When T/2 Fractionally Spaced blind Equalization Algorithm based Constant Modulus Algorithm (T/2-FSE- CMA) is employed for equalizing higher order Quadrature Amplitude Modulation signals (QAM), it has disadvantages of ...When T/2 Fractionally Spaced blind Equalization Algorithm based Constant Modulus Algorithm (T/2-FSE- CMA) is employed for equalizing higher order Quadrature Amplitude Modulation signals (QAM), it has disadvantages of low convergence speed and large Mean Square Error (MSE). For overcoming these disadvantages, a Modified T/2 Fractionally Spaced blind Equalization algorithm based on Coordinate Transformation and CMA (T/2-FSE-MCTCMA) was proposed by analyzing the character of 16QAM signal constellations. In the proposed algorithm, real and imaginary parts of input signal of T/2 fractionally spaced blind equalizer are equalized, respectively, and output signals of equalizer are transformed to the same unit circle by coordinate transformation method, a new error function is defined after making coordinate transformation and used to adjust weight vector of T/2 fractionally spaced blind equalizer. The proposed algorithm can overcome large misjudgments of T/2 fractionally spaced blind equalization algorithm for equalizing multi-modulus higher order QAM. Simulation results with underwater acoustic channel models demonstrate that the proposed T/2-FSE-MCTCMA algorithm outperforms T/2 Fractionally Spaced blind Equalization algorithm bas-ed on Coordinate Transformation and CMA (T/2-FSE-CTCMA) and the T/2-FSE-CMA in convergence rate and MSE.展开更多
Light pen coordinate measuring system(LPCMS)is a kind of portable coordinate measuring technique based on vision metrology.In classical LPCMS,the measuring range is limited to the camera’s field of view.To overcome t...Light pen coordinate measuring system(LPCMS)is a kind of portable coordinate measuring technique based on vision metrology.In classical LPCMS,the measuring range is limited to the camera’s field of view.To overcome this defect,a new LPCMS is designed in this paper to fulfil whole space coordinate measurement.The camera is installed on a turntable instead of a tripod,so that the camera can rotate to track the movement of the light pen.The new system can be applied to large scale onsite measurement,and therefore it notably extends the application of LPCMS.To guarantee the accuracy of the new system,a method to calibrate the parameters of the tracking turntable is also proposed.Fixing the light pen at a stationary position,and changing the azimuth angles of the turntable’s two shafts,so that the camera can capture the images of the light pen from different view angles.According to the invariant spatial relationship between the camera and the pedestal of the tracking turntable,a system of nonlinear equations can be established to solve the parameters of the turntable.Experimental results show that the whole space coordinate measuring accuracy of the new system can reach 0.25 mm within 10 m.It can be concluded that the newly designed system can significantly expand the measuring range of LPCMS without losing too much accuracy.展开更多
An afne space is a set consisting of points and vectors.A vector space(or linear space)is an afne space with a specied origin.For a given afne coordinate system,there exists a one-to-one correspondence between vectors...An afne space is a set consisting of points and vectors.A vector space(or linear space)is an afne space with a specied origin.For a given afne coordinate system,there exists a one-to-one correspondence between vectors and coordinates.In order to provide a theoretical basis for coordinate and frame transformations,and to simplify the transformation process in specic problem studies,the geometric product of vectors is redened(the geometric product of vectors is the sum of the negative inner product and the outer product of the vectors),thus the one-to-one correspondence relationship between unit vectors and imaginary units is established.According to Hurwitz's theorem,the vector space of the outer product is gotten and dened,and its dimension cannot be chosen arbitrarily.Based on Arthur Cayley's(1845)multiplication rules of octonions,transformation formulas for a seven-dimensional vector space and rotation matrices for coordinate frame transformations are derived.It is pointed out that the three-dimensional rotation matrices commonly used in astrometry and geodesy are special cases thereof.According to the redefinition of the geometric product of vectors,the multiplication rules of quaternions can be directly obtained,as well as the multiplication table of imaginary units of octonions.It is further indicated that the multiplication tables of imaginary units for octonions and hypercomplex numbers of higher dimensions are not unique.展开更多
