CAJ | 학술논문

该文首次给出了任意平面离散阵列对水下窄带源和宽带源进行近场测距的克拉美-罗界(CRB),并进一步全面地推导了相应远场测向的CRB表达式.由此揭示了近场测距和远场测向的CRB的影响因素和特点:(1)两者的影响因素均可分为两部分:阵列相关因素,如阵列结构和阵列孔径等;目标信号相关因素,如目标的相对方位、信号频率、带宽和信噪比等.(2)两者均与信号带宽和谱密度函数构成的一个联合量成反比.(3)近场测距的CRB与目标距离的四次方成正比.(4)近场测距的 CRB 与基阵参考点的选择有关,而远场测向的 CRB 则与其无关.(5)对于均匀直线阵,近场测距CRB大致与阵列孔径的五次方成反比,而远场测向CRB则大致与阵列孔径的三次方成反比;对于均匀圆周阵,两者均与阵列孔径成反比,且与目标的相对方位无关.Monte-Carlo仿真结果验证了理论分析和上述结论的正确性.该文CRB不仅给出了近场测距和远场测向的最佳估计性能,而且为阵列及信号的设计提供了理论指导,以达到最优的测距和测向效果.
해문수차급출료임의평면리산진렬대수하착대원화관대원진행근장측거적극랍미-라계(CRB),병진일보전면지추도료상응원장측향적CRB표체식.유차게시료근장측거화원장측향적CRB적영향인소화특점:(1)량자적영향인소균가분위량부분:진렬상관인소,여진렬결구화진렬공경등;목표신호상관인소,여목표적상대방위、신호빈솔、대관화신조비등.(2)량자균여신호대관화보밀도함수구성적일개연합량성반비.(3)근장측거적CRB여목표거리적사차방성정비.(4)근장측거적 CRB 여기진삼고점적선택유관,이원장측향적 CRB 칙여기무관.(5)대우균균직선진,근장측거CRB대치여진렬공경적오차방성반비,이원장측향CRB칙대치여진렬공경적삼차방성반비;대우균균원주진,량자균여진렬공경성반비,차여목표적상대방위무관.Monte-Carlo방진결과험증료이론분석화상술결론적정학성.해문CRB불부급출료근장측거화원장측향적최가고계성능,이차위진렬급신호적설계제공료이론지도,이체도최우적측거화측향효과.
The Craomér-Rao Bound (CRB) expression of near-field distance estimation for underwater source is first presented. Furthermore, the CRB of far-field Direction-Of-Arrival (DOA) estimation is deduced. The characteristics and factors of CRB results are shown as following:(1)Both of the distance estimation CRB and the DOA estimation CRB can be divided into two items, one of which is relative to the geometry of array, including array manifold and array aperture, while the other one depends on the signal characteristics, containing source direction, frequency, bandwidth and SNR etc;(2)Both of them are inversely proportional to an item which is composed of bandwidth and spectrum density function;(3)The distance estimation CRB is directly proportional to the forth power of distance;(4)The distance estimation CRB is relative to the position of reference point, while the DOA estimation CRB is not;(5)For Uniform Linear Array (ULA), the distance estimation CRB is close to be inversely proportional to the fifth power of array aperture, and the DOA estimation CRB is close to be inversely proportional to the cube of array aperture;for Uniform Circle Array (UCA), both of them is inversely proportional to the array aperture and independent of source direction. The Monte-Carlo simulation results validate the theoretical analysis and the conclusions. This paper not only presents the best performance of distance estimation and DOA estimation, but also provides the theoretical guidance of array and signal design to achieve the optimum estimation.