GDOP-Weighted Direction-Finding Scheme In Closed Form Based On Time-Difference-of-Arrival

In the field of sensor measurement and signal processing,time difference of arrival(TDOA)is an important physical value to detect far-field and near-field signals.With the development of high-sensitivity data acquisition technology,sensor networks or arrays can accurately measure weak signals,which brings new development opportunities to the far-field signal orientation.With the help of TDOA value,accurate estimation of direction of arrival(DOA)technology has good practical application requirements,which can be used in radio,air acoustics,sonar,ultrasonic and seismic wave and other fields.In this paper,we consider the problem of TDOA direction discovery of three-dimensional space plane wave.On the basis of summarizing the existing technical methods,the following research contents have been completed(1)A closed orientation method based on the least measured data is proposed,that is,the DOA of the signal can be calculated linearly according to the intersection point of two TDOA nonlinear measurement equation curves.However,the iterative numerical method is usually used to determine the intersection point of two nonlinear equation curves,and the closed form calculation is generally difficult.In this paper,a method of rotating coordinate system is designed.According to the invariance of TDOA values before and after the rotation of coordinate system,the linear solution of the intersection point of TDOA measurement equation curve is ingeniously solved by determining the coordinate transformation matrix,which has the advantages of intuitive and simple.(2)A geometric dilution of precision(GDOP)weighted orientation scheme based on pair by pair measurement is proposed.The weight is determined according to the geometric accuracy factor of each intersection point,and the orientation results of each pair of TDOA measurement equations are linearly weighted averaged,which is used as the direction estimation of the target.In this paper,different weighting methods are analyzed,and the theoretical estimation mean and variance of linear synthetic weighted orientation error based on GDOP are derived,which shows that the weighted direction finding scheme is unbiased.Through MATLAB simulation,the orientation root mean square error,cumulative distribution probability index and other performance of the proposed scheme are verified by experiments,and the effect is compared with the existing orientation methods.The results show that the proposed GDOP weighted orientation scheme based on pair by pair measurement has good performance and can approach the Cramer-Rao Lower Bound.Figure [29] table [4] reference [72]...