广义稳健中国剩余定理及其在空间欠采样信号DOA估计中的应用  

A Generalized Robust Chinese Remainder Theorem(GRCRT) and its Successful Application to DOA Estimation for Undersampled Spatial Signals

作　　者：梁红[1] 张琦[1] 杨长生[1] 

机构地区：[1]西北工业大学航海学院,陕西西安710072

出　　处：《西北工业大学学报》2010年第3期409-414,共6页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(60702067)资助

摘　　要：传统的中国剩余定理给出了从几组模数和余数重构正整数的方法,但当余数有误差时重构整数可能存在很大的误差。文中提出了广义的稳健中国剩余定理,采用一组非互质的模数(正整数)和相应的余数为实数且存在误差时重构任意实数的方法,并给出了详细的定理证明,得出算法重构实数的误差仅与余数的误差有关,解决了传统中国剩余定理重构整数时,余数的极小误差可能引起被估计整数相当大误差的问题。首次将该定理用于估计空间欠采样下相邻阵元间距大于半波长,且相位差估计存在误差时信号方位,仿真实验验证了所提算法的正确性和稳健性。Aim. We generalize the RCRT in Ref. 9 and call it GRCRT. We explain our GRCRT algorithm in section 2 of the full paper. Theorem 1 in section 2 is the GRCRT; its mathematical proof is given in the appendix. The core of section 2 is： ＂we reconstruct a real number when its remainders are real numbers and have errors, we show that, using our GRCRT algorithm, the reconstruction error is upper bounded by the maximum remainder error range named remainder error bound, if the remainder error bound is less than one quarter of the greatest common divisor （GCD） of all the moduli. ＂ For the first time, section 3 apples the GRCRT algorithm to estimating the DOA of spatial signals when the adjacent pairs of antenna interelement spacing are greater than the half - wavelength and when the measured phased differences between the undersampled spatial signals have errors. Section 4 presents a numerical example; the simulation results, given in Figs. 1 and 2, show preliminarily that our GRCRT algorithm is robust and can accurately estimate DOAS.

关 键 词：估计 信号处理 算法 DOA 广义稳健中国剩余定理 空间欠采样 

分 类 号：TN911.7[电子电信—通信与信息系统]