基于MCMC方法的运输类飞机鸟撞冲击能量研究

鸟撞冲击能量是运输类飞机结构安全设计和鸟撞适航条款制定的重要基础,目前我国运输类飞机鸟撞相关研究都是参照FAA中的鸟撞冲击能量标准要求,并没有考虑我国的自然环境等特点.针对这一问题,运用马尔科夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)估计方法,采用Gibbs抽样原理,在贝叶斯理论的框架下,对我国运输类飞机鸟撞冲击能量开展了研究,在小样本条件下对鸟撞冲击能量概率分布进行估算,为后续鸟撞安全性分析提供了重要基础.     

基于RJ-MCMC的DS-CDMA信号扩频码与信息序列盲估计

针对非合作低信噪比环境下的DS-CDMA信号参数估计问题,在分析信号模型的基础上,提出一种基于可逆跳跃的马尔科夫链蒙特卡罗(RJ-MCMC)扩频序列和信息序列联合估计算法。该算法通过建立信号参数和用户个数的联合后验分布模型,迭代抽样得到待估分布的样本,并有效地在不同维数的子空间中跳转,从而构造一条马尔科夫链,使其平稳分布为待估参数的后验分布。仿真结果表明,该算法在功率相同和不同的条件下均能适应较低的信噪比,并且对不同的用户个数具有较强的适应性,同时算法的估计性能相对现有的方法也有很大的改善。     

Hierarchical Bayesian modeling of ionospheric TEC disturbances as non-stationary processes

We model regular and irregular variation of ionospheric total electron content as stationary and non-stationary processes, respectively. We apply the method developed to SCINDA GPS data set observed at Bahir Dar, Ethiopia $\left(11.6°\text{N,}37.4°\text{E}\right)$. We use hierarchical Bayesian inversion with Gaussian Markov random process priors, and we model the prior parameters in the hyperprior. We use Matérn priors via stochastic partial differential equations, and use scaled $\text{Inv}-{\chi }^2$ hyperpriors for the hyperparameters. For drawing posterior estimates, we use Markov Chain Monte Carlo methods: Gibbs sampling and Metropolis-within-Gibbs for parameter and hyperparameter estimations, respectively. This allows us to quantify model parameter estimation uncertainties as well. We demonstrate the applicability of the method proposed using a synthetic test case. Finally, we apply the method to real GPS data set, which we decompose to regular and irregular variation components. The result shows that the approach can be used as an accurate ionospheric disturbance characterization technique that quantifies the total electron content variability with corresponding error uncertainties.