The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and ...The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.展开更多
To denoise the diffusion weighted images （DWls） featured as multi-boundary, which was very important for the calculation of accurate DTIs （diffusion tensor magnetic resonance imaging）, a modified Wiener filter was...To denoise the diffusion weighted images （DWls） featured as multi-boundary, which was very important for the calculation of accurate DTIs （diffusion tensor magnetic resonance imaging）, a modified Wiener filter was proposed. Through analyzing the widely accepted adaptive Wiener filter in image denoising fields, which suffered from annoying noise around the edges of DWIs and in turn greatly affected the denoising effect of DWIs, a local-shift method capable of overcoming the defect of the adaptive Wiener filter was proposed to help better denoising DWIs and the modified Wiener filter was constructed accordingly. To verify the denoising effect of the proposed method, the modified Wiener filter and adaptive Wiener filter were performed on the noisy DWI data, respectively, and the results of different methods were analyzed in detail and put into comparison. The experimental data show that, with the modified Wiener method, more satisfactory results such as lower non-positive tensor percentage and lower mean square errors of the fractional anisotropy map and trace map are obtained than those with the adaptive Wiener method, which in turn helps to produce more accurate DTIs.展开更多
The non-linearity problem of aircraft system could not be overcome by using the MEMS sensor only.In order to improve the accuracy of aerial vehicle attitude,an aircraft attitude estimation of the MEMS sensor based on ...The non-linearity problem of aircraft system could not be overcome by using the MEMS sensor only.In order to improve the accuracy of aerial vehicle attitude,an aircraft attitude estimation of the MEMS sensor based on modified particle filter is proposed.The aircraft attitude is optimized by the conjugate gradient method,and the drift error of gyroscope is reduced.Moreover,the particle weight is updated by the observed value to obtain an optimized state estimate.Finally,the conjugate gradient method and the modified particle filter are weightily combined to determine the optimal weighting factor.The attitude estimation is carried out with STM32 and MEMS sensor as the core to design system.The experimental results show that the static and dynamic attitude estimation performances of the aircraft are improved.The performances are well,the attitude data is relatively stable,and the tracking characteristics are better.Moreover,it has better robustness and stability.展开更多
文摘The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.
基金Project(2009AA04Z214) supported by the National High Technology Research and Development Program of ChinaProject(07JJ6133) supported by the Natural Science Foundation of Hunan Province, China
文摘To denoise the diffusion weighted images （DWls） featured as multi-boundary, which was very important for the calculation of accurate DTIs （diffusion tensor magnetic resonance imaging）, a modified Wiener filter was proposed. Through analyzing the widely accepted adaptive Wiener filter in image denoising fields, which suffered from annoying noise around the edges of DWIs and in turn greatly affected the denoising effect of DWIs, a local-shift method capable of overcoming the defect of the adaptive Wiener filter was proposed to help better denoising DWIs and the modified Wiener filter was constructed accordingly. To verify the denoising effect of the proposed method, the modified Wiener filter and adaptive Wiener filter were performed on the noisy DWI data, respectively, and the results of different methods were analyzed in detail and put into comparison. The experimental data show that, with the modified Wiener method, more satisfactory results such as lower non-positive tensor percentage and lower mean square errors of the fractional anisotropy map and trace map are obtained than those with the adaptive Wiener method, which in turn helps to produce more accurate DTIs.
基金National Natural Science Foundation of China(No.61261029)
文摘The non-linearity problem of aircraft system could not be overcome by using the MEMS sensor only.In order to improve the accuracy of aerial vehicle attitude,an aircraft attitude estimation of the MEMS sensor based on modified particle filter is proposed.The aircraft attitude is optimized by the conjugate gradient method,and the drift error of gyroscope is reduced.Moreover,the particle weight is updated by the observed value to obtain an optimized state estimate.Finally,the conjugate gradient method and the modified particle filter are weightily combined to determine the optimal weighting factor.The attitude estimation is carried out with STM32 and MEMS sensor as the core to design system.The experimental results show that the static and dynamic attitude estimation performances of the aircraft are improved.The performances are well,the attitude data is relatively stable,and the tracking characteristics are better.Moreover,it has better robustness and stability.