文摘When T/2 Fractionally Spaced blind Equalization Algorithm based Constant Modulus Algorithm (T/2-FSE- CMA) is employed for equalizing higher order Quadrature Amplitude Modulation signals (QAM), it has disadvantages of low convergence speed and large Mean Square Error (MSE). For overcoming these disadvantages, a Modified T/2 Fractionally Spaced blind Equalization algorithm based on Coordinate Transformation and CMA (T/2-FSE-MCTCMA) was proposed by analyzing the character of 16QAM signal constellations. In the proposed algorithm, real and imaginary parts of input signal of T/2 fractionally spaced blind equalizer are equalized, respectively, and output signals of equalizer are transformed to the same unit circle by coordinate transformation method, a new error function is defined after making coordinate transformation and used to adjust weight vector of T/2 fractionally spaced blind equalizer. The proposed algorithm can overcome large misjudgments of T/2 fractionally spaced blind equalization algorithm for equalizing multi-modulus higher order QAM. Simulation results with underwater acoustic channel models demonstrate that the proposed T/2-FSE-MCTCMA algorithm outperforms T/2 Fractionally Spaced blind Equalization algorithm bas-ed on Coordinate Transformation and CMA (T/2-FSE-CTCMA) and the T/2-FSE-CMA in convergence rate and MSE.
基金State Administration of Science,Technology and Industry for the National Defense(No.JSJL2014206B001)。
文摘Light pen coordinate measuring system(LPCMS)is a kind of portable coordinate measuring technique based on vision metrology.In classical LPCMS,the measuring range is limited to the camera’s field of view.To overcome this defect,a new LPCMS is designed in this paper to fulfil whole space coordinate measurement.The camera is installed on a turntable instead of a tripod,so that the camera can rotate to track the movement of the light pen.The new system can be applied to large scale onsite measurement,and therefore it notably extends the application of LPCMS.To guarantee the accuracy of the new system,a method to calibrate the parameters of the tracking turntable is also proposed.Fixing the light pen at a stationary position,and changing the azimuth angles of the turntable’s two shafts,so that the camera can capture the images of the light pen from different view angles.According to the invariant spatial relationship between the camera and the pedestal of the tracking turntable,a system of nonlinear equations can be established to solve the parameters of the turntable.Experimental results show that the whole space coordinate measuring accuracy of the new system can reach 0.25 mm within 10 m.It can be concluded that the newly designed system can significantly expand the measuring range of LPCMS without losing too much accuracy.
基金supported by the National Natural Science Foundation of China(No.42574047,No.12473068,No.41774039,No.42074002).
文摘An afne space is a set consisting of points and vectors.A vector space(or linear space)is an afne space with a specied origin.For a given afne coordinate system,there exists a one-to-one correspondence between vectors and coordinates.In order to provide a theoretical basis for coordinate and frame transformations,and to simplify the transformation process in specic problem studies,the geometric product of vectors is redened(the geometric product of vectors is the sum of the negative inner product and the outer product of the vectors),thus the one-to-one correspondence relationship between unit vectors and imaginary units is established.According to Hurwitz's theorem,the vector space of the outer product is gotten and dened,and its dimension cannot be chosen arbitrarily.Based on Arthur Cayley's(1845)multiplication rules of octonions,transformation formulas for a seven-dimensional vector space and rotation matrices for coordinate frame transformations are derived.It is pointed out that the three-dimensional rotation matrices commonly used in astrometry and geodesy are special cases thereof.According to the redefinition of the geometric product of vectors,the multiplication rules of quaternions can be directly obtained,as well as the multiplication table of imaginary units of octonions.It is further indicated that the multiplication tables of imaginary units for octonions and hypercomplex numbers of higher dimensions are not unique.
