Consistency proof of two denoising methods and the parameter selection of PDE filtering method for ESPI

Electronic speckle pattern interferometry （ESPI） is a nondestructive, whole-field optical measurement technique. The removal of speckle noise is fundamental to extract measurement information accurately. In this letter, two filtering methods based on the oriented feature of ESPI fringes, i.e., the second-order oriented partial differential equation （SOOPDE） and oriented, regularized quadratic-cost function filtering methods, are first proven to be consistent. An important question in solving partial differential equation, i.e., how to select suitable parameters in an adaptive manner, is then discussed. The computer-simulated and experimentally obtained ESPI fringe patterns and phase map are processed by the SOOPDE filtering model with adaptive selective parameters. The qualitative and quantitative analyses demonstrate that the parameters selected by the adaptive method are effective and suitable for the SOOPDE filtering model.     

广义Kac方程的解的渐近稳定性

讨论了碰撞核具有一定奇异性的广义Kac方程的解的唯一性和渐近稳定性,证明了广义Kac方程的解在概率距离下以指数形式快速收敛到函数δ(v).     

甲型H1N1流感早期传播的数学模型

根据甲型H1N1流感早期在我国的传播规律,给出了一种描述甲型H1N1流感早期在我国传播的数学模型,分析了模型的解及其性质,证明了在严格的防控措施下,发病者最终将会完全消失,但处于潜伏期者最终将会达到一个固定的比例,指出了甲型H1N1流感的防控工作是一项长期而艰巨的任务.     

一类耗散Boltzmann方程的渐近稳定性

探讨了满足质量、动量守恒,能量耗散的空间齐次硬位势Boltzmann方程,对方程作PseudoMaxwellian逼近处理,证明了方程的解按概率距离指数收敛到稳定态解.     

基于INS/GPS组合导航的自适应模糊卡尔曼滤波

针对组合导航系统量测噪声统计特性随实际工作条件的不同而变化的特点,提出了一种基于模糊自适应卡尔曼滤波的INS/GPS组合导航算法。该方法通过监视理论残差和实际残差的协方差一致程度,应用模糊系统不断调整滤波器的增益系数,对卡尔曼滤波器进行在线自适应控制,最终实现最优估计。通过对INS/GPS组合导航系统的跑车试验,结果表明该方法在高噪声环境中具有良好的信息融合能力,能有效跟踪研究对象的状态变化。进一步表明该方法是有效、实用的。