免声速迭代式TDOA测向研究
|
摘要
针对到达时间差的声源测向问题,如果能够知道声源现场的速度参量,结合线性最小二乘法(Linear Least Squares,LLS)的波达方向(Direction of Arrival,DOA)的估计结果,则可以采用基于最大似然原理的迭代式算法进行求解。但在某些环境下,声信号传播的速度参量无法获得,或测量偏差较大,势必会影响DOA的估计精度。根据LLS无需声速的特点,以及基于最大似然原理的迭代式算法可直接求解声源方位角与俯仰角的特点,文中提出免声速迭代式模型,并采用泰勒级数展开法以及莱温伯格-马夸特法进行求解,该方法无需预先知道声音信号的速度参量。另外,文中推导了泰勒级数展开法、莱温伯格-马夸特法的测向均方差以及免声速迭代式模型的克拉姆-拉奥下界。模拟实验结果表明,在存在声速测量误差的情况下,所提方法明显优于现有方法。
In view of the time-difference-of-arrival sound-source direction finding problem,if the velocity parameter of propagating signal about sound source is known,combining with estimated result of the Direction of Arrival(DOA) of Linear Least Squares(LLS),the direction finding problem can be solved by iterative algorithm based on maximum likelihood principle.However,in some conditions,it is difficult to obtain velocity parameter of sound source,or measured deviation is large,which will affect the estimation accuracy of DOA.According to the characteristic of LLS about direction finding without sound velocity,and the characteristic of iterative algorithm based on maximum likelihood principle directly solving the azimuth and elevation of sound source,this paper proposed an iterative model without sound speed.The Taylor Series expansion method and the Levenberg-Marquart method are used to solve the problem,without knowing the velocity parameters of the sound signal beforehand.In addition,the mean square error of direction finding about Taylor Series expansion method and the Levenberg-Marquart method,and the Cramer-Rao Lower Bound of iterative model without sound speed are derived.The simulation results show that when measurement errors exist in sound speed,the proposed method is obviously superior to the existing methods.
In view of the time-difference-of-arrival sound-source direction finding problem,if the velocity parameter of propagating signal about sound source is known,combining with estimated result of the Direction of Arrival(DOA) of Linear Least Squares(LLS),the direction finding problem can be solved by iterative algorithm based on maximum likelihood principle.However,in some conditions,it is difficult to obtain velocity parameter of sound source,or measured deviation is large,which will affect the estimation accuracy of DOA.According to the characteristic of LLS about direction finding without sound velocity,and the characteristic of iterative algorithm based on maximum likelihood principle directly solving the azimuth and elevation of sound source,this paper proposed an iterative model without sound speed.The Taylor Series expansion method and the Levenberg-Marquart method are used to solve the problem,without knowing the velocity parameters of the sound signal beforehand.In addition,the mean square error of direction finding about Taylor Series expansion method and the Levenberg-Marquart method,and the Cramer-Rao Lower Bound of iterative model without sound speed are derived.The simulation results show that when measurement errors exist in sound speed,the proposed method is obviously superior to the existing methods.
引文
[1] HAO B J,LI Z,REN Y M,et al.Passive Multiple Disjoint Sources Localization Using TDOAs and GROAs[J].Acta Electronica Sinica,2012,40(12):2374-2381.(in Chinese)郝本建,李赞,任妘梅,等.基于TDOAs与GROAs的多信号源被动定位[J].电子学报,2012,40(12):2374-2381.
[2] YIN J,WAN Q,HOK C.A Simple and Accurate TDOA-AOA Localization Method Using Two Stations[J].IEEE Signal Processing Letters,2015,23(1):144-148.
[3] 孙仲康,郭福成,冯道旺.单站无源定位跟踪技术[M].北京:国防工业出版社,2008.
[4] GH Z,DZ F,H X,et al.An approximately efficient bi-iterative method for source position and velocity estimation using TDOA and FDOA measurements [J].Signal Processing,2016,125:110-121.
[5] BARUCH B,DORON M A,ROSENHOUSE J,et al.On direction finding of an emitting source from time delays[J].Journalofthe Acoustical Society of America,1999,105(6):3355-3363.
[6] WANG S Q,NIE J N.An Approach of Performance Analysis and Optimization forWireless Sensor Networks[J].Acta Electronica Sinica,2010,38(4):882-886.(in Chinese)王绍青,聂景楠.一种无线传感器网络性能评估及优化方法[J].电子学报,2010,38(4):882-886.
[7] NIELSEN R O.Estimation of azimuth and elevation angles for a plane wave sine wave with a 3-D array[J].IEEE Transactions on Signal Processing,1994,42(11):3274-3276.
