Threshold Decryption Scheme with Multiple Policies

Based on the difficulty in computing discrete logarithm and square root on some special conditions, we propose a basic threshold secret sharing scheme for muhiple secrets with muhiple policies, which allows a group of users to share muhiple secret keys and only one secret shadow to be kept by each user. An efficient threshold decryption scheme with multiple policies is designed on the basis of the basic threshold scheme. This decryption scheme allows muhiple secret keys to be shared among a group of users, and each user to keep only one secret shadow. Different public keys can be used to encrypt documents. If and only if the number of cooperated users who keep the secret shadows is greater than or equal to the threshold value of the corresponding secret key, they can cooperate to decrypt the documents. It is proved that the proposed scheme has very strong security, unless the at tackers can solve the discrete logarithm problem and the square root problem.     

完全域上方阵有平方根的充要条件

本文借助λ－矩阵理论，引入了根方互导多项式等概念，得到了完全域上方阵平方根的充要条件。     

基于无迹卡尔曼滤波的LSSVR在线多步时间序列预测

准确宽范围多步预测在时间序列预测应用中带来了巨大挑战.提出了一种基于最小二乘支持向量回归(LSSVR)和无迹卡尔曼滤波(UKF)的在线多步预测方法,利用时间滑动窗口减小算法的计算负荷,UKF方法实现LSSVR模型参数更新以提高预测精度.当预测范围达到预定步长p时,由核宽度σ、支持值参数{α_k}_k~L_(=1)以及偏移项b所构成的模型参数通过新的测量值和UKF进行在线更新.提出的方法不仅以较少的训练数据建立在线预测模型(所需训练数据集大小为相空间维数与滑动窗口长度之和),且多步预测值的精度相比于传统方法得到进一步提高.最后,通过几个实验研究论证了提出方法的有效性和优越性.     

基于UKF的机动目标跟踪处理方法

提出了基于UKF的机动目标跟踪处理方法,能有效抑制动力学模型非线性和观测模型非线性带来的模型误差。和传统EKF滤波方法相比,该方法不仅避免了截断误差造成的滤波发散,而且避免了求解雅克比矩阵,简化计算流程,可以模块化处理,非常适合工程实现。仿真实验表明,当目标呈现明显非线性特征并且大机动运动时,该方法可以有效确定目标轨迹,实现高精度目标跟踪。     

带常值偏差的机动目标跟踪数据处理方法

机动目标跟踪中的系统误差是影响跟踪精度的关键因素之一。为了抑制系统误差带来的影响,本文提出了基于UKF的常值偏差估计的机动目标跟踪处理方法,通过对状态变量的扩维处理,不仅能有效抑制动力学模型非线性和观测模型非线性带来的模型误差,还能对观测模型中产生的系统误差进行估计,从而提高机动目标跟踪精度。仿真实验表明,在测距和测速跟踪模式下,测距系统误差能有效估计出来,常值偏差不会对跟踪精度产生影响。     

基于UKF神经网络的姿态测量信息融合算法

针对融合系统建模误差、噪声统计特性不精确性和环境的动态变化性致使传统联合滤波过程中融合权值难以确定,引入人工智能中的神经网络,提出了基于神经网络的多信息自适应智能估计融合算法研究;利用神经网络的自适应能力对状态估计融合结果进行实时辅助补偿和修正,将非线性最优估计与神经网络技术相结合,重点研究了基于UKF的神经元融合权重在线自适应学习算法,以便在缺少准确局部子滤波器协方差信息情况下,仍能使全局估计融合结果最优,从理论上证明了UKF学习算法优于传统EKF学习方法,并以卫星多姿态测量信息融合定姿系统为例,给出了计算实例和结论分析,表明了所提出的模型与算法在实际应用中的有效性。

Abstract：

The fusion weight of traditional Federal Kalman Filter is difficult to be determined because of the fusion system modeling error,the inaccuracy of noise statistic characteristics as well as the dynamic variability in the fusion filtering process.In order to solve this problem,a self-adaptive fusion estimation algorithm for multi-information measurement based on neural networks was presented,which used the self-adaptive ability of neural networks to make real-time compensation and amendment for the state fusion estimation results.Combining a nonlinear optimal estimation with neural network,an online adaptive training algorithm for the weights of neuron based on Unscented Kalman filter （UKF） was researched,which could still realize the optimal fusion for the global estimation even if the accurate covariance information of each local sub-filter were absent.The performances of UKF training algorithm and the traditional EKF algorithm were analyzed and compared,and moreover taking the multi-information fusion system for satellite attitude determination as the experimental example,the simulation calculation and analysis were advanced,which show that the presented models and algorithms are effective in the actual application.     

Unscented extended Kalman filter for target tracking

A new method of unscented extended Kalman filter (UEKF) for nonlinear system is presented. This new method is a combination of the unscented transformation and the extended Kalman filter (EKF). The extended Kalman filter is similar to that in a conventional EKF. However, in every running step of the EKF the unscented transformation is running, the deterministic sample is caught by unscented transformation, then posterior mean of nonlinearity is caught by propagating, but the posterior covariance of nonlinearity is caught by linearizing. The accuracy of new method is a little better than that of the unscented Kalman filter (UKF), however, the computational time of the UEKF is much less than that of the UKF.     

基于平方根UKF的多传感器融合再入段目标跟踪研究

为了提高再入段目标跟踪的精度,将平方根不敏卡尔曼滤波（unscented Kalman filter, UKF）算法与多传感器分布式融合算法相结合,提出了基于平方根UKF的多传感器融合跟踪算法。在各个独立的传感器中利用平方根UKF滤波器进行状态估计,然后通过分布式融合方法融合各传感器的状态估计值得到全局的状态估计值和误差协方差,将全局误差协方差进行加权对各传感器进行分配更新。通过仿真验证,基于平方根UKF的多传感器融合跟踪算法具有较高的跟踪性能,是一种有效的非线性融合跟踪算法。     

函数φ(a2k(n))及其推广形式的渐近公式

本文利用解析的方法讨论了函数φ（a2^k（n））及其推广形式的均值问题,并给出了两个有规律的渐近公式,其中φ（n）是Euler函数,a2（n）是F．Smarandache提出的平方根序列．     

一道极限题的推广及其应用

本文对一道极限题进行推广,并应用推广结果对任意正数a开平方根,更一般地推广到对任意正数a开k次方根．