• Volume 32,Issue 4,2010 Table of Contents
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    • >航天工程
    • Hybrid LES/RANS Simulation of 2D Shock/TurbulentBoundary-layer Interactions

      2010, 32(4):1-6.

      Abstract (12871) HTML (80) PDF 457.83 K (8364) Comment (0) Favorites

      Abstract:In order to reduce the computational cost of LES for high Reynolds number, a hybrid Large Eddy Simulation/Reynolds-Averaged Navier-Stokes (hybrid LES/RANS) approach which combined two-equation k-ω SST turbulence model and Yoshizawa's one-equation sub-grid scale model with a blending function was developed. The hybrid method together with AUSM+-up scheme was conducted to investigate a Mach 2.85 flow field of a 20-degree compression ramp. The effects of two kinds of inflow boundary conditions (fixed inlet and inlet with super-imposed white noise) were investigated. Separation and reattachment of the boundary layer along with separation shock were obtained from the simulation. The separation zone predicted was significantly larger than the experimental result. Defects of the hybrid method were analyzed and possible improvements were presented.

    • Entry Guidance Law Design for Lunar Return Crew Module

      2010, 32(4):7-12.

      Abstract (8238) HTML (84) PDF 414.58 K (6374) Comment (0) Favorites

      Abstract:Aiming at entry guidance mission of a mooncraft with the second universe velocity more or less, the reentry guidance law which meets various constraints, including G-load, heating and landing site location constraints, was studied. The lunar return crew module is a ballistic-lift vehicle with low lift-to-drag ratio, the strategy calls for controlling the trajectory by modulation of the magnitude and sign of the vehicle's bank angle. The determination of the magnitude of bank angle was formulated as a nonlinear univariante root finding problem, while the sign of the angle was dependent upon the reversals in accordance with the lateral corridor, which was treated as a function of velocity. Integrated dispersions Monte Carlo simulations were performed to evaluate the performance of the proposed approach, and the results show that the downrange standard deviation is about 30 km, and the cross range standard deviation is smaller than 5 km. In addition, the working factors on bank rate are analyzed, and the relation between the feedback gain factor regulation and guidance precision is proposed.

    • GNSS Autonomous Navigation Integrity Separation Technique

      2010, 32(4):13-18.

      Abstract (6750) HTML (89) PDF 331.63 K (6197) Comment (0) Favorites

      Abstract:Under GNSS autonomous navigation mode, in order to keep constellation stabilization and integrity, failure satellites must be separated in time. A GNSS autonomous navigation integrity separation technique was developed, and satellite failure judgment method was analyzed. Satellite failure separation procedures were designed, and then a failure check and separation technique was presented. Simulation of this technique suggests that it ensures services precision by effectively separating failure satellites among autonomous navigation constellation. Furthermore, this technique is not very complex and easy for engineering.

    • A Data Fusion Method for Navigation ConstellationAutonomous Navigation Based on X-Ray Pulsar

      2010, 32(4):19-24.

      Abstract (7016) HTML (79) PDF 291.18 K (5988) Comment (0) Favorites

      Abstract:To solve the problem of deficiency of rank existing in navigation constellation long-time auto-navigation based on inter-satellite measurement, a method of integrated navigation based on the Inter-Satellite Links (ISL) and X-ray Pulsar was proposed. The fundamentals of this method were described. To rationalize the computational burden, the generalized federated filters were simplified and improved to fuse the measurements based on ISL and X-ray Pulsar. Finally, the simulation was carried out, and the results proved the rationality and feasibility of this method.

    • Geometric Parameters Sensitivity Analysis for Star GrainBased on Secondary Development of Patran

      2010, 32(4):25-29.

      Abstract (7963) HTML (84) PDF 327.34 K (5957) Comment (0) Favorites

      Abstract:In order to analyze the effect of geometric parameters on the structural integrity of star grain, the parameterized model of star grain was constructed through PCL(Patran Command Language) on the platform of FM software MSC.Patran/Nastran. The law of maximum Von Mises strain variation with geometric parameters was studied, and the geometric parameters sensitivity was analyzed based on the parameterized model. The results show that grain web thickness, star angle coefficient, star-hole number, and the rounding radius of groove top have great effect on the structure integrity of star grain. Therefore, more attention should be paid to these parameters in motor design. The analytical method and conclusion are beneficial for designing SRM.

