In passive localization, the synthetic aperture positioning (SAP) method can achieve high precision and high-resolution positioning. However, existing research neglects the issue of target adaptability. For radar emitter targets, receivers can only periodically capture signals when the emitter’s beam scans toward the receiving antenna, resulting in spectral aliasing of the received signals. This leads to multiple false targets in localization images and reduced accuracy. This study employs the Fractional Fourier Transform (FrFT) integrated with compressed sensing for continuous signal reconstruction, aiming to eliminate spurious targets and enhance positioning accuracy. Initially, spectral aliasing is suppressed through FrFT, capitalizing on the approximately linear frequency-modulated (LFM) characteristics inherent in Doppler signals. Subsequently, continuous signal is reconstructed using compressed sensing with FrFT basis vectors forming the sensing matrix. Finally, the SAP method is implemented to achieve precise positioning. The effectiveness of the proposed method has been validated through simulations and Unmanned Aerial Vehicle (UAV) experiments, demonstrating that it significantly enhances the adaptability of SAP methods to radar emitter targets.

In passive localization, the synthetic aperture positioning (SAP) method enables high-precision positioning under low signal-to-noise ratio (SNR) conditions. However, higher-order phase errors induced by platform self-localization errors degrade image focusing and reduce localization accuracy. In this paper, a polynomial fitting approach based on designing optimal pre-whitening filters using autoregressive models and employing iteratively reweighted least squares (IRLS) is applied to the unwrapped phase to eliminate higher-order error components. Additionally, a multiple sub-aperture phase stitching method is proposed to mitigate phase susceptibility to noise interference and error accumulation during phase unwrapping. The effectiveness of the proposed method is validated through both simulations and UAV experiments. Results demonstrate that meter-level localization accuracy can be achieved for the emitter target.

This letter studies the issue of robust multitask distributed estimation under the error-in-variable (EIV) model where input noise and output impulsive noise are considered. In such cases, existing distributed algorithms suffer from severe performance degradation. To tackle this problem, a robust multitask diffusion bias-compensated least mean M-estimate (R-MD-BCLMM) is proposed. We adopt a new real-time input noise variance estimation method which utilizes piecewise linearity of the modified Huber function to resist input noises. To further improve network information exchange capability and estimation performance, a robust spatial average combination based multitask adaptive clustering strategy is proposed. Finally, simulations demonstrate that the proposed R-MD-BCLMM algorithm outperforms some state-of-the-art distributed algorithms.

In emitter localization, the synthetic aperture positioning technique can achieve high-precision positioning even at a low signal-to-noise ratio (SNR). However, existing methods overlook the impact of receiver motion errors on the phase history of the received signal, leading to a reduction in localization accuracy. In this study, we propose a motion compensation (MoCo) technique for synthetic aperture passive localization using weather radar signals. Weather radar stations are chosen as reference stations due to their widespread coverage, high transmission power, and continuous signal transmission. The proposed method involves estimating and compensating for phase errors in the received signal, enabling phase coherency accumulation and achieving high-precision emitter localization. First, pulse compression is applied to the received weather radar signals to extract the phase information containing motion error details. Subsequently, we estimate motion errors using the extracted radar signal phase and apply phase compensation to the emitter target signal. Finally, the existing synthetic aperture positioning method is used to estimate the position of the target. Simulation results demonstrate that the method proposed in this paper offers superior accuracy in emitter localization compared to relying solely on real-time kinematic (RTK) for MoCo. The effectiveness of our proposed method is validated through actual unmanned aerial vehicle (UAV) experiments.

In emitter localization, the synthetic aperture positioning (SAP) technique can achieve high-precision positioning even at a low signal-to-noise ratio (SNR). However, existing methods require 2-D search implementation, which produces a huge amount of computation. In this study, the synthetic aperture map drift (MD) positioning method aided by an interferometer is proposed. This method reduces the amount of computation while achieving high-precision positioning. First, the exact azimuth position and approximate range position can be determined by a double-interference antenna via least-squares estimation. Doppler history is then used to correct range positioning error via an MD algorithm, which avoids the search of range and reduces the computational complexity. Simulation results show that the positioning accuracy of this method is close to the Cramer–Rao lower bound (CRLB). The effectiveness of the proposed method is verified through actual unmanned aerial vehicle (UAV) experiments.

Emitter localization has been an active research subject in electronic reconnaissance, target tracking, emergency response, and satellite interference source localization. Recently, researchers applied passive synthetic aperture in the emitter localization to improve the positioning accuracy. Passive synthetic aperture uses Doppler rate and zero Doppler point to target range and azimuth locations, respectively. In spaceborne model, effective satellite velocity is used in the range equation to fit the passive synthetic aperture model. Therefore, this study proposed a convex optimization approach to calculate the effective satellite velocity. We established an objective function by calculating the relationship among beam footprint velocity, satellite velocity, and effective satellite velocity. The optimal effective satellite velocity and range distance are obtained through iterating different range distances. Finally, the experimental results show that the positioning accuracy of proposed method is one order of magnitude higher than that of traditional FOA and FDOA method.

