干扰极化估计精度是影响雷达极化抗干扰能力的重要因素,而雷达天线空域极化特性存在一定的病态性,使来波极化估计的最小二乘解在病态情况下变得不稳定. 针对最小二乘方法估计来波极化所存在的病态性问题,提出一种改进极化矢量估计的约束最小二乘方法.首先分析影响来波极化估计稳定性的因素,针对具体的天线型式给出病态情况下的计算机仿真结果,推导了带二次约束的极化估计最小二乘解并给出了算法流程. 仿真结果表明了改进极化估计均方误差的有效性,该方法可显著提高干扰极化估计精度,提高雷达极化抗干扰能力.
Precision of interference polarization estimation is a major factor influencing radar polarization anti-jamming capability. To a certain extent, the spatial polarization characteristic (SPC) of radar is ill-conditioned, resulting in unstable solution to the estimation of received wave polarization. A least squares method with a quadratic constraint is presented to estimate polarization of the received wave. It treats the ill-conditioning problem in estimating the polarization state based on least square methods. Factors affecting stability of polarization estimation are analyzed, with computer simulation results in ill-conditioned cases for particular antenna forms. Theoretical analysis is then made and algorithmic steps given according to the principle of the proposed method. The simulation shows that the method can significantly reduce variance of polarization estimation so as to improve the estimation accuracy, useful in improving radar polarization anti-jamming capability.
[1] Dai H Y, Wang X S, Luo J, Li Y Z. A new polarimetric method by using spatial polarization characteristics of scanning antenna [J]. IEEE Transaction on Antennas and Propagation, 2012, 60(3): 1653-1656.
[2] 戴幻尧,李永祯,王雪松,刘勇. 主瓣干扰极化抑制的新方法研究[J]. 中国科学:F辑,2012, 42(4): 460-466. Dai H Y, Li Y Z, Wang X S, Liu Y. New polarization method for the suppression of main lobe interference [J]. Scientia Sinica: Informationis, 2012, 42(4): 460-466. (in Chinese)
[3] Meng C Z, Xia X G, Liu F L. Ten MIMO-SAR waveforms separation based on virtual polarization filter [J]. Science China Information Sciences, 2015, 58(4): 113-117.
[4] 任博,施龙飞,王洪军,李永祯,王国玉. 抑制雷达主波束内GSM干扰的极化滤波方法研究[J]. 电 子与信息学报,2014, 36(2): 459-464. Ren B, Shi L F, Wang H J, Li Y Z. Investigation on of polarization filtering scheme to suppress GSM interference in radar main beam [J]. Journal of Electronics & Information Technology, 2014, 36(2): 459-464. (in Chinese)
[5] 张树银,郭英,齐子森,苏令华. 共形阵列LFM信号DOA和极化参数的联合估计[J]. 应用科学学 报,2013, 31(3): 252-258. Zhang S Y, Guo Y, Qi Z S, Su L H. Joint estimation of DOA and polarization for LFM signals using conformal array antenna [J]. Journal of Applied Sciences, 2013, 31(3): 252-258. (in Chinese)
[6] 罗佳,王雪松,李永祯,肖顺平. 一种估计来波信号极化状态的新方法[J]. 国防科技大学学报,2008, 30(5): 56-61. Luo J, Wang X S, Li Y Z, Xiao S P. A novel method for polarization states estimation of receiving wave [J]. Journal of National University of Defense Technology, 2008, 30(5): 56-61. (in Chinese)
[7] 吴杰,苗恒严. 测量数据处理中病态矩阵和部分有偏估计方法[J]. 测绘通报,2010(9): 9-11. Wu J, Miao H Y. Ill-posed matrix and partial biased estimation method in measurement data processing [J]. Bulletin of Surveying and Mapping, 2010(9): 9-11. (in Chinese)
[8] 王永弟,赵好好. 病态线性模型参数估计的主元加权迭代法[J]. 测绘通报,2014(2): 23-25. Wang Y D, Zhao H H. Pivot element weighted iterative method of ill-conditioned linear model parameter estimation [J]. Bulletin of Surveying and Mapping, 2014(2): 23-25. (in Chinese)
[9] Burke J V, Curtis F E, Wang H, Wang J S. Iterative reweighted linear least squares for exact penalty subproblems on product sets [J]. SIAM Journal on Optimization, 2015, 25(1): 261-294.
[10] Dykes L, Reichel L. Simplified GSVD computations for the solution of linear discrete ill-posed problems [J]. Journal of Computational and Applied Mathematics, 2014, 255: 15-27.
[11] 亓万锋,罗钟铉,樊鑫. 基于逼近型细分的诱导细分格式[J]. 中国科学:数学,2014, 44(7): 755-768. Qi W F, Luo Z X, Fan X. Induced subdivision scheme based on approximation subdivision [J]. Chinese Science Mathematics, 2014, 44(7): 755-768. (in Chinese)
[12] 顾勇为,归庆明,张璇,魏萌. 大地测量与地球物理中病态性问题的正则化迭代解法[J]. 测绘学 报,2014, 43(4): 331-336. Gu Y W, Gui Q M, Zhang X, Wei M. Iterative solution of regularization to ill-conditioned problems in geodesy and geophysics [J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(4): 331-336. (in Chinese)
[13] Reichel L, Rodriguez G. Old and new parameter choice rules for discrete ill-posed problems[J]. Numberical Algorithms, 2013, 63: 65-87.
[14] Liu C S. A dynamical tikhonov regularization for solving Ill-posed linear algebraic systems [J]. Acta Applicandae Mathematicae, 2013, 123: 285-307.
