Thinning of antenna arrays has been a popular topic for the last several decades. With increasing computational power, this optimization task acquired a new hue. This paper suggests a genetic algorithm as an instrument for antenna array thinning. The algorithm with a deliberately chosen fitness function allows synthesizing thinned linear antenna arrays with low peak sidelobe level (SLL) while maintaining the half-power beamwidth (HPBW) of a full linear antenna array. Based on results from existing papers in the field and known approaches to antenna array thinning, a classification of thinning types is introduced. The optimal thinning type for a linear thinned antenna array is determined on the basis of a maximum attainable SLL. The effect of thinning coefficient on main directional pattern characteristics, such as peak SLL and HPBW, is discussed for a number of amplitude distributions.

Jamming suppression is traditionally achieved through the use of spatial filters based on array signal processing theory. In order to achieve better jamming suppression performance, many studies have applied blind source separation (BSS) to jamming suppression. BSS can achieve the separation and extraction of the individual source signals from the mixed signal received by the array. This paper proposes a perspective to recognize BSS as spatial band-pass filters (SBPFs) for jamming suppression applications. The theoretical derivation indicates that the processing of mixed signals by BSS can be perceived as the application of a set of SBPFs that gate the source signals at various angles. Simulations are performed using radar jamming suppression as an example. The simulation results suggest that BSS and SBPFs produce approximately the same effects. Simulation results are consistent with theoretical derivation results.

Most of the existing direction of arrival (DOA) estimation algorithms are applied under the assumption that the array manifold is ideal. In practical engineering applications, the existence of non-ideal conditions such as mutual coupling between array elements, array amplitude and phase errors, and array element position errors leads to defects in the array manifold, which makes the performance of the algorithm decline rapidly or even fail. In order to solve the problem of DOA estimation in the presence of amplitude and phase errors and array element position errors, this paper introduces the first-order Taylor expansion equivalent model of the received signal under the uniform linear array from the Bayesian point of view. In the solution, the amplitude and phase error parameters and the array element position error parameters are regarded as random variables obeying the Gaussian distribution. At the same time, the expectation-maximization algorithm is used to update the probability distribution parameters, and then the two error parameters are solved alternately to obtain more accurate DOA estimation results. Finally, the effectiveness of the proposed algorithm is verified by simulation and experiment.

According to the measurement principle of the traditional interferometer, a narrowband signal model is established and used, however, for wideband signals or multiple signals, this model is invalid. For the problems of direction finding with interferometer for wideband signals and multiple signals scene, a frequency domain phase interferometer is proposed and the concrete implementation scheme is given. The proposed method computes the phase difference in frequency domain, and finds multi-target results with judging the spectrum amplitude changing, and uses the frequency phase difference to compute the arrival angle. Theoretical analysis and simulation results show that the proposed method effectively solves the problem of the angle estimation with phase interferometer for wideband signals, and has good performance in multiple signals scene with non-overlapping spectrum or partially overlapping. In addition, the wider the signal bandwidth, the better direction finding performance of this algorithm.

In wideband noncooperative interference cancellation, the reference signals obtained through auxiliary antennas are weighted to cancel with the interference signal. The correlation between the reference signal and the interference signal determines interference cancellation performance, while the auxiliary antenna array affects the correlation by influencing the amplitude and phase of the reference signals. This paper analyzes the effect of auxiliary antenna array on multiple performances of wideband noncooperative interference cancellation. Firstly, the array received signal model of wideband interference is established, and the weight vector coupled with the auxiliary antennas array manifold is solved by spectral analysis and eigen-subspace decomposition. Then, multiple performances which include cancellation resolution, grating null, wideband interference cancellation ratio (ICR), and convergence rate are quantitatively characterized with the auxiliary antenna array. It is obtained through analysis that the performances mutually restrict the auxiliary antenna array. Higher cancellation resolution requires larger array aperture, but when the number of auxiliary antennas is fixed, larger array aperture results in more grating nulls. When the auxiliary antennas are closer to the main antenna, the wideband ICR is improved, but the convergence rate is reduced. The conclusions are verified through simulation of one-dimensional uniform array and two-dimensional nonuniform array. The experiments of three arrays are compared, and the results conform well with simulation and support the theoretical analysis.