Geospatial object detection (GOD) of remote sensing imagery has been attracting increasing interest in recent years, due to the rapid development in spaceborne imaging. Most of the previously proposed object detectors are very sensitive to object deformations, such as scaling and rotation. To this end, we propose a novel and efficient framework for GOD in this letter, called Fourier-based rotation-invariant feature boosting (FRIFB). A Fourier-based rotation-invariant feature is first generated in polar coordinate. Then, the extracted features can be further structurally refined using aggregate channel features. This leads to a faster feature computation and more robust feature representation, which is good fitting for the coming boosting learning. Finally, in the test phase, we achieve a fast pyramid feature extraction by estimating a scale factor instead of directly collecting all features from the image pyramid. Extensive experiments are conducted on two subsets of NWPU VHR-10 data set, demonstrating the superiority and effectiveness of the FRIFB compared to the previous state-of-the-art methods.

The problem of finite impulse response (FIR) filtering in errors‐in‐variables (EIV) system is studied. Due to the input noise, traditional recursive least‐squares (RLS) algorithms are biased in EIV system. Most existing bias‐compensated approaches are proposed in the case that both the input–output noises are white Gaussian random processes. However, taking account of the situation where the output is corrupted by coloured noise, there are rare existing algorithms work well. Two bias‐compensated RLS algorithms with acceptable computational complexity are proposed, which can obtain unbiased real‐time filtering in non‐stationary system when the input noise is white while the output noise is coloured. Under the assumption that the input signal is a coloured process, linear prediction technique is used to estimate the sample of the input signal. Exploiting the statistical properties of the cross‐correlation function between the least‐squares error and the forward/backward prediction error, the input noise variance can be estimated and the bias can be compensated. Simulation results illustrate the good performance of the proposed algorithms.

Fast acquisition in space telemetry and telecontrol communication system is challenged significantly by the high dynamic and low signal‐to‐noise ratio. Increasing the dwell time to obtain better acquisition sensitivity, based on two‐dimensional time‐frequency search, is impossible because of resource limitation in receiver. To tackle these problems, this study proposes a two‐stage differential acquisition (TSDA) algorithm. The differential coherent integration is employed by the first stage of TDSA to extend integration time, during which keystone transform and fast Fourier transform are used to compensate the linear code phase drift and obtain high accumulation gain. The carrier‐frequency offset is estimated in terms of the code phase difference between the two parts of received signal divided by the second stage of TSDA in which the two‐dimensional searching process is avoided. The proposed TSDA algorithm and the traditional acquisition methods are compared under the same acquisition time and typical parameters of S‐band space telemetry and telecontrol communication system. Simulation results demonstrate that the proposed TSDA algorithm attains a higher acquisition probability and better acquisition sensitivity than the traditional acquisition methods.

This study exploits wireless channel response and fractional Fourier transform (FrFT) to achieve anti‐eavesdropping downlink transmission over a multipath channel. The proposed system works in time‐division duplexing mode, and only the transmitter knows the main channel response through uplink services. With the use of the main channel information, a time‐varying spread‐spectrum orthogonal frequency division multiplexing (TS‐OFDM) subsystem is proposed to realise confidential transform order (TO) transmission, and a security‐enhanced FrFT‐OFDM (SE‐FrFT‐OFDM) subsystem is presented for high‐rate data transmission. The optimal power allocation algorithms that optimise the average secrecy outage capacity of the TS‐OFDM subsystem and the bit error rate performance of the SE‐FrFT‐OFDM subsystem are also provided. Given channel reciprocity and spatial decorrelation, the legitimate user can achieve optimal anti‐multipath fading performance, but the intercepted data symbols will be randomised by both channel fading and TO deviations. To avoid randomisation, the eavesdropper has to test all possible TO combinations of multiple SE‐FrFT‐OFDM symbols, which is usually an impractical task. Compared to other typical methods, the transmitting power of the proposed system can be used more efficiently because the data symbol is not transmitted along with additional interference. Computer simulations are carried out to validate this scheme.

With the explosive growth of video data, managing and browsing videos in a timely and effective manner has become an urgent problem, particularly in surveillance applications. Video summarization as a feasible solution is considerably attracting more attention. In this paper, we propose a novel motion-state-adaptive video summarization method based on spatiotemporal analysis. To overcome the low efficiency of traditional video summarization, the proposed method utilizes spatiotemporal slices to analyze object motion trajectories and selects motion state changes as a metric to summarize videos. Initially, a motion-active segment is detected using motion power. Subsequently, motion state changes are modeled as a collinear segment on a spatiotemporal slice (STS-CS) and an attention curve based on the STS-CS model is formed to extract the key frames. Finally, a visually distinguishing mechanism is employed to refine the key frames. The experimental results demonstrate that the proposed method outperforms the existing state-of-the-art methods in terms of both computational efficiency and detailed video motion dynamic maintenance. This is accomplished with a comparable subjective performance.

