AI 中文总结
本文提出基于非麦克斯韦分布函数的开放系统改进卡尔曼滤波，通过构建非高斯闭包，在Alcator C-Mod探针数据的留一预测中，双INMDF在偏滤器条件预测性能优于麦克斯韦分布，验证了该方法的泛化性与区域依赖性。
AI 中文摘要
卡尔曼滤波适用于线性动力学且状态与观测统计为高斯分布的情形，但均值-协方差表示无法保留源驱动动力学演化产生的有限非高斯结构。本文针对开放等离子体系统构建了一种改进滤波理论，其中额外的状态结构源自非麦克斯韦速度空间分布函数（NMDF），而非作为经验残差族引入。动力学流形定义为$f_s(\boldsymbol X_s,\boldsymbol v)$，固定诊断映射$H_D$生成测量概率密度函数（PDF）$p_{D,s}$；投影动力学方程确定状态预测动力学，后验概率密度函数连续演化并通过贝叶斯规则修正，必要时采用正性约束的相对熵投影。具有仿射动力学和线性高斯观测模型的高斯后验可恢复卡尔曼-布西滤波与离散卡尔曼滤波极限。首个显式非高斯闭包是通过精确五矩反演得到的五坐标INMDF，同时保留Kappa作为宽尾替代分布。利用7个Alcator C-Mod朗缪尔探针离子饱和电流PDF，6个动力学流形在相同源统计、噪声模型、归一化及探针响应下传播。因已发表直方图缺乏时间排序，未测试递归跟踪；在通用留一条件预测中，双INMDF在所有4个保留的偏滤器条件中排名第一，平均误差为0.0989，而麦克斯韦分布函数（MDF）的平均误差为0.1089。区域内校准显示，一阶INMDF与双INMDF的偏滤器误差几乎相同，分别为0.0936和0.0937，而双麦克斯韦分布函数的中平面误差最小，为0.0718。预测结果依赖已发表的源与噪声控制，但表明冻结的源-动力学响应可推广至未见过的电流PDF，且优选响应与区域相关。
英文摘要
Kalman filtering (KF) recursively infers plasma quantities, represented by a state, from noisy diagnostics while propagating uncertainty in the inferred state separately from diagnostic noise. For linear dynamical and measurement models with Gaussian probability density functions (PDFs), the state mean and covariance provide the KF description. We modify this KF for open plasmas with particle and energy sources by extending the physical state from Maxwellian variables to retained NMDF coordinates, whose evolution follows a projection of the nonlinear Landau-Fokker-Planck equation. The same NMDF state is propagated through a fixed diagnostic response to obtain the corresponding measurement PDF. Because a non-Gaussian likelihood can drive the posterior outside the Gaussian family, the mean-covariance representation is extended to a finite moment closure whose coordinates are related to the retained moments through their Jacobian. The recursive prediction-correction structure is preserved, recovering conventional KF results for linear models with Gaussian PDFs. As a proof of concept, we use seven published non-Gaussian Alcator C-Mod Langmuir-probe current PDFs. For each target PDF, NMDF response parameters are calibrated from the other probe PDFs and frozen; this excluded target tests independent prediction. This test shows that different plasma regions require different NMDF structures, instead of the standard assumption of Maxwellian velocity distributions across all regimes and locations. Because the published measurement PDFs do not retain time ordering, this proof of concept does not yet test recursive uncertainty dynamics. Implementing the projected Landau-Fokker-Planck prediction with time-resolved diagnostics is the next step toward full validation of the modified KF.
Comments34 pages, 9 figures