    • Research on Attitude Control of Kinetic Energy Interceptor under Blended Operation of Lateral Thrust and Aerodynamic Force

      2010, 32(4):30-36.

      Abstract (7535) HTML (82) PDF 290.10 K (6815) Comment (0) Favorites

      Abstract:An attitude control method of kinetic energy interceptor under blended operation of lateral thrust and aerodynamic force was developed and a short period movement model of interceptor was presented. A combined control system was designed, using linear quadratic optimal tracking control theory and the fire logic of attitude control missiles. Through analyzing the nonlinear tolerance, a conclusion was drawn that the system has strong robusticity to the thrust bias. Simulation results of attitude control and six-dimension intercept trajectory with lateral jet interaction show that the control method proposed has quick response characteristic and good tracking performance for guidance command, and it can meet the demands of direct interception in the terminal phase.

    • Optimal Design of Conical Cavitator of Supercavitating Vehicles

      2010, 32(4):37-41.

      Abstract (6935) HTML (88) PDF 207.71 K (5735) Comment (0) Favorites

      Abstract:Different empirical formulae in the calculation of the supercavity shape were analyzed, showing that the Guzevsky formulae has good precision and scope of application. Targeting on reducing the drag, enhancing the cavitation number and enlarging the volume of the supercavitating vehicle, an optimal design model of the conical supercavitator was built based on the Guzevsky formulae. The weight method and genetic algorithm were applied in solving the optimal problem. The results are consistent with the current theory. Effect of aspect ratios, cavitation numbers in the design process were studied. The results indicate that cavitation number is the most important factor that affects the dimension of the supercavity and the volume of the vehicle has been increased significantly through the optimal design process.

    • Comparative Analysis of Two Types of Strap-on LaunchVehicle's Elastic Vibration Modeling Method and the Influenceon Attitude Control System

      2010, 32(4):42-48.

      Abstract (7285) HTML (86) PDF 386.60 K (6038) Comment (0) Favorites

      Abstract:In view of the different characteristics of modes between long and short strap-on launch vehicles, the differences and relations of elastic vibration modeling method of them were analyzed firstly. Then a new attitude dynamic model of solid strap-on launch vehicle was derived, the elastic vibration equation in the model was also derived by finite element method. Finally, the coupling among three channels based on the new model was studied. Inverse Nyquist Array method was used to design the controller. The results show that the new model can reflect more exactly the coupling characteristics of longitudinal, lateral and torsinal vibration of strap-on launch vehicle. Although the coupling among three channels exists, the coupling matrix has the diagonal dominance characteristics and the controller designed by Inverse Nyquist Array method can obtain a good performance.

    • Effects of the Attached Apex Drogue on Phenomenon of BullWhipping in the Deployment Process of Large Parachute

      2010, 32(4):49-54.

      Abstract (6625) HTML (85) PDF 254.59 K (5444) Comment (0) Favorites

      Abstract:Based on the finite element thought, a multistage, multi-finite-element and multi-freedom dynamic model of the deployment process of a large parachute was built. The effects of the attached apex drogue and peel off band on the phenomenon of bull whipping formed after the deployment process of the main parachute were studied through simulation. The analysis was focused on the comparison of shape movements of canopy, velocity of bull whipping and distance of departure with or without the attached apex drogue. The conclusion can provide theoretic help for the engineering design department in designing, improving and using the large parachute.

    • Technology of Aeroengine Testing Data PreprocessingBased on Robust Kalman Filter

      2010, 32(4):55-60.

      Abstract (6572) HTML (78) PDF 253.46 K (6196) Comment (0) Favorites

      Abstract:The standard Kalman filter algorithm cannot accurately preprocess the measured data of aeroengine with exceptional errors. The principle of standard Kalman filter and the impact of test errors to the filter estimate results were analysed, and the method of dynamically adjusting the weight of observation information in the filter estimate result was introduced. Then, based on M-estimation theory, the Robust Kalman filter principle and the recursion formula were presented. The state-space equations and observation equations of the measured parameters were established in terms of CA(Constant Acceleration)model. In order to decrease the calculation consumption, the sequence filter was applied separately to process the different sensed data. Furthermore, the preprocessing to the simulation sensed data of a given turbofan engine's steady operation was carried out as an example, using the given Robust Kalman filter. The calculation results, compared with standard Kalman filter, show that the designed Robust Kalman filter has better estimate precision with a given model error.

