基于DSP的协方差矩阵求逆的数值问题研究  

A Study on Numerical Accuracy of Inversion of Covariance Matrix Based on DSP

作　　者：任磊[1,2] 王永良[2] 陈建文[2] 陈风波[2] 

机构地区：[1]国防科技大学电子科学与工程学院,长沙410073 [2]空军雷达学院兵器运用工程军队重点实验室,武汉430019

出　　处：《现代雷达》2009年第3期48-52,共5页Modern Radar

基　　金：武器装备预研基金;国家自然科学基金重点项目(60736009)

摘　　要：机载雷达多通道空时自适应处理(STAP)系统的实时实现的难点在于大数据流下的高精度实时处理,其中STAP权值计算有数据域和均方域2种方法,分别以QR分解和样本协方差矩阵求逆(SM I)方法为代表。QR分解方法一般映射到脉动阵并行实现,然而脉动阵实现的结构缺乏通用性和可重构性导致这种设计成本较高,SM I方法实现则相对简单。文中基于数字信号处理(DSP)量化分析了SM I方法的舍入误差和数值溢出问题,推导出舍入误差表示成复数噪声的方差的公式,从机理上给出数值精度和稳定性改善方法,最后通过实测数据验证了方法的有效性。The difficulty of real-time implementation of airborne radar multi-channel Space-Time Adaptive Processing（STAP） system is its high precision implementation with tremendous dataflow. There are two methods to compute the STAP weights named data domain algorithm and mean square domain algorithm, for example QR decomposition algorithm and Sample Matrix Inversion （SMI） algorithm. Compared with SMI algorithm, QR decomposition algorithm can be mapped onto systolic array while its design cost is high. Based on Digital Signal Processing（DSP） the round-off error and numerical overflow problem of SMI algorithm are analyzed, and a formula of the round-off error is devied. A method of numerical accuracy and stability improvement is obtained by mechanism analysis and is validated with measured data.

关 键 词：空时自适应处理 样本协方差矩阵求逆 数值精度 缩放 

分 类 号：TN957.52[电子电信—信号与信息处理]