In this article, the efficient sparse Bayesian learning (SBL)-based 2-D joint high-resolution inverse synthetic aperture radar (ISAR) imaging approach with random missing observations in both the range-frequency and slow-time domains caused by frequency agility and pulse repetition interval (PRI) jitter is proposed. First, the target return signal model containing the translational motion caused envelope migration and phase error and rotation caused range spatial-variant phase error (RSVPE) with 2-D randomly missing observations is established. Next, considering the rotation caused RSVPE needs to be estimated and compensated for each range cell individually in the range domain, the modified conditional mean estimator-based missing observations recover method and its fast implementation method based on fast Fourier transform (FFT) is designed. Following, the SBL-based cyclic iteration approach is proposed to recover missing observations, estimate target motion parameters and compensate for the translational motion and RSVPE, and achieve the focused and cross-range scaled ISAR image. In addition, to alleviate the computational complexity increase caused by data filling for SBL, a novel low cyclic displacement rank decomposition (LCDRD) for the Toeplitz-block-Toeplitz (TBT) structured covariance matrix of the completed observations in SBL is proposed and applied to design efficient SBL-based ISAR imaging algorithms for two different types of observations. Finally, the effectiveness of the proposed algorithms is validated using both simulated and measured data.

In this article, the problem of inverse synthetic aperture radar (ISAR) high-resolution imaging and cross-range scaling with periodically gapped coherent processing interval (CPI) caused by the radar performing multiple tasks time divisionally is addressed. In the case of periodically gapped CPI, the traditional fast Fourier transform (FFT) based ISAR imaging method is no longer applicable, and sparse reconstruction is an effective approach to solve this problem. Sparse Bayesian learning (SBL) is the most robust and accurate reconstruction method among all sparse reconstruction algorithms, and it is also an implementation of optimal estimation of the random signal model under the minimum mean square error (MMSE) criterion. Based on the fact that the noise variance of radar observation can be estimated with secondary data, and the amplitudes of the target scatterers can be regarded as unknown deterministic variables, we propose another implementation method for the MMSE estimator, i.e., iterative Wiener filter (IWF), for ISAR imaging and cross-range scaling of periodically gapped data. Compared with SBL, the proposed method has the advantages of lower computational complexity, faster convergence, and higher reconstruction accuracy. Further, we design two fast IWF algorithms based on the triangular-circulant low displacement rank decomposition by utilizing the Toeplitz-block-Toeplitz (TBT) structure, in which almost all operations except matrix decomposition can be calculated using FFT, which can efficiently and accurately process two different types of periodically gapped echo data. Finally, the performance of the algorithm was verified with both simulation and measured data.

For multifunctional phased array radar systems, inverse synthetic aperture radar (ISAR) imaging typically requires multidwell coherent processing to achieve adequate cross-range resolution. In such cases, the traditional fast Fourier transform (FFT)-based Doppler processing method can result in grating lobes in the cross-range dimension. Additionally, the range resolution is insufficient when the radar transmission bandwidth is relatively narrow. To address these two issues, this article proposes a fast sparse Bayesian learning (SBL)/iterative Wiener filter (IWF)-based 2-D joint super-resolution ISAR imaging method, which enhances the resolution in both range and cross-range dimensions while suppressing grating lobes. The proposed fast SBL and IWF algorithms incorporate the lower-triangular-Toeplitz-cyclic (LC) decomposition of the unfolded fourth-order Toeplitz tensor of the covariance matrix. Except for the LC decomposition, all operations utilize the FFT, allowing for efficient, precise, and memory-efficient processing of two types of multidwell observations. Furthermore, during image reconstruction, the target’s rotational velocity is estimated using the minimum entropy criterion, thereby achieving range-variant autofocus and 2-D super-resolution ISAR imaging. Finally, simulated and measured data are employed to validate the effectiveness of the proposed algorithms.

Sparse aperture (SA) autofocusing and imaging is a hot research problem in the signal processing field and has been widely used. Under SA, the absence of echoes destroys the coherence between the pulses, which then affects the autofocusing accuracy of the imaging, leading to defocus of the image. In this article, a novel SA autofocusing and imaging algorithm based on sparse Bayesian learning (SBL) is proposed, which uses a fast SBL algorithm to achieve SA high-resolution imaging and the minimum Tsallis entropy algorithm to realize autofocusing. As is known to all, SBL has strong robustness and high precision. Unfortunately, the direct calculation of the inversion and multiplication operations involved in each iteration of SBL results in significant computational costs. In the proposed fast SBL algorithm, the matrix required to be inverted has a special structure. The inverse matrix can then be represented by Gohberg–Semencul (G–S) factorization. Also, almost all operations except for G–S factorization during each iteration can be completed by fast Fourier transform (FFT) or inverse FFT (IFFT), which greatly reduces the amount of computation by several orders of magnitude. In each SBL iteration, the minimum Tsallis entropy algorithm is used for estimating the phase error, which has better noise sensitivity and obtains the images with the best focused degree. Finally, the effectiveness and high efficiency of the proposed fast algorithm are verified by experimental results obtained by simulation and measured data.