    • Characteristic Analysis and Design of Hybrid Trajectory for MannedLunar Landing Mission Based on Double Two-body Model

      2010, 32(4):61-67.

      Abstract (6723) HTML (83) PDF 429.85 K (5609) Comment (0) Favorites

      Abstract:Hybrid trajectory is one of the most important trajectory types for manned lunar landing mission. Using the componential characteristic of hybrid trajectory, a hybrid trajectory calculation method based on free return trajectory was proposed under double two-body model. Then, the major characteristics of hybrid trajectory were analyzed, such as energy requirement and time of flight. A little modification was made when calculating the ephemeris of the Moon, in which the Moon motion around Earth was considered as noncircular orbit instead of circular orbit. Finally, a design example was presented while the results of the simulation validate the method proposed.

    • >Information & Communication Engineering
    • Novel EBG Loaded Microstrip Antenna Array

      2010, 32(4):68-71,77.

      Abstract (6656) HTML (85) PDF 377.85 K (6586) Comment (0) Favorites

      Abstract:Microstrip antenna array mounted over electromagnetic bandgap (EBG) substrate was studied The EBG was mounted below the microstrip antenna array to replace the conducting ground plane of antenna array, which can widen the operational bandwidth and promote the gain of antenna array. The measured results show that the operational bandwidth of antenna unit is promoted from 3.81% to 8.86%, and in the operational band the gain of antenna array is over 10dB. Meanwhile the coupling coefficient between units of antenna array is reduced.

    • Study of Space time Frequency Processing forSpaceborne MIMO-GMTI Radar Based on Stepped FrequencyOrthogonal Waveform

      2010, 32(4):72-77.

      Abstract (6868) HTML (86) PDF 392.36 K (6461) Comment (0) Favorites

      Abstract:Synthesizing the multiple-channel and multiple-frequency techniques, the multiple-input multiple-output (MIMO) radar can provide a feasible approach for solving the problems in spaceborne GMTI, such as slowly-moving target detection, and blind speed zones reduction. Effective orthogonal waveform design is crucial for MIMO radar implementation. Therefore, based on an analysis of the performance of orthogonal waveform, with the application of GMTI, the optimized basic parameter choice criteria for stepped frequency orthogonal waveform of spaceborne MIMO radar was proposed. Then, the basic principle of combined space, time and frequency adaptive processing was studied. Finally, simulation results were presented to demonstrate the superiority of MIMO radar in improving clutter suppression and GMTI performance.

    • Low Frequency SAR Multi-channel Equalization MethodBased on Subaperture Image

      2010, 32(4):78-83.

      Abstract (7264) HTML (82) PDF 467.87 K (6421) Comment (0) Favorites

      Abstract:When the multi-channel SAR system is used for moving target indication, the imbalance in amplitude and phase among channels severely affects the performance of moving target detection and parameter estimation. For multi-channel low frequency SAR/GMTI system, a multi-channel equalization method based on subaperture image was proposed. The method makes use of multi-channel subaperutre images with the same view-angle, and estimates the amplitude and phase errors related to this view-angle at the same time. It can estimates the amplitude and phase errors accurately and adapts to the errors changing with the view-angle. The experiment based on vehicle-borne low frequency multi-channel SAR/GMTI real data demonstrates that this method can effectively compensate for the amplitude and phase errors among different channels and improve the performance of moving target detection.

    • Multi-frequency Fusion Based on Compressive Sensing

      2010, 32(4):84-87.

      Abstract (7082) HTML (85) PDF 277.32 K (6256) Comment (0) Favorites

      Abstract:Traditional multi-frequency radar signal fusion can reconstruct full-band signal from some continuous sampled sub-band signals, and can improve range resolution and quality of range profile. But by the theory of Compressive Sensing, the more the incoherence between sampled matrix and measurement matrix is, the better the full-band signal can be reconstructed. Therefore, the performance of signal fusion based on random sampling is better than that of fusion based on continuous sampled theoretically. In the current study, traditional multi-band signal fusion was extended to random sampled signal reconstruction, and Basic Pursuit was used for reconstructing full-frequency signal. Then, the sufficient condition of successful reconstruction with high probability was presented. The experimental results prove the advantage of this fusion method.

    • Automatic Modulation Recognition of Both Digital and AnalogCommunication Signals

      2010, 32(4):88-93.