[8] WANG H D,SUN L M.A Study of Localization Mechanims in Wireless Sensor Networks[J].Computer Science,2006,33(4):36-39.(in Chinese)王海东,孙利民.无线传感器网络的定位机制[J].计算机科学,2006,33(4):36-39.
[9] W Z,J B,J Y.Sensitivityreanalysis of static displacement using Taylor series expansion and combined approximate method[J].Structural & Multidisciplinary Optimization,2016,53(5):953-959.
[10] MARQUARDTD.An algorithm for least-squares estimation of nonlinear parameters[J].SIAM Journal on Applied Mathema-tics,1963,11(2):431-441.
[11] CHEN D Z,TANG H,WU J D.Research of TDOA Cooperative Location Algorithm Based on Chan and Taylor[J].Computer Science,2011,38(10):406-411.(in Chinese)陈德章,唐皓,吴季达.基于Chan和Taylor的TDOA协同定位算法研究[J].计算机科学,2011,38(10):406-411.
[12] KEGEN Y,IAN S,JAY GY.Ground-Based Wrieless Positioning [M].Beijing:Publishing House of Electronics Industry,2012.(in Chinese)KEGEN Y,IAN S,JAY GY.地面无线定位技术[M].北京:电子工业出版社,2012.
[13] FY Q,XW M.Source localization using TDOA and FDOAmeasurements based on Constrained Weighted Least Square algorithm[J].Journal of Electronics & Information Technology,2014,36(5):1075-1081.
[14] CUI X X,YU K G,LU S S.Direction finding for transient acoustic source based on biased TDOA measurement[J].IEEE Transactions on Instrumentation and Measurement,2016,65(11):2442-2453.
[2] YIN J,WAN Q,HOK C.A Simple and Accurate TDOA-AOA Localization Method Using Two Stations[J].IEEE Signal Processing Letters,2015,23(1):144-148.
[3] 孙仲康,郭福成,冯道旺.单站无源定位跟踪技术[M].北京:国防工业出版社,2008.
[4] GH Z,DZ F,H X,et al.An approximately efficient bi-iterative method for source position and velocity estimation using TDOA and FDOA measurements [J].Signal Processing,2016,125:110-121.
[5] BARUCH B,DORON M A,ROSENHOUSE J,et al.On direction finding of an emitting source from time delays[J].Journalofthe Acoustical Society of America,1999,105(6):3355-3363.
[6] WANG S Q,NIE J N.An Approach of Performance Analysis and Optimization forWireless Sensor Networks[J].Acta Electronica Sinica,2010,38(4):882-886.(in Chinese)王绍青,聂景楠.一种无线传感器网络性能评估及优化方法[J].电子学报,2010,38(4):882-886.
[7] NIELSEN R O.Estimation of azimuth and elevation angles for a plane wave sine wave with a 3-D array[J].IEEE Transactions on Signal Processing,1994,42(11):3274-3276.
[8] WANG H D,SUN L M.A Study of Localization Mechanims in Wireless Sensor Networks[J].Computer Science,2006,33(4):36-39.(in Chinese)王海东,孙利民.无线传感器网络的定位机制[J].计算机科学,2006,33(4):36-39.
[9] W Z,J B,J Y.Sensitivityreanalysis of static displacement using Taylor series expansion and combined approximate method[J].Structural & Multidisciplinary Optimization,2016,53(5):953-959.
[10] MARQUARDTD.An algorithm for least-squares estimation of nonlinear parameters[J].SIAM Journal on Applied Mathema-tics,1963,11(2):431-441.
[11] CHEN D Z,TANG H,WU J D.Research of TDOA Cooperative Location Algorithm Based on Chan and Taylor[J].Computer Science,2011,38(10):406-411.(in Chinese)陈德章,唐皓,吴季达.基于Chan和Taylor的TDOA协同定位算法研究[J].计算机科学,2011,38(10):406-411.
[12] KEGEN Y,IAN S,JAY GY.Ground-Based Wrieless Positioning [M].Beijing:Publishing House of Electronics Industry,2012.(in Chinese)KEGEN Y,IAN S,JAY GY.地面无线定位技术[M].北京:电子工业出版社,2012.
[13] FY Q,XW M.Source localization using TDOA and FDOAmeasurements based on Constrained Weighted Least Square algorithm[J].Journal of Electronics & Information Technology,2014,36(5):1075-1081.
[14] CUI X X,YU K G,LU S S.Direction finding for transient acoustic source based on biased TDOA measurement[J].IEEE Transactions on Instrumentation and Measurement,2016,65(11):2442-2453.