认知下视雷达空时滤波的几何机制与流形上的优化方法研究

项目名称： 认知下视雷达空时滤波的几何机制与流形上的优化方法研究

项目编号： No.61771484

项目类型： 面上项目

立项/批准年度： 2018

项目学科： 无线电电子学、电信技术

项目作者： 范西昆

作者单位： 中国人民解放军空军工程大学

项目金额： 16万元

中文摘要： 认知下视雷达的空时滤波是现有空时滤波的拓展，直观表述为多种统计先验知识与有限空时样本统计信息融合下的协方差矩阵估计问题，实质是一个非线性约束最大熵泛函极值问题。受限于现有空时滤波的求解架构，知识（约束）与矩阵结构具有紧耦合性，处理要根据不同的知识选择方法，导致多种知识难于统一处理的问题。提出现代几何与优化相结合的研究方法，充分利用矩阵流形丰富的内蕴结构，将约束集转化为矩阵流形的拓扑和几何结构约束条件，从而将原问题转化流形上的无约束优化问题。通过空时协方差矩阵流形的拓扑与几何结构、空时滤波优化约束集的流形表达机制、流形上的协方差矩阵的极大似然估计优化方法与算法等问题的研究，形成统一处理先验知识的几何空时滤波机制，有望克服现有模式的弊端并在同等样本条件下获得更精确协方差矩阵估计。研究成果可为下视雷达的认知探测提供技术储备，简化版本也可直接用于现有自适应体制雷达的性能提升，具有广阔应用前景。

中文关键词： 空时处理；认知雷达；协方差矩阵估计；矩阵流形；优化

英文摘要： Space-time filtering of cognitive down-looking radar extends existing space-time adaptive filtering research to covariance matrices estimation conditioned on statistical priori knowledge of multi-resource and limited samples, and can be thereby modeled as maximum entropy problem with non-linear constraints. A bottleneck problem of cognitive space-time filtering results from the processing method that is highly dependent on knowledge type. No optimization can be found in handling multi-types of knowledge involved when there is tight coupling in knowledge and covariance matrices structure. An optimization method based on modern geometry is proposed to convert the constraint set to a matrix manifold’s inherent topological and geometrical structure constraints, transforming the original optimization problem to the unconstrained optimization on matrix manifold. A geometric mechanism of space-time filtering for uniformly processing multi-types knowledge and obtaining better covariance estimations will be established through the research into topological and geometrical structures of space-time covariance matrices, the conversion of original constraint set to matrices manifolds and algorithms of maximum likelihood estimation of covariance matrices on manifolds. The theoretical exploration is expected to be applied on cognitive down-looking radar, and also can be used to improve performance of existing STAP radar.

英文关键词： Space-Time Processing;Cognitive Radar; Covariance Matrices Estimation;Matrix Manifolds;Optimization