      Abstract (6409) HTML (90) PDF 250.21 K (6035) Comment (0) Favorites

      Abstract:In order to automatically classify the modulation types of both digital and analog communication signals, nine feature parameters based on the first statistical moments of the received signals were proposed. All those feature parameters were calculated using the conventional signal processing methods. The calculation process is less complicated and it is suitable for real time online analysis. Next, an automatic modulation recognition algorithm based on the decision-theoretic approach was also developed and its realization was also presented in the form of a flowchart. Computer simulations shows that all the aforementioned types of communication signals have been recognized with an average success rate ≥97% at SNR≥9dB and the method proposed is suitable for the practical application of signal detection and fast recognition in non-cooperation communication systems.

    • >计算机科学与技术
    • Design and Performance Analysis of an InterconnectInterface for Multi-Core Microprocessor

      2010, 32(4):94-99.

      Abstract (6208) HTML (0) PDF 376.00 K (6416) Comment (0) Favorites

      Abstract:Parallelism is the most important way to improve the performance of computer. With the development of the integrated circuits' manufacture process, besides integrating more processor cores into one processor chip, building multi-way parallelism system through high-speed interconnect interface is the main method to increase the parallelism of high-performance computer. A design scheme of an interconnect interface for multi-core microprocessor was proposed. The proposed interface was based on a simplified PCI Express bus protocol and adopted the technology of high-speed serial data transferring. Cache coherence packet and large block data transfer packet were all supported. The interface can be used for connecting four processor nodes directly. Simulation results show that the max valid bandwidth per interface can reach 64Gbps and the minimum transfer delay is 120ns. The balance of the bandwidth and the transfer delay is reached, meeting the requirement of transferring different type of packets.

    • Research on Ship Thermodynamic System RMS SimulationArgumentation Based on Feasible Using Schemes

      2010, 32(4):100-104.

      Abstract (6898) HTML (0) PDF 236.67 K (5971) Comment (0) Favorites

      Abstract:Because of complexity related to operation, maintenance, support and malfunction of ship steam power system, establishing math analytical model cannot satisfy the RMS argumentation demand. Based on the minimal equipment listing, Monte Carlo simulation method is not fit for system failure criterion either. The current research utilized feasible using schemes based on thermal model instead of minimal equipment listing based on logic relation. According to whether there were feasible using schemes when system partial equipment faulted, the research designed ship thermal system RMS simulation flow based on feasible using schemes. The ship thermal system RMS software was programmed based on improved simulation flow. Calculation examples demonstrated that the improved flow can satisfy the simulation precision, and the calculation efficiency is also improved.

    • Panoramic Unwrapping Interpolation Method of OmnidirectionalImages Based on Bidirectional Mapping

      2010, 32(4):105-109.

      Abstract (6943) HTML (0) PDF 290.64 K (6098) Comment (0) Favorites

      Abstract:Original omnidirectional images usually need to be unwrapped to cylindrical panoramic images according to human visual habits because of concentric annular distortion. According to the characteristics of catadioptric omnidirectional imaging, an interpolation method for panoramic unwrapping based on bidirectional mapping was proposed. The coordinate mapping relationships were obtained by tracking optical path. Firstly, each pixel in the target cylindrical panoramic image was projected backward onto the original omnidirectional image, and the neighboring pixels for interpolation were located. Then, all the neighboring pixels were projected forward onto the cylindrical panoramic image, and the color value of the target pixel was interpolated by using inverse distance weighted method or 3D-plane interpolation method due to the scattered distribution of the neighboring pixels in cylindrical panoramic images. The proposed method avoids the adverse effect on computing the interpolation weight of neighboring pixels caused by the nonlinear distortion, and the neighboring pixels for interpolation are also accurately located. The experimental results indicate that the proposed method is effective for enhancing the precision of interpolation and the image quality of unwrapped panoramic images.

    • >Control Science & Engineering
    • A Twist-based Method for 3D Optimal Guidance Law

      2010, 32(4):110-115.

      Abstract (6695) HTML (83) PDF 250.93 K (6320) Comment (0) Favorites

      Abstract:Aiming at the coupling of bank-to-turn (BTT) missile, a non-decoupling three-dimensional (3D) guidance law was proposed. Firstly, the 3D guidance model was established after the line of sight (LOS) angles velocity model was established through vectors description, and the azimuth' change of LOS was described based on the twist method. Secondly, the guidance model was simplified and the linear model was derived on the assumption that LOS angles' change is slow. Finally, the 3D optimal guidance laws were designed respectively using the quadratic optimal control, corresponding to no ending constraints and ending constraints. The proposed guidance law can be satisfied with the guidance precision of BTT missile since it is able to avoid the information loss caused by the decoupling method.