A specialized Hungarian algorithm was developed here for the maximum likelihood data association problem with two implementation versions due to presence of false alarms and missed detections. The maximum likelihood data association problem is formulated as a bipartite weighted matching problem. Its duality and the optimality conditions are given. The Hungarian algorithm with its computational steps, data structure and computational complexity is presented. The two implementation versions, Hungarian forest (HF) algorithm and Hungarian tree (HT) algorithm, and their combination with the naïve auction initialization are discussed. The computational results show that HT algorithm is slightly faster than HF algorithm and they are both superior to the classic Munkres algorithm.

In this paper, the newly-derived maximum correntropy Kalman filter (MCKF) is re-derived from the M-estimation perspective, where the MCKF can be viewed as a special case of the M-estimations and the Gaussian kernel function is a special case of many robust cost functions. Based on the derivation process, a unified form for the robust Gaussian filters (RGF) based on M-estimation is proposed to suppress the outliers and non-Gaussian noise in the measurement. The RGF provides a unified form for one Gaussian filter with different cost functions and a unified form for one robust filter with different approximating methods for the involved Gaussian integrals. Simulation results show that RGF with different weighting functions and different Gaussian integral approximation methods has robust anti-jamming performance.

To address the issue of neglecting scenarios involving joint operations and collaborative drone swarm operations in air combat target intent recognition. This paper proposes a transfer learning-based intention prediction model for drone formation targets in air combat. This model recognizes the intentions of multiple aerial targets by extracting spatial features among the targets at each moment. Simulation results demonstrate that, compared to classical intention recognition models, the proposed model in this paper achieves higher accuracy in identifying the intentions of drone swarm targets in air combat scenarios.

Traditional multi-band frequency selective surface (FSS) approaches are hard to achieve a perfect resonance response in a wide band due to the limit of the onset grating lobe frequency determined by the array. To solve this problem, an approach of combining elements in different period to build a hybrid array is presented. The results of series of numerical simulation show that multi-periodicity combined element FSS, which are designed using this approach, usually have much weaker grating lobes than the traditional FSS. Furthermore, their frequency response can be well predicted through the properties of their member element FSS. A prediction method for estimating the degree of expected grating lobe energy loss in designing multi-band FSS using this approach is provided.

The theory of compressed sensing (CS) provides a new chance to reduce the data acquisition time and improve the data usage factor of the stepped frequency radar system. In light of the sparsity of radar target reflectivity, two imaging methods based on CS, termed the CS-based 2D joint imaging algorithm and the CS-based 2D decoupled imaging algorithm, are proposed. These methods incorporate the coherent mixing operation into the sparse dictionary, and take random measurements in both range and azimuth directions to get high resolution radar images, thus can remarkably reduce the data rate and simplify the hardware design of the radar system while maintaining imaging quality. Experimentsfrom both simulated data and measured data in the anechoic chamber show that the proposed imaging methods can get more focused images than the traditional fast Fourier transform method. Wherein the joint algorithm has stronger robustness and can provide clearer inverse synthetic aperture radar images, while the decoupled algorithm is computationally more efficient but has slightly degraded imaging quality, which can be improved by increasing measurements or using a robuster recovery algorithm nevertheless

In this paper, we propose a beam space coversion (BSC)-based approach to achieve a single near-field signal localization under uniform circular array (UCA). By employing the centro-symmetric geometry of UCA, we apply BSC to extract the two-dimensional (2-D) angles of near-field signal in the Vandermonde form, which allows for azimuth and elevation angle estimation by utilizing the improved estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. By substituting the calculated 2-D angles into the direction vector of near-field signal, the range parameter can be consequently obtained by the 1-D multiple signal classification (MUSIC) method. Simulations demonstrate that the proposed algorithm can achieve a single near-field signal localization, which can provide satisfactory performance and reduce computational complexity.

