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The weighting used tends to orthogonalize the least squares terms.


These various bands are mixed using the projection method and care has been taken to orthogonalize the bands.


The changes in interaction serve to orthogonalize opponent signals with respect to the adapting modulation, and the changes in response functions serve to equalize the relative frequencies of different levels of response to the adapting modulation.


The changes in interaction serve to orthogonalize opponent signals with respect to the adapting modulation, and the changes in response functions serve to equalize the relative frequencies of different levels of response to the adapting modulation.


Unfortunately, the number of sweeps required to orthogonalize the columns of J is usually not known a priori.

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 A simple method for Zernike polynomial fitting in fringe analysis is given. Though the method is still based on a GramSchmidt orthogonalizing technique, it is not necessary to orthogonalize the polynomials during fitting. The linear transposition of the covariance matrix of the polynomiala can work out the Zernike coeflicinces directly. So it offers a better algorithm to Zernike polynomial fitting.  本文介绍了一种实现干涉条纹Zernike多项式拟合的简单算法。该算法虽然仍是基于GramSchmidt正交化方法,但用该算法求解Zernike系数时并不需要经过正交化过程,而是用谱Zernike多项式的协方差矩阵的线性变换来直接求解。因而它很适合于编写拟合过程的计算机程序,是一种比较理想的实现Zernike多项式拟合的算法。  In this paper, a ptactical openloop alignment scheme for strapdown inertial navigation systems is discussed in detail. The alignment process is separated into two steps, i.e.,coarse alignment, or analytical alignment, and openloop fine alignment. GramSchmidt method, which can result in an ideal orthogonal matrix, is used to orthogonalize coarse alignment matrix. Least Squares estimators are used to estimate instantaneous misalignment angle between the true geographic frame and the computed one, which... In this paper, a ptactical openloop alignment scheme for strapdown inertial navigation systems is discussed in detail. The alignment process is separated into two steps, i.e.,coarse alignment, or analytical alignment, and openloop fine alignment. GramSchmidt method, which can result in an ideal orthogonal matrix, is used to orthogonalize coarse alignment matrix. Least Squares estimators are used to estimate instantaneous misalignment angle between the true geographic frame and the computed one, which is determined by the coarse alignment matrix. To eliminate efficiently the affections of environment disturbance on alignment process the misalignment angle is divided into two components, i. e., instantaneous one and average one. All measurement equations used to estimate the two components are in the same form. This feature will be helpful in implementing the scheme in a real strapdown system, since it can reduce the burden on online computer. Lowpass digital filters are introduced into the openloop alignment process to enhance the accuracy and shorten the time needed.Digital simulations are employed to verify the effectiveness of such an alignment scheme. The simulation results reveal that this scheme can reach the accuracy superior to 1 arcminute in azimuth misalignment and less than 6 minutes is needed to complete the alignment process under the simulation conditions listed in Table 1 . Other results also indicate that this scheme is efficient and satisfactory.  本文对一种捷联惯导系统的开环初始对准方法作了详尽的讨论。对准过程分作二步完成,即解析对准与开环精对准。根据解析对准的具体特点,采用了GramSchmidt正交化方法来确保所得粗对准矩阵的正交性,最小二乘估计器的应用免除了最佳滤波器对各种噪声模型的要求。并且,开环对准中还引入了低通数字滤波器来改善对准的精度及快速性。不同条件下的数字仿真用来验证这种对准方法的可行性,取得了满意的结果。  A modified analytical approach is proposed to orthogonalize the measured modes of airplane structures. Firstly, a generalized flexibility matrix is derived as Gravitz proposed. But this matrix is furthersettled to satisfy the requirements of structural symmetry and the subsequent matrix is only used to reviseone selected mode having the highest testing accuracy. By using this modified mode as the initial vector,the least square method is adopted to compute the rest successively. Applications to several... A modified analytical approach is proposed to orthogonalize the measured modes of airplane structures. Firstly, a generalized flexibility matrix is derived as Gravitz proposed. But this matrix is furthersettled to satisfy the requirements of structural symmetry and the subsequent matrix is only used to reviseone selected mode having the highest testing accuracy. By using this modified mode as the initial vector,the least square method is adopted to compute the rest successively. Applications to several fighters andbombers show that the proposed procedure is more reasonable and economical than others in computation.  提出了一种改进的飞机结构测量振型正交化方法。该法首次考虑了飞机结构对称性及测量指示函数高低的影响。算例表明，本文方法更符合实际，且能大大提高计算效率。   << 更多相关文摘 
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