    • >Electronic Science & Technology
    • Design of Impulse Generation Circuit for Ultra-widebandFuze Target Return Simulation

      2010, 32(4):116-120.

      Abstract (6836) HTML (78) PDF 295.32 K (6267) Comment (0) Favorites

      Abstract:Ultra-Wideband (UWB) fuze return signals simulator is an effective way for efficient and quick testing of UWB fuzes. The circuit for UWB impulse generation is one key element of the simulator. Current impulse generators are mainly designed for Gaussian pulse or Gaussian doublet, which cannot be used in the simulator directly. Based on sphere target assumption, the current research presented a circuit that can generate second order Gaussian impulse for fuse return signal simulator, using step recovery diode and UWB filter co-design. Parameters of SRD circuit and UWB filter were determined by simulation. According to simulation results, a impulse circuit was fabricated and measured. The measured results coincide with theoretical second order Gaussian signal.

    • The Method of Eliminating Nonlinear Effect for RadioFrequency Module

      2010, 32(4):121-125.

      Abstract (6452) HTML (83) PDF 225.73 K (6334) Comment (0) Favorites

      Abstract:The nonlinear effect of phase performance and the dependency relationship of envelope delay with the change of frequency for a radio frequency module are owed to a good many factors uncertainty, which may cause the waveform of output radio frequency signal to be distorted. Based on the recursive least square adaptive filter, the novel method to eliminate nonlinear effect of radio frequency module was proposed. By regarding the GPS simulating system as an example, the model parameters were estimated precisely by using its self-revising module, software radio technique and digital signal processing technique. Then in order to eliminate the nonlinear phase and variable envelope delay, the synthetic signal in baseband was processed using a digital filter, which was the inverse filter of radio frequency module. The corresponding computation was accomplished utilizing the self-programming emulating package with the help of Matlab. The simulation results indicate that the method proposed in this paper can eliminate the impact on radio frequency signals by the nonlinear effect of phase, and the waveform distortion of output signals can be reduced to less than 0.01 percent.

    • >Mechanical Engineering
    • A Method to Eliminate the Influence on Phase Change PointsCaused by the End Effect of the Linear PM BLDC Motor

      2010, 32(4):126-130.

      Abstract (6468) HTML (86) PDF 218.16 K (5923) Comment (0) Favorites

      Abstract:The linear PM BLDC motor(LPMBLDCM) used in an electromagnetic launcher has a short broken permanent magnet(PM) mover whose end magnetic field is deformed. When hall cells are used in detecting magnetic induction and helping realize phase change, the phase change points(PCPs) will be shifted by this type of end effect. The phase change principle of the LPMBLDCM was analyzed and how the short broken PM mover shifts the PCPs was presented. It was concluded that this type of end effect is mainly affected by the pole-arc factor of the PM poles. An asymmetric hysteresis comparator, as well as a common single threshold comparator, was used to reshape the output of hall cells to eliminate the influence caused by the end effect. Experiment results of a prototype motor prove that the common single threshold comparator method is feasible.

    • >计算机科学与技术
    • Research of CGF Agent Decision-making ModelingBased on Prospect Theory

      2010, 32(4):131-136.

      Abstract (6955) HTML (0) PDF 243.97 K (5911) Comment (0) Favorites

      Abstract:Prospect Theory (PT) describes the rules of individual's decision-making under uncertainty, which can well characterize decision-makers' risk preference. PT has certain valuable feasibility and applicability in operational decision-making modeling. Based on PT, a method of CGF Agent decision-making modeling was proposed. The Computer Generated Forces (CGF) Agent framework was presented. The detailed description of concrete process and algorithm for course of action (COA) selection in Agent decision-making was also given. The experiment shows that the proposed method has good performance and can improve the authenticity of CGF Agent's decision-making behavior.

    • Square Attack on Some Special Feistel Ciphers

      2010, 32(4):137-140 ,149.