Performance-based warranties (PBWs) are widely used in industry and manufacturing. Given that PBW can impose financial burdens on manufacturers, rational maintenance decisions are essential for expanding profit margins. This paper proposes an optimization model for PBW decisions for systems affected by Gamma degradation processes, incorporating periodic inspection. A system performance degradation model is established. Preventive maintenance probability and corrective renewal probability models are developed to calculate expected warranty costs and system availability. A benefits function, which includes incentives, is constructed to optimize the initial and subsequent inspection intervals and preventive maintenance thresholds, thereby maximizing warranty profit. An improved sparrow search algorithm is developed to optimize the model, with a case study on large steam turbine rotor shafts. The results suggest the optimal PBW strategy involves an initial inspection interval of approximately 20 months, with subsequent intervals of about four months, and a preventive maintenance threshold of approximately 37.39 mm wear. When compared to common cost-minimization-based condition maintenance strategies and PBW strategies that do not differentiate between initial and subsequent inspection intervals, the proposed PBW strategy increases the manufacturer’s profit by 1% and 18%, respectively. Sensitivity analyses provide managerial recommendations for PBW implementation. The PBW strategy proposed in this study significantly increases manufacturers’ profits by optimizing inspection intervals and preventive maintenance thresholds, and manufacturers should focus on technological improvement in preventive maintenance and cost control to further enhance earnings.

The wheel brake system safety is a complex problem which refers to its technical state, operating environment, human factors, etc., in aircraft landing taxiing process. Usually, professors consider system safety with traditional probability techniques based on the linear chain of events. However, it could not comprehensively analyze system safety problems, especially in operating environment, interaction of subsystems, and human factors. Thus, we consider system safety as a control problem based on the system-theoretic accident model, the processes (STAMP) model and the system theoretic process analysis (STPA) technique to compensate the deficiency of traditional techniques. Meanwhile, system safety simulation is considered as system control simulation, and Monte Carlo methods are used which consider the range of uncertain parameters and operation deviation to quantitatively study system safety influence factors in control simulation. Firstly, we construct the STAMP model and STPA feedback control loop of the wheel brake system based on the system functional requirement. Then four unsafe control actions are identified, and causes of them are analyzed. Finally, we construct the Monte Carlo simulation model to analyze different scenarios under disturbance. The results provide a basis for choosing corresponding process model variables in constructing the context table and show that appropriate brake strategies could prevent hazards in aircraft landing taxiing.

A three-dimensional path-planning approach has been developed to coordinate multiple fixed-wing unmanned aerial vehicles (UAVs) while avoiding collisions. The hierarchical path-planning architecture that divides the path-planning process into two layers is proposed by designing the velocity-obstacle strategy for satisfying timeliness and effectiveness. The upper-level layer focuses on creating an efficient Dubins initial path considering the dynamic constraints of the fixed wing. Subsequently, the lower-level layer detects potential collisions and adjusts its flight paths to avoid collisions by using the three-dimensional velocity obstacle method, which describes the maneuvering space of collision avoidance as the intersection space of half space. To further handle the dynamic and collision-avoidance constraints, a priority mechanism is designed to ensure that the adjusted path is still feasible for fixed-wing UAVs. Simulation experiments demonstrate the effectiveness of the proposed method.

Considering the relatively poor robustness of quality scores for different types of distortion and the lack of mechanism for determining distortion types, a no-reference image quality assessment (NR-IQA) method based on the AdaBoost BP neural network in the wavelet domain (WABNN) is proposed. A 36-dimensional image feature vector is constructed by extracting natural scene statistics (NSS) features and local information entropy features of the distorted image wavelet sub-band coefficients in three scales. The ABNN classifier is obtained by learning the relationship between image features and distortion types. The ABNN scorer is obtained by learning the relationship between image features and image quality scores. A series of contrast experiments are carried out in the laboratory of image and video engineering (LIVE) database and TID2013 database. Experimental results show the high accuracy of the distinguishing distortion type, the high consistency with subjective scores and the high robustness of the method for distorted images. Experiment results also show the independence of the database and the relatively high operation efficiency of this method.

In this paper, we study the orthogonal time frequency space signal transmission over multi-path channel in the presence of phase noise (PHN) at both sides of millimeter wave (mmWave) communication links. The statistics characteristics of the PHN-induced common phase error and inter-Doppler interference are investigated. Then, a column-shaped pilot structure is designed, and training pilots are used to realize linear-complexity PHN tracking and compensation. Numerical results demonstrate that the proposed scheme enables the signal to noise ratio loss to be restrained within 1 dB in contrast to the no PHN case.

The exploration of unmanned aerial vehicle (UAV) swarm systems represents a focal point in the research of multi-agent systems, with the investigation of their fission-fusion behavior holding significant theoretical and practical value. This review systematically examines the methods for fission-fusion of UAV swarms from the perspective of multi-agent systems, encompassing the composition of UAV swarm systems and fission-fusion conditions, information interaction mechanisms, and existing fission-fusion approaches. Firstly, considering the constituent units of UAV swarms and the conditions influencing fission-fusion, this paper categorizes and introduces the UAV swarm systems. It further examines the effects and limitations of fission-fusion methods across various categories and conditions. Secondly, a comprehensive analysis of the prevalent information interaction mechanisms within UAV swarms is conducted from the perspective of information interaction structures. The advantages and limitations of various mechanisms in the context of fission-fusion behaviors are summarized and synthesized. Thirdly, this paper consolidates the existing implementation research findings related to the fission-fusion behavior of UAV swarms, identifies unresolved issues in fission-fusion research, and discusses potential solutions.Finally, the paper concludes with a comprehensive summary and systematically outlines future research opportunities.

The non-minimum phase feature of tail-controlled missile airframes is analyzed. Three selection strategies for desired performance indexes are presented. An acceleration autopilot design methodology based on output feedback and optimization is proposed. Performance and robustness comparisons between the two-loop and classical three-loop topologies are made. Attempts to improve the classical three-loop topology are discussed. Despite the same open-loop structure, the classical three-loop autopilot shows distinct characteristics from a two-loop autopilot with PI compensator. Both the two-loop and three-loop topologies can stabilize a static unstable missile. However, the finite actuator resource is the crucial factor dominating autopilot function.

To utilizing the characteristic of radar cross section (RCS) of the low detectable aircraft, a special path planning algorithm to eluding radars by the variable RCS is presented. The algorithm first gives the RCS changing model of low detectable aircraft, then establishes a threat model of a ground-based air defense system according to the relations between RCS and the radar range coverage. By the new cost functions of the flight path, which consider both factors of the survival probability and the distance of total route, this path planning method is simulated based on the Dijkstra algorithm, and the planned route meets the flight capacity constraints. Simulation results show that using the effective path planning algorithm, the low detectable aircraft can give full play to its own advantage of stealth to achieve the purpose of silent penetration.

In this paper, an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed. Firstly, the affine system is used to build a dynamic model and analyze the state constraints. The midcourse guidance problem is transformed into a continuous time optimization problem. Secondly, the problem is transformed into a discrete convex programming problem by affine control variable relaxation, Gaussian pseudospectral discretization and constraints linearization. Then, the off-line midcourse guidance trajectory is generated before midcourse guidance. It is used as the initial reference trajectory for online correction of midcourse guidance. An online guidance framework is used to eliminate the error caused by calculation of guidance instruction time. And the design of discrete points decreases with flight time to improve the solving efficiency. In addition, it is proposed that the terminal guidance capture is used innovatively space to judge the success of midcourse guidance. Numerical simulation shows the feasibility and effectiveness of the proposed method.

Complex systems widely exist in nature and human society. There are complex interactions between system elements in a complex system, and systems show complex features at the macro level, such as emergence, self-organization, uncertainty, and dynamics. These complex features make it difficult to understand the internal operation mechanism of complex systems. Networked modeling of complex systems is a favorable means of understanding complex systems. It not only represents complex interactions but also reflects essential attributes of complex systems. This paper summarizes the research progress of complex systems modeling and analysis from the perspective of network science, including networked modeling, vital node analysis, network invulnerability analysis, network disintegration analysis, resilience analysis, complex network link prediction, and the attacker-defender game in complex networks. In addition, this paper presents some points of view on the trend and focus of future research on network analysis of complex systems.

In a cloud-native era, the Kubernetes-based workflow engine enables workflow containerized execution through the inherent abilities of Kubernetes. However, when encountering continuous workflow requests and unexpected resource request spikes, the engine is limited to the current workflow load information for resource allocation, which lacks the agility and predictability of resource allocation, resulting in over and under-provisioning resources. This mechanism seriously hinders workflow execution efficiency and leads to high resource waste. To overcome these drawbacks, we propose an adaptive resource allocation scheme named adaptive resource allocation scheme (ARAS) for the Kubernetes-based workflow engines. Considering potential future workflow task requests within the current task pod’s lifecycle, the ARAS uses a resource scaling strategy to allocate resources in response to high-concurrency workflow scenarios. The ARAS offers resource discovery, resource evaluation, and allocation functionalities and serves as a key component for our tailored workflow engine (KubeAdaptor). By integrating the ARAS into KubeAdaptor for workflow containerized execution, we demonstrate the practical abilities of KubeAdaptor and the advantages of our ARAS. Compared with the baseline algorithm, experimental evaluation under three distinct workflow arrival patterns shows that ARAS gains time-saving of 9.8% to 40.92% in the average total duration of all workflows, time-saving of 26.4% to 79.86% in the average duration of individual workflow, and an increase of 1% to 16% in centrol processing unit (CPU) and memory resource usage rate.

With the rapid development of informatization, autonomy and intelligence, unmanned swarm formation intelligent operations will become the main combat mode of future wars. Typical unmanned swarm formations such as ground-based directed energy weapon formations, space-based kinetic energy weapon formations, and sea-based carrier-based formations have become the trump card for winning future wars. In a complex confrontation environment, these sophisticated weapon formation systems can precisely strike mobile threat group targets, making them extreme deterrents in joint combat applications. Based on this, first, this paper provides a comprehensive summary of the outstanding advantages, strategic position and combat style of unmanned clusters in joint warfare to highlight their important position in future warfare. Second, a detailed analysis of the technological breakthroughs in four key areas, situational awareness, heterogeneous coordination, mixed combat, and intelligent assessment of typical unmanned aerial vehicle (UAV) swarms in joint warfare, is presented. An in-depth analysis of the UAV swarm communication networking operating mechanism during joint warfare is provided to lay the theoretical foundation for subsequent cooperative tracking and control. Then, an in-depth analysis of the shut-in technology requirements of UAV clusters in joint warfare is provided to lay a theoretical foundation for subsequent cooperative tracking control. Finally, the technical requirements of UAV clusters in joint warfare are analysed in depth so the key technologies can form a closed-loop kill chain system and provide theoretical references for the study of intelligent command operations.

In the realm of missile defense systems, the self-sufficient maneuver capacity of missile swarms is pivotal for their survival. Through the analysis of the missile dynamics model, a time-efficient cooperative attack strategy for missile swarm is proposed. Based on the distribution of the attackers and defenders, the collision avoidance against the defenders is considered during the attack process. By analyzing the geometric relationship between the relative velocity vector and relative position vector of the attackers and defenders, the collision avoidance constrains of attacking swarm are redefined. The key point is on adjusting the relative velocity vectors to fall outside the collision cone. This work facilitates high-precision attack toward the target while keeping safe missing distance between other attackers during collision avoidance process. By leveraging an innovative repulsion artificial function, a time-efficient cooperative attack strategy for missile swarm is obtained. Through rigorous simulation, the effectiveness of this cooperative attack strategy is substantiated. Furthermore, by employing Monte Carlo simulation, the success rate of the cooperative attack strategy is assessesed and the optimal configuration for the missile swarm is deduced.

Numerous works prove that existing neighbor-averaging graph neural networks (GNNs) cannot efficiently catch structure features, and many works show that injecting structure, distance, position, or spatial features can significantly improve the performance of GNNs, however, injecting high-level structure and distance into GNNs is an intuitive but untouched idea. This work sheds light on this issue and proposes a scheme to enhance graph attention networks (GATs) by encoding distance and hop-wise structure statistics. Firstly, the hop-wise structure and distributional distance information are extracted based on several hop-wise ego-nets of every target node. Secondly, the derived structure information, distance information, and intrinsic features are encoded into the same vector space and then added together to get initial embedding vectors. Thirdly, the derived embedding vectors are fed into GATs, such as GAT and adaptive graph diffusion network (AGDN) to get the soft labels. Fourthly, the soft labels are fed into correct and smooth (C&S) to conduct label propagation and get final predictions. Experiments show that the distance and hop-wise structures encoding enhanced graph attention networks (DHSEGATs) achieve a competitive result.