In micromotion feature extraction, the incomplete and phase-corrupted radar echo may cause bad time–frequency representation (TFR) and prevent micromotion feature extraction. To solve the problem, we establish a sparse regularization model to reconstruct well-focused TF distributions. The regularization model is solved by the iterative soft-thresholding algorithm (ISTA). In each iteration, the hard thresholding function and least-square-error criterion are developed to estimate the phase errors. For micro-Doppler signal real-time processing to save radar time resources, the received signal can be directly sparse recovered in real time rather than waiting for the complete signal. Finally, the effectiveness of the proposed method is validated by the simulation results.

Precession of the cone-shaped warhead is the typical micromotion of ballistic targets, and 3-D inverse synthetic aperture radar (ISAR) imaging of the precession warhead is of great significance for ballistic target identification. This letter proposes a novel method for the precession parameter estimation and the 3-D ISAR imaging of the cone-shaped target. First, the imaging model of the precession cone-shaped target is developed, and the relationship between the radial-range curve on the range–slow-time plane and the precession parameters is derived. Subsequently, the wideband measurements from two-aspect radars are jointly processed to solve the target precession parameters implicitly involved in the radial-range curve of the scatterer at the cone top. Finally, based on the estimation of precession parameters, the 3-D images of the target can be reconstructed, which reveal the structure characteristics and spatial attitude of the target. Simulation results verify the effectiveness of the proposed method.

Interferometric inverse synthetic aperture radar (InISAR) has proven to be an effective tool for 3-D imaging of noncooperative targets. The traditional InISAR imaging algorithms are almost entirely based on the assumption of a constant amplitude polynomial phase signal (PPS) model. However, target’s maneuverability tends to cause the echo signal to exhibit the characteristic of time-varying amplitude (TVA) in practice. To remedy this problem, a novel InISAR imaging algorithm for maneuvering targets based on quadratic frequency modulated (QFM) signal model with TVA is presented. First, the echo of each range cell is modeled as a multicomponent TVA-QFM signal. Then, through the matrix derivation, the parameter estimation problem of this signal is converted to a convex optimization problem. Subsequently, with the help of the scaled Fourier transform (SCFT), an efficient iterative update approach based on alternative direction method of multipliers (ADMM) framework is proposed to solve this optimization problem. Furthermore, associated with the range instantaneous Doppler (RID) method and multichannel interference technology, 2-D ISAR images and 3-D space shape of the target can be generated. Finally, some simulation results are provided to evaluate the effectiveness and robustness of the proposed algorithm.

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.

Sheu and Chang (IEEE Trans. Rel., vol. 58, no. 2, pp. 397-404, 2009) presented an interesting extended periodic imperfect preventive maintenance (EPIPM) model for a system with age-dependent failure type. Many cases studied previously are special cases of the EPIPM model. In the Errata (IEEE Trans. Rel., vol. 60, no. 2, 2011), Sheu and Chang showed that the proposed effective age and the proposed hazard rate function after the PM are incorrect. In this paper, based on the correct failure characteristics (effective age and hazard rate function after PM), the corrects-expected total cost per unit time for the EPIPM model is presented. By assigning three types of failure characteristics for the EPIPM model, we analyse and compare the correspondings-expected total costs per unit time. We find that thes-expected total cost per unit time developed by Sheu and Chang (IEEE Trans. Rel., vol. 58, no. 2, pp. 397-404, 2009) is only one upper bound of the exacts-expected total cost per unit time. In addition, we also give some results on the existence of the optimal solution for the exacts-expected total cost.

Manufacturing systems run in time-varying environmental and operational conditions. For the effective manager to make a long-term preventive maintenance decision, it is necessary to integrate the time-varying environment into preventive maintenance (PM) policies. This paper considers PM for systems running in the time-varying environment, modeled as a two-state homogeneous Markov process, where one state represents a typical condition, and the other represents a severe condition. Environmental conditions affect the hazard rate function through a proportional hazard model. To avoid sudden failures in a system due to either minor failures or catastrophic failures, an extended periodic imperfect preventive maintenance model is carried out, and the maintenance effect is modeled with an age reduction factor, and a hazard improvement factor. We prove the discontinuity of the hazard rate function of the system in a time-varying environment through a Markov additive process. We also give a method to compute the probability density function of failure at any time. Further, the$s$-expected cost rate of the system in the time-varying environment is compared with the$s$-expected cost rates of the system always working in typical, and severe conditions. Finally, numerical examples fully verify our main results.

An error in the above titled paper (ibid., vol. 58, pp. 397-405, Jun 2009) is pointed out and a revision is presented here.