      Abstract (6623) HTML (0) PDF 232.25 K (5696) Comment (0) Favorites

      Abstract:Securities of two special Feistel ciphers with SP-structured round functions against Square attack were studied. By changing the position of P permutation of the round functions in an equivalent manner, some new cryptanalytic results of round-reduced SNAKE(2) and CLEFIA were presented. Time complexity of Square attack against 6-round SNAKE(2) was reduced from 224 to 213.4, and for 6-round CLEFIA, time complexity of Square attack was reduced from 234.4to 212.4. The results show that, in designing Feistel ciphers with SP-structured round functions, influence of equivalent structures and Square attack should be taken into consideration.

    • The Algebraic Structure of Information and InformationSpace Based on Ontology

      2010, 32(4):141-144.

      Abstract (6500) HTML (0) PDF 168.31 K (5571) Comment (0) Favorites

      Abstract:For achieving information resource service in the specific information field based on organizations of information, more appropriate and more formal description of information and information space is needed. The mathematic definition of information, information operations, relationship of information and information space based on ontology, and their algebraic structure were studied. So a theoretical support was provided for information resource service in the specific information field.

    • Information Resource Focusing Mathematical Model Besed onSaturation Information Dimension

      2010, 32(4):145-149.

      Abstract (6647) HTML (0) PDF 207.16 K (5657) Comment (0) Favorites

      Abstract:The increasing or decreasing technology of the saturated information dimension was applied to decompose and analyze the structure of information acquisition subspace one, and the acquisition of the value of saturated information dimension was divided into two parts—White and Grey. The saturation information dimension was used as the correlative order, applied to describe the grey correlative space, and the correlative oder was used to describe the correlative degree between information, thus obtaining a new mathematical model focusing on information resource.

    • A Clustering Method for Gene Expression Data Based onLinear Manifold

      2010, 32(4):150-156.

      Abstract (6264) HTML (0) PDF 262.23 K (5946) Comment (0) Favorites

      Abstract:Conventional clustering methods fail to obtain good clustering performances for gene expression data due to the inherent sparsity of data and the existence of noise. A new linear manifold clustering method was proposed to address this problem. The basic idea of this method is to search the line manifold clusters hidden in datasets and then fuse some of the line manifold clusters to construct higher dimensional manifold clusters. The method considers the orthogonal distance and the tangent distance as the linear manifold distance metrics, utilizes spatial neighbor information and takes the real gene expression profile as the transition vector. The experimental results show the superiority of this method over other competing clustering methods in terms of clustering accuracy and the anti-noise capability of this method. Moreover, the proposed method is able to obtain some clusters with significant biological meaning for Hela gene expression data. All these demonstrate the method proposed is suitable and valid for the gene expression data clustering.

    • WZ Factorization for a Kind of Special Structured Matrix

      2010, 32(4):157-164.

      Abstract (6334) HTML (0) PDF 301.79 K (5992) Comment (0) Favorites

      Abstract:The kind of WZ factorizations is the basic mathematics theory for a series of parallel algorithms in solving linear systems. For the symmetric p-tridiagonal matrix, the WZ factorization and its properties were proposed and proved. Furthermore, it also shows that the W-factor of the WZ factorization owns the character that the elements in itare real numbers when the real matrix is symmetric positive definite, and the factorization is unique when the elements in diagonal are positive real numbers.

    • >Mathematics & Systems Science
    • Real Matrix Representation of Quaternions

      2010, 32(4):165-168.

      Abstract (6320) HTML (83) PDF 169.52 K (6532) Comment (0) Favorites

      Abstract:Quaternion algebra plays an important role in computer graphics, modern physics, attitude representation of satellite among many others. It is valuable to make a thorough study of quaternion from a mathematical point of view. However, due to the non-commutative nature, quaternion algebra is not so easy to handle as people expected. One of the methods to deal with quaternions is to identify them with real matrices, the entries of which are of course commutative. These identifications are actually embeddings from quaternion algebra to Rn×nThe current method investigated the algebraic embedding problem from the quaternion algebra to Rn×n ,and found out all the possible algebraic embeddings under the condition that maps the imaginary units to signed permutation matrices. The method is to consider the images of the generators (i.e. the imaginary units) of quaternion algebra., then investigated the properties of these images and determined what kind of real matrices fulfilled them. Next, it solved the problem by invoking the language of group action. The conclusion turns out to be interesting: the crucial pairs of matrices, which determine the embeddings, are made up of real matrix pairs And there are essentially two pairs of the latter kind.

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