Three-dimensional (3-D) imaging plays a vital role in the recognition of spinning space debris. However, the image may be blurred due to the range migration caused by fast rotation of space debris. Moreover, the image quality, which depends on the estimation accuracy of Doppler frequency and chirp rate of scattering centers, is influenced by cross-terms and sidelobes. In this paper, we propose a novel 3-D imaging method based on smoothed Lv distribution (SLVD). Firstly, the selection criterion for best imaging time based on the time-frequency moment is proposed to guarantee that the echo is approximated as a linear frequency modulation signal. Then, we operate the Khatri-Rao product on the centroid frequency and chirp rate (CFCR) representation and the range-Doppler (RD) image to obtain the 3-D image. To decrease the influence of range migration, we process a short time window during the RD imaging procedure. For cross-term and sidelobe suppression, the SLVD is proposed to obtain the CFCR representation by expressing the Lv distribution (LVD) in a convolution form and introducing a centroid frequency window. Experimental results verify the effectiveness of the proposed imaging method and the good performance of the proposed SLVD for cross-term and sidelobe suppression.

Smoothed Lv Distribution based Three-dimensional Imaging for Spinning Space Debris

As more and more satellites are launched into the space, dynamic estimation of spin satellites has become a critical component of the space situation awareness application. Some explored studies using exterior measurements from different sensors such as optical device and inverse synthetic aperture radar (ISAR) to estimate dynamic parameters of spin satellites. As a single sensor normally provides two-dimensional observation, three-dimensional estimations resulting from these algorithms are strictly related to the prior knowledge of targets characteristics. As a result, it is difficult to expand these methods to other satellites. In order to support the dynamic estimation of most spin satellites, this paper presents a novel dynamic estimation approach which employs synchronized optical-and-radar images. The optical-and-radar fusion strategy has demonstrated its superiority in image analysis field, and breaks down the dynamic estimation of spin satellites into two sub-problems: target attitude estimation and spin parameters estimation. In this work, the proposed algorithm deduces two explicit expressions of target dynamic parameters under the imaging projection model of the joint optical-and-radar observation. Through the particle swarm optimization (PSO), target dynamic parameters are determined in two stages. This paper presents some experiments illustrating the feasibility of the proposed method and subsequent conclusions, which reflect advantages of the joint optical-and-radar observation mode in image interpretation.

Optical-and-Radar Image Fusion for Dynamic Estimation of Spin Satellites

A software defect report is a bug in the software system that developers and users submit to the software defect library during software development and maintenance. Managing a software defect report that is overwhelming is a challenging task. The traditional method is manual identification, which is time-consuming and laborious and delays the repair of important software defects. Based on the above background, the purpose of this paper is to study the software defect prediction (SDP) model based on LASSO–SVM. In this paper, the problem of poor prediction accuracy of most SDP models is proposed. A SDP model combining minimum absolute value compression and selection method and support vector machine algorithm is proposed. Firstly, the feature selection ability of the minimum absolute value compression and selection method is used to reduce the dimension of the original data set, and the data set not related to SDP is removed. Then, the optimal value of SVM is obtained by using the parameter optimization ability of cross-validation algorithm. Finally, the SDP is completed by the nonlinear computing ability of SVM. The accuracy of simulation results is 93.25% and 66.67%, recall rate is 78.04%, and f-metric is 72.72%. The results show that the proposed defect prediction model has higher prediction accuracy than the traditional defect prediction model, and the prediction speed is faster.

Software defect prediction model based on LASSO–SVM

Dynamic estimation of spin spacecraft is a challenge and plays a significant role in space situation awareness applications like potential space collision warning. Based on remote sensing technologies of laser and radar sensors, current methods almost adopt a match strategy to estimate the dynamic parameters of a particular target with the long-term measurement collection. These kinds of data-driven methods merely consider the inherent connection between the measured characters and target dynamic patterns, and can hardly be expanded to other spacecraft when the measurement collection is insufficient. Therefore, this article presents a novel approach to interpreting multiple-station inverse synthetic aperture radar (ISAR) images for the dynamic estimation of spin spacecraft. As a unique phenomenon of radar imaging, the imaging plane of ISAR observation not only depends on the change of the relative position between the target and radar, but also changes with the spin of the target. In order to decouple the target dynamic estimation from the determination of the imaging geometry, the angular diversity of multiple-station images is employed. The proposed algorithm deduces an explicit expression of target dynamic parameters under the imaging projection model of the multiple-station observation. By utilizing the chaotic grasshopper optimization algorithm (CGOA), it determines three crucial elements of the target spin motion with a two-step optimization, including instantaneous attitude, rotation shaft and rotation speed. Simulation experiments of a typical spin spacecraft, Tiangong-I (TG-I), illustrate the feasibility of the proposed method under different motion patterns.

