constructed signal and complete motion parameter estimation. Compared with several existing methods, the proposed algorithm shows better antinoise ability and estimation performance; furthermore, it is computationally efficient and can be easily implemented by using complex multiplication, the fast Fourier transform (FFT) and the inverse FFT. In addition, generalized detection ability for various motion patterns is achieved by adjusting the zoom factors. Performance analysis shows that the proposed method can achieve a good balance among the computational cost, antinoise performance, detection ability and estimation performance. Finally, several simulation experiments and real dataset experiments are presented to verify the effectiveness of the proposed method.