Signal reconstruction from non‐uniform samples, especially for non‐stationary signals, is an important issue in the area of digital signal processing. As a type of signal processing tool, the fractional Fourier transform has been proved to be effective for solving problems in non‐stationary signal processing. For non‐stationary discrete‐time signals, the reconstruction of uniformly sampled signals from non‐uniform samples in the fractional Fourier domain is first derived in this study. Since only finite non‐uniform samples are collected in practical applications, for preferable reconstruction, two types of symmetric extensions are considered in the reconstruction to overcome the discontinuity problem that exists in the periodisation of short non‐stationary sequences, which is more critical than that of long sequences. In addition, the average signal‐to‐noise ratio is used to evaluate the performance of the reconstruction with two types of symmetric extensions. Simulations and two applications are given to verify the effectiveness of the proposed reconstruction method.

High-resolution inverse synthetic aperture radar (ISAR) imaging of a ship target is a challenging task because of fluctuation with the ocean waves. The images obtained with a standard range-Doppler algorithm are usually blurred. Consequently, the range-instantaneous-Doppler (RID) technique should be used to improve the image quality. In this paper, the received signal in a range cell is modeled as a multicomponent quadratic frequency-modulated (QFM) signal after range compression and motion compensation, and then a new RID ISAR imaging algorithm is proposed that introduces a new method for estimating parameters of the QFM signal. By defining a new function and using the scaled Fourier transform (SCFT) with respect to the time axis, the coherent integration of auto-terms can be realized via the subsequent Fourier transformation with respect to the lag-time axis, and a peak can be obtained in the 2-D frequency plane, which is appropriate for parameter estimation of the QFM signal to reconstruct RID images. The proposed algorithm is accurate and fast since the defined function has moderate order nonlinearity and the SCFT can be performed via chirp z-transform. Experiments demonstrate the performance of the new algorithm. Comparisons with existing algorithms are also given, which show that the proposed algorithm can efficiently produce a focused image with less fake scatterers.

The ambiguity function (AF) as an important tool for time–frequency analysis, has widely been used in radar signal processing, sonar technology and so on. It does well in analysing chirp signals. However, it fails in estimating the cubic phase (CP) signal, which is required in many applications. As the generalisation of the Fourier transform (FT), the linear canonical transform (LCT) has received much attention, and has found many applications in filter design, pattern recognition, optics and so on. In this study, the authors define a new kind of AF – the AF based on the LCT (LCTAF), which is proposed to estimate the CP signal. Some important properties of LCTAF are discussed, such as symmetry and conjugation property, shifting property and Moyal formula. The relationships between the LCTAF and other time–frequency analysis distributions are derived, including the classical AF, the Wigner distribution function (WDF) based on LCT, the short-FT and the wavelet transform. The linear canonical AF (LCAF) is another kind of AF. The authors also discuss its relation with AF and WDF and give some new properties of the LCAF. At last, the LCTAF is applied for estimating the CP signal. The simulation indicates that the LCTAF is useful and effective.

Contourlets have been attracting increasing attention in despeckling of synthetic aperture radar (SAR) images in recent years. However, contourlets produce undesirable artifacts while despeckling. This letter presents a novel contourlet-based regularization method to remove speckle without introducing extra artifacts. In this method, a nonlocal regression function is constructed for the regularization term through patch weighting on the contourlet reconstruction. Moreover, by employing the intrinsic dependence of contourlet coefficients, a parameterized shrinkage algorithm is proposed to resolve the contourlet reconstruction. This contourlet despeckling method enables significant elimination of speckle and resultant artifacts with well-protected strong scatters and structures of the scene. Experiments demonstrate such superiority on real SAR images.

A recent letter proposed a new convolution structure for the linear canonical transform, and claimed that theirs was clearly easier to implement in the designing of filters than the one suggested earlier in. However, we find that the two kinds of filtering methods are essentially the same through the theoretic deduction. That is to say, the two kinds of filtering methods can obtain the same effect through the same filtering steps. Taking digital signal processing into account, we analyze further the computation complexity according to the steps of multiplicative filter.

The original information in the existing security system based on the fractional Fourier transform (FRFT) is essentially protected by only a certain order of FRFT. In this paper, we propose a novel method to encrypt an image by multiorders of FRFT. In the image encryption, the encrypted image is obtained by the summation of different orders inverse discrete FRFT of the interpolated subimages. And the original image can be perfectly recovered using the linear system constructed by the fractional Fourier domain analysis of the interpolation. The proposed method can be applied to the double or more image encryptions. Applying the transform orders of the utilized FRFT as secret keys, the proposed method is with a larger key space than the existing security systems based on the FRFT. Additionally, the encryption scheme can be realized by the fast-Fourier-transform-based algorithm and the computation burden shows a linear increase with the extension of the key space. It is verified by the experimental results that the image decryption is highly sensitive to the deviations in the transform orders.

In this letter, we generalize the fractional Hilbert transform of a real signal to get an analytic version which contains no negative spectrum while maintaining the essential information of the real signal. We also present a secure single-sideband (SSB) modulation system in which the angle of the fractional Fourier transform and the phase of the fractional Hilbert transform are used as double keys for demodulation.