Dynamic Estimation of Spin Spacecraft Based on Multiple-Station ISAR Images

An echo signal received from a cone-shaped target with micro-motion is composed of a linear mixture of individual signals radiated from multiple effective scatterers with the occlusion effect, resulting in difficulties in parameter estimation for ballistic target discrimination (BTD). To solve this, conventional methods have been based on the sophisticated signal decomposition techniques using a 2D joint time–frequency (JTF) image or a 2D radial-range (RR) history image; however, they are inefficient for real-time BTD due to complex 2D image processing. Therefore, we propose a new parameter estimation framework consisting of five stages: 1) a normalization step; 2) signal decomposition and data association using independent component analysis in the distributed radar network; 3) estimation of dynamic parameters using 1D micro-Doppler frequency trajectories; 4) restoration of 1D RR histories; and 5) estimation of geometric parameters using the restored 1D RR histories. In particular, ICA of stage 2 is more time-saving than the conventional mathematical model-based methods using the 2D JTF image due to signal decomposition using the 1D normalized echo signals. Moreover, in the stage 4, high-quality 1D RR histories can be restored in spite of using the 2D RR history image with low resolution, compared with the conventional methods using 2D RR history image of very high resolution. In the simulations, we observed that our proposed framework is capable of performing efficient parameter estimation for the real-time BTD.

Efficient Parameter Estimation for Cone-Shaped Target Based on Distributed Radar Networks

Sparse Doppler-only snapshot imaging for space debris

The invention discloses a sparse reconstruction-based broadband radar high-speed group-target resolving method, which comprises the following steps: 1, keystone transformation is carried out on broadband radar echo signals of a space high-speed group-target, keystone transformation is realized through chirp-z transformation, and a discrete spectrum SCZT (m, n) of the mth broadband radar echo signal of the space high-speed group-target in a Doppler ambiguity-existing range frequency domain is obtained; 2, a relationship between an observation data matrix XCZT and a range Doppler two-dimensional complex amplitude matrix GMN of the space high-speed group-target is deduced; 3, a relationship between the observation data matrix XCZT and a range Doppler two-dimensional complex amplitude matrix G'(M*L)N of the high-speed group-target between space and time with different Doppler ambiguity times is deduced; 4, a problem of detecting and resolving the high-speed group-target between space and time with different Doppler ambiguity times is converted into a sparse optimization problem, and the range Doppler two-dimensional complex amplitude matrix G'(M*L)N of the high-speed group-target between space and time with different Doppler ambiguity times is obtained; and a range Doppler plane of the space high-speed group-target is drawn, and coherent accumulation and resolution of the space high-speed group target can be realized.

Sparse reconstruction-based broadband radar high-speed group-target resolving method

The occlusion effect of targets with the spinning motion is usually ubiquitous when illuminated by the radar. Considering this effect in a single range Doppler imaging for spinning targets is of practical significance. In this paper, we develop a novel approach to image spinning targets with occlusion effect, which is referred to as a fused-Lasso-based Doppler-only snapshot imaging. Due to the spinning motion, the radar illuminates different parts of the target at each observation instant, which causes the backscattering intensities of the scatterers, are slowly time-varying. The 2D fused-Lasso model is introduced to capture this time-varying characteristic. Furthermore, the underlying factors for the imaging performance are thoughtfully analyzed. The proposed method is able to adaptively estimate the shadowed region, do Doppler imaging, and work well in low radar pulse repetition frequency situations. Finally, a series of simulations is carried out to validate the performance of the proposed method.

A Fused-Lasso-Based Doppler Imaging Algorithm for Spinning Targets With Occlusion Effect

The invention discloses a sparse Doppler imaging method suitable for a rotating target with a shielding effect, which comprises the following steps: firstly, establishing a time-varying radar echo model for the rotating target with the shielding effect; performing sparse signal expression on the time-varying radar echo model for the rotating target with the shielding effect; then, according to the form of the sparse signal expression of the time-varying radar echo model, converting the imaging process of the rotating target with the shielding effect to the sparse optimization process of a two-dimensional Fused Lasso model, and furthermore solving the sparse optimization process of the two-dimensional Fused Lasso model by means of a convex optimization toolkit CVX, and obtaining an estimation matrix B of a sparse backward scattering intensity matrix B; and finally, acquiring the maximum value of each line in the estimation matrix B for forming an equivalent backward scattering intensity vector, namely imaging is realized.

Sparse Doppler imaging method suitable for rotating target with shielding effect

Nutation and precession parameter estimation is of great importance for attitude estimation of spin-stabilized space targets. In this paper, we propose a novel method to estimate the nutation and precession parameters of a rigid-body object from the one-dimensional high-resolution radial-range measurements. First, we elaborately derive the kinematic equations and one-dimensional radial-projection model of the precession-with-nutation object, where fixed-point and slipping scatterers are separately taken into account. Second, by using the radial-range trajectories of multiple scatterers, we employ the factorization-based algorithm to obtain the motion reconstruction. Third, we estimate the nutation and precession parameters based on the reconstructed motion and the spectrum analysis of the associated trajectories. Moreover, the l1-norm-based one-dimensional trajectory-recovering technique is developed to deal with the incomplete radial-range trajectories caused by the shadowing effect, specularity, and so on. Finally, experiments are carried out on the electromagnetic analysis data to verify the proposed model and parameter-estimation method.

Motion-Parameter Estimation for precession-with-Nutation Space Targets

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