Study On Three Dimentional Localization Method Using One Dimentional Angle Measurements

The positioning method based on the angle of arrival(AOA)measurement is one of the most widely studied methods.The traditional AOA based positioning method usually uses the one-dimensional angle measurement of the signal from the target to estimate the two-dimensional position of the target.While in the more practical three-dimensional positioning,the azimuth and pitch angle of the target is required at the same time,that is,each sensor is equipped with two-dimensional array.This not only increases the cost of positioning,but also makes the array deployment and array calibration more complex.Therefore,in this thesis,we study the method of three-dimensional target positioning using one-dimensional angle measurement.The main contents are as follows:1.Based on the uniform linear array,a new linear array angle measurement model is established by analyzing the geometric position relationship between the three-dimensional target and the uniform linear array.Compared with the measurement model in traditional linear array,using the one-dimensional angle measurement obtained from our model can achieve the accurate positioning of target in both two-dimensional and three-dimensional scenario,and a unified description of the AOA measurement based two-dimensional and three-dimensional positioning models is established.Moreover,when the target and the array are in the same plane,the two-dimensional positioning of the target using our model is equivalent to the traditional AOA measurement based positioning method.On this basis,aiming at the problem in two-dimensional positioning that the tangent of one-dimensional angle measurement in traditional positioning method will lead to 180?direction ambi-guity,we propose a cross positioning method based on positive constraints.The false positioning points caused by this problem can be eliminated,thus improving the position-ing accuracy.2.Aiming at positioning the target with the one-dimensional angle measurement model in three-dimensional scenario,this thesis proposes a three-dimensional positioning method based on one-dimensional angle measurement.The Cramér-Rao Lower Bound(CRLB)for this scenario is deduced and analyzed,and suggestions on the optimized array arrangement are given.3.Since the positioning problem is nonