The proliferation of unmanned aerial vehicle (UAV) applications in contemporary society has introduced significant security vulnerabilities. While existing spoofing methodologies can deceive UAVs into deviating from preset trajectories by manipulating global navigation satellite system (GNSS) signals, their practical efficacy remains constrained by prevalent anti-spoofing mechanisms. This study proposes an innovative covert directional spoofing framework designed to circumvent advanced anti-spoofing systems, including Kalman filter innovation-based monitoring, least-squares residual receiver autonomous integrity monitoring (LSR-RAIM), and parameter rationality checks. The spoofing algorithm incorporates UAV dynamics and navigation models, with radar employed to measure the UAV's real-time position and velocity. Mathematical models of anti-spoofing algorithms are constructed, and the range of spoofing measurements that can avoid detection is established. The spoofing algorithm needs to know the preset trajectory of the target UAV and gradually changes the direction of UAV. A closed-loop spoofing strategy is introduced to dynamically adjust the deceptive gain matrix and modify counterfeit measurements. Experimental results demonstrate the algorithm's capability to successfully divert a UAV 230 meters from designated flight paths while inducing a 5° northward directional deviation within 250 seconds. Minor fluctuations in Kalman innovation, navigation parameters, and sensor zero biases were observed during the spoofing attack. The proposed algorithm demonstrates reliable capability in directing UAVs along predetermined spoofing trajectories while remaining undetectable to integrated anti-spoofing mechanisms.

The Gram-Schmidt orthogonalization algorithm and its related modified algorithms often show numerical instability when computing ill-conditioned or large-scale matrices.To solve this problem,this paper explores the cumulative effect of round-off errors of modified Gram-Schmidt algorithm(MGS),and then designs and implements a double-double precision modified Gram-Schmidt orthogonalization algorithm(DDMGS) based on the error-free transformation technology and double-double precision algorithm.A variety of accuracy tests illustrate that DDMGS algorithm has better numerical stability than the varients of BMGS_SVL,BMGS_CWY,BCGS_PIP and BCGS_PIO algorithms,which proves that DDMGS algorithm can effectively reduce the loss of orthogonality of matrix,improve the numerical accuracy,and demonstrate the stability of our algorithm.In the performance test, the floating point computations(flops) of different algorithms are calculated and then compared DDMGS algorithm with the modified Gram-Schmidt algorithm on ARM and Intel processors,the runtime of the DDMGS algorithm proposed in this paper isabout 5.03 and 18.06 times that of MGS respectively,but the accuracy is improved significantly.

Singular value decomposition (SVD) plays a significant role in matrix analysis, and the differential quotient difference with shifts (DQDS) algorithm is an important technique for solving singular values of upper bidiagonal matrices. However, ill-conditioned matrices and large-scale matrices may cause inaccurate results or long computation times when solving singular values. At the same time, it is difficult for users to effectively find the desired solution according to their needs. In this paper, we design a precision-adjustable computational framework for solving singular values, named PACF. In our framework, the same solution algorithm contains three options: original mode, high-precision mode, and mixed-precision mode. The first algorithm is the original version of the algorithm. The second algorithm is a reliable numerical algorithm we designed using Error-free transformation (EFT) technology. The last algorithm is an efficient numerical algorithm we developed using the mixed-precision idea. Our PACF can add different solving algorithms for different types of matrices, which are universal and extensible. Users can choose different algorithms to solve singular values according to different needs. This paper implements the high-precision DQDS and mixed-precision DQDS algorithms and conducts extensive experiments on a supercomputing platform to demonstrate that our algorithm is reliable and efficient. Besides, we introduce the error analysis of the inner loop of the DQDS and HDQDS algorithms.

Due to the cumulative effect of rounding errors, the Gram-Schmidt orthogonalization algorithm and its variants often exhibit numerical instability phenomena. Therefore, we analyze the data dependencies of the Modified Gram-Schmidt algorithm (MGS), and propose the compensated MGS algorithm (CompMGS) based on the idea of error-free transformation (EFT) technology and compensated algorithms. The theoretical analysis demonstrates that our algorithm has $\mathcal{O}(u)$ loss of orthogonality(in double working precision, $u=10^{-16}$ ) with the relaxed conditions $(\kappa_{2}(A) < 1^{-}0^{16})$ . A range of numerical experiments illustrate that CompMGS has similar effects to the double-double precision Modified Gram-Schmidt orthog-onalization algorithm (DDMGS) and is more accurate than the algorithms proposed in [1] and [2], which verifies the correctness of the theoretical analysis and proves the accuracy of our algorithm. While satisfying the same loss of orthogonality, the CompMGS is faster than DDMGS on both ARM and Intel processors by about 1.5 times and 2.3 times on average respectively, showing the high efficiency of our algorithm.

A Bayesian approach based on the vulnerability distribution is proposed to estimate the confidence limits of the state probability and the threat level of multistate electronic systems interfered by intentional electromagnetic interference (IEMI). The vulnerability distribution is used to describe the state probability function of the multi-state system (MSS) for a given IEMI threat level. When a small number of test samples are under a specific threat level and prior MSS information is known, the posterior estimation of the state probability function can be obtained based on Bayesian theory. Furthermore, to effectively apply the state probability function to assess the vulnerability of the MSS, the uncertainty of the state probability function is discussed. Considering state probabilities under the same threat level as random variables, all these state probabilities also follow the Dirichlet distribution. Thus, the confidence limits of the posteriori state probability and the threat level can be inferred by the marginal distribution of the state probability, which is induced by combining the Dirichlet and vulnerability distributions. Finally, a case study is given to demonstrate the details of the calculation process of the vulnerability distribution, the state probability function, and the confidence limits under a lognormal distribution.

针对复杂环境下多探测传感器网络难以准确协同定位的问题,提出了一种多传感器协同定位优化布站方法.基于后验克拉美罗下界构建了目标定位精度几何稀释因子评价指标,考虑复杂外界环境,分析了起伏地形、杂波干扰和光照对传感器探测定位能力的影响.建立了多传感器协同定位优化布站模型,并采用智能优化算法进行快速求解.仿真实验结果表明:所提方法能够有效提高多探测传感器网络的协同定位能力,对多传感器协同优化布站具有指导意义.

The health of aero-engines is pivotal to the safe operation of aircraft. With increasing service time, the internal components of the engine will be damaged by threats from different sources, so it is necessary to regularly detect the damage inside the engine. At present, most of the detection methods of major airlines rely on the internal images of the engine obtained by manual use of a borescope to detect damage or traditional machine learning methods, which consume high levels of human and computational resources but have low efficiency. Artificial intelligence in various fields can achieve better performance than traditional methods, but to achieve the industrialization standard of Green AI, we need further research. Accordingly, we introduce a multi-layer contrastive learning method to a lightweight target detection model design, which is applied to real aero-engine borescope images of complex components to accomplish real-time damage detection. We intensively conduct comparative experiments to evaluate the effectiveness of our method. The verification results demonstrate that the method can help our model perform excellently compared with other available baseline models.

The Horner and Goertzel algorithms are frequently used in polynomial evaluation. Each of them can be less expensive than the other in special cases. In this paper, we present a new compensated algorithm to improve the accuracy of the Goertzel algorithm by using error-free transformations. We derive the forward round-off error bound for our algorithm, which implies that our algorithm yields a full precision accuracy for polynomials that are not too ill-conditioned. A dynamic error estimate in our algorithm is also presented by running round-off error analysis. Moreover, we show the cases in which our algorithms are less expensive than the compensated Horner algorithm for evaluating polynomials. Numerical experiments indicate that our algorithms run faster than the compensated Horner algorithm in those cases while producing the same accurate results, and our algorithm is absolutely stable when the condition number is smaller than 1016. An application is given to illustrate that our algorithm is more accurate than MATLAB’s fft function. The results show that the relative error of our algorithm is from 1015 to 1017, and that of the fft was from 1012 to 1015.

Aero-engine is the 'heart' of the aviation aircraft.Practical failure prediction of aero-engines is difficult due to the performance degradation covered by the continuous switching between various operating conditions.In order to solve the above problem, we propose a new type of aero-engine fault diagnosis model-RIRCNN (Residual Independently Reccurent and Convolutional Neural Network).It can process long sequences, and has superior feature extraction effect.We gather flight data sets through ground bench experiment of the aviation turboprop engine, and intensively conduct comparative experiments to evaluate the effectiveness of our model.The verification results demonstrate that our model can achieve excellent performance compared with other available baseline models.

针对激光大气传输湍流效应不确定度量化中采用蒙特卡罗(MC)方法计算效率低的问题,提出了一种基于多项式混沌(PC)的不确定度量化方法.该方法采用拉丁超立方抽样随机抽取少量样本,经过数值模拟后通过多项式混沌构造代理模型,并依据代理模型进行不确定度量化.以准直Gauss光束的地空垂直上行传输为例,不确定度计算中考虑了激光器出口光束质量和大气相干长度对远场功率密度的影响,并以大样本量MC方法的不确定度量化结果作为基准,对PC方法进行了验证.结果表明,PC方法只需对少量样本进行数值模拟计算,便可快速构建远场功率密度的代理模型,得到的不确定度量化结果与MC方法的量化结果吻合较好.

With the rise of high-performance computing, the precision requirements for numerical calculations are getting higher and higher. Rounding errors cannot be avoided in floating point operations, and therefore the calculation result can be inaccurate and even incorrect when rounding errors are not taken into account. We study and analyze in detail the Differential Quotient Difference with Shifts (DQDS) algorithm, used in algorithms to calculate the eigenvalues of tridiagonal matrices, and propose a novel High Precision DQDS algorithm (HDQDS) based on Error Free Transformations (EFT). We use EFT to reduce the accumulation of errors and obtain a much more precise algorithm. The relative error of the HDQDS algorithm remains constant at the machine precision error level, while the relative error of the DQDS algorithm has fluctuations in the same experimental scenario. Numerical experiments show that the proposed high-precision HDQDS algorithm allows for higher precision and more stability than the original alagrithm.

在电子系统电磁脉冲易损性评估问题中,电子系统各层元素的易损性信息具有显著的不均衡性,为了降低系统电磁脉冲易损性评估计算过程中的不确定度,本文基于分层贝叶斯网络模型及贝叶斯信息融合算法,建立了电子系统电磁脉冲易损性评估模型及易损性信息融合算法,并以某星用模数转换系统的电磁脉冲易损性评估问题为例,应用本文提出的信息融合算法,给出了系统后验概率分布及后验均值估计,验证了本文计算的有效性.

Subspace clustering has been widely applied to detect meaningful clusters in high-dimensional data spaces. And the sparse subspace clustering (SSC) obtains superior clustering performance by solving a relaxed ℓ0-minimization problem with ℓ1-norm. Although the use of ℓ1-norm instead of the ℓ0 one can make the object function convex, it causes large errors on large coefficients in some cases. In this paper, we study the sparse subspace clustering algorithm based on a nonconvex modeling formulation. Specifically, we introduce a nonconvex pseudo-norm that makes a better approximation to the ℓ0-minimization than the traditional ℓ1-minimization framework and consequently finds a better affinity matrix. However, this formulation makes the optimization task challenging due to that the traditional alternating direction method of multipliers (ADMM) encounters troubles in solving the nonconvex subproblems. In view of this, the reweighted techniques are employed in making these subproblems convex and easily solvable. We provide several guarantees to derive the convergence results, which proves that the nonconvex algorithm is globally convergent to a critical point. Experiments on two real-world problems of motion segmentation and face clustering show that our method outperforms state-of-the-art techniques.

The alternating direction method of multipliers (ADMM) is one of most foundational algorithms for linear constrained composite minimization problems. For different specific problems, variations of ADMM (like linearized ADMM, proximal ADMM) are developed. By using the Bregman distances, lots of ADMMs can be formulated into a uniform mathematical scheme. Although variational inequalities have been well used to study ADMMs, the use for BADMM has still been missing. In this paper, we study the convergence of BADMM by variational inequalities. We present a proof framework for BADMMs. And then, we present very concise convergence proof for the basic BADMM. As applications, we consider several variations of BADMM and obtain corresponding convergence results.

This article proposes a bivariate compensated Volk and Schumaker (CompVSTP) algorithm, which extends the compensated Volk and Schumaker (CompVS) algorithm, to evaluate Bèzier tensor product surfaces with floating-point coefficients and coordinates. The CompVSTP algorithm is obtained by applying error-free transformations to improve the traditional Volk and Schumaker tensor product (VSTP) algorithm. We study in detail the forward error analysis of the VSTP, CompVS and CompVSTP algorithms. Our numerical experiments illustrate that the Comp-VSTP algorithm is much more accurate than the VSTP algorithm, relegating the influence of the condition numbers up to second order in the rounding unit of the computer.

We present the ORTHOPOLY software that permits to evaluate, efficiently and accurately, finite series of any classical family of orthogonal polynomials (Chebyshev, Legendre, ultraspherical or Gegenbauer, Jacobi, Hermite and Laguerre orthogonal polynomials) and their derivatives. The basic algorithm is the BCS-algorithm (Barrio-Clenshaw-Smith derivative algorithm), that permits to evaluate the kth derivative of a finite series of orthogonal polynomials at any point without obtaining before the previous derivatives. Due to the presence of rounding errors, specially in the case of high order derivatives, we introduce the compensated BCS-algorithm, based on Error-Free Transformation techniques, that permits to relegate the influence of the conditioning of the problem up to second order in the round-off unit of the computer. The BCS and compensated BCS algorithms may also give running-error bounds to provide information about the accuracy of the evaluation process. The ORTHOPOLY software includes C and Mat lab versions of all the algorithms, and they are designed to be easily used in longer softwares to solve physical, mathematical, chemical or engineering problems (illustrated on the Schrodinger equation for the radial hydrogen atom). Program summary Program Title: ORTHOPOLY Program Files doi: http://dx.doi.org/10.17632/n55bpy5bsr.1 Licensing provisions: GPLv3 Programming language: C and Matlab versions Nature of problem: Accurate numerical evaluation of finite series of classical orthogonal polynomials and their derivatives. Solution method: Barrio-Clenshaw-Smith algorithm for the evaluation of derivatives of finite series of classical orthogonal polynomials. Error-Free Transformation techniques for the Compensated Barrio-Clenshaw-Smith algorithm in order to provide accurate evaluations. Running-error techniques to provide error bounds of the evaluations. (C) 2018 Elsevier B.V. All rights reserved.

The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference (qd) algorithm can be numerically unstable. The Compqd algorithm is obtained by applying error-free transformations to improve the traditional qd algorithm. We study in detail the error analysis of the qd and Compqd algorithms and we introduce new condition numbers so that the relative forward rounding error bounds can be derived directly. Our numerical experiments illustrate that the Compqd algorithm is much more accurate than the qd algorithm, relegating the influence of the condition numbers up to second order in the rounding unit of the computer. Three applications of the new algorithm in the obtention of continued fractions and in pole and zero detection are shown.

A Chebyshev tensor product surface is widely used in image analysis and numerical approximation. This article illustrates an accurate evaluation for the surface in form of Chebyshev tensor product. This algorithm is based on the application of error-free transformations to improve the traditional Clenshaw Chebyshev tensor product algorithm. Our error analysis shows that the error bound is u+Ou2×condP,x,y in contrast to classic scheme u×cond(P,x,y), where u is working precision and condP,x,y is a condition number of bivariate polynomial P(x,y), which means that the accuracy of the computed result is similar to that produced by classical approach with twice working precision. Numerical experiments verify that the proposed algorithm is stable and efficient.

A compensated algorithm is presented to evaluate finite Laguerre series.We record round-off error in Clenshaw algorithm by using error-free transformations (EFTs).In this work, we establish a valid error estimate that is as accurate as the Clenshaw scheme using twice the working precision.Numerical experiments illustrate that our compensated algorithm is more accurate than the Clenshaw algorithm and faster than the DDClenshaw algorithm (Clenshaw in double-double arithmetic).