Cloud manufacturing is a specific implementation form of the "Internet + manufacturing" strategy. Why and how to develop cloud manufacturing platform (CMP), however, remains the key concern of both platform operators and users. A microscopic model is proposed to investigate advantages and diffusion forces of CMP through exploration of its diffusion process and mechanism. Specifically, a three-stage basic evolution process of CMP is innovatively proposed. Then, based on this basic process, a more complex CMP evolution model has been established in virtue of complex network theory, with five diffusion forces identified. Thereafter, simulations on CMP diffusion have been conducted. The results indicate that, CMP possesses better resource utilization, user satisfaction, and enterprise utility. Results of simulation on impacts of different diffusion forces show that both the time required for CMP to reach an equilibrium state and the final network size are affected simultaneously by the five diffusion forces. All these analyses indicate that CMP could create an open online cooperation environment and turns out to be an effective implementation of the "Internet + manufacturing" strategy.

A novel feature fusion method is proposed for the edge detection of color images. Except for the typical features used in edge detection, the color contrast similarity and the orientation consistency are also selected as the features. The four features are combined together as a parameter to detect the edges of color images. Experimental results show that the method can inhibit noisy edges and facilitate the detection for weak edges. It has a better performance than conventional methods in noisy environments.

For the large number of nonlinear degradation devices existing in a project, the existing methods have not systematically studied the effects of random effect on the remaining lifetime (RL), the accuracy and efficiency of the parameters estimation are not high, and the current degradation state of the target device is not accurately estimated. In this paper, a nonlinear Wiener degradation model with random effect is proposed and the corresponding probability density function (PDF) of the first hitting time (FHT) is deduced. A parameter estimation method based on modified expectation maximum (EM) algorithm is proposed to obtain the estimated value of fixed coefficient and the priori value of random coefficient in the model. The posterior value of the random coefficient and the current degradation state of target device are updated synchronously by the state space model (SSM) and the Kalman filter algorithm. The PDF of RL with random effect is deduced. A simulation example is analyzed to verify that the proposed method has the obvious advantage over the existing methods in parameter estimation error and RL prediction accuracy.

Equipment selection is an essential work in the research and development planning of equipment. The scientific and rational development of weapons equipment portfolios is of considerable significance to the optimization of equipment architecture design, the adequate resources allocation, and the joint combat performance. From the system view, this paper proposes a method of weapons equipment portfolios selection (WEPS) based on the contribution rate of weapon systems, providing a new idea for weapon equipment portfolio selection. Firstly, we analyze the WEPS problem and the concept of the contribution rate under the systems background. Secondly, we propose a combat network modeling method for weapon equipment systems based on the function chain. Thirdly, we propose a WEPS method based on the contribution rate, fully considering the correlation relationships between potential weapons and the old weapon systems by the combat network model, under the limitation of capability demands and budget resources, with the objective to maximally increasing the combat ability of weapon systems. Finally, we make a case study with a specific WEPS problem where the whole calculation processes and results are analyzed and exhibited to verify the feasibility and effectiveness of the proposed method model.

Accurate modeling and parameter estimation of sea clutter are fundamental for effective sea surface target detection. With the improvement of radar resolution, sea clutter exhibits a pronounced heavy-tailed characteristic, rendering traditional distribution models and parameter estimation methods less effective. To address this, this paper proposes a dual compound-Gaussian model with inverse Gaussian texture (CG-IG) distribution model and combines it with an improved Adam algorithm to introduce a method for parameter correction. This method effectively fits sea clutter with heavy-tailed characteristics. Experiments with real measured sea clutter data show that the dual CG-IG distribution model, after parameter correction, accurately describes the heavy-tailed phenomenon in sea clutter amplitude distribution, and the overall mean square error of the distribution is reduced.

A schlieren detection algorithm is proposed for the ground-to-air background oriented schlieren (BOS) system to achieve high-speed airplane shock waves visualization. The proposed method consists of three steps. Firstly, image registration is incorporated for reducing errors caused by the camera motion. Then, the background subtraction dual-model single Gaussian model (BS-DSGM) is proposed to build a precise background model. The BS-DSGM could prevent the background model from being contaminated by the shock waves. Finally, the twodimensional orthogonal discrete wavelet transformation is used to extract schlieren information and averaging schlieren data. Experimental results show our proposed algorithm is able to detect the aircraft in-flight and to extract the schlieren information. The precision of schlieren detection algorithm is 0.96. Three image quality evaluation indices are chosen for quantitative analysis of the shock waves visualization. The white Gaussian noise is added in the frames to validate the robustness of the proposed algorithm. Moreover, we adopt two times and four times down sampling to simulate different imaging distances for revealing how the imaging distance affects the schlieren information in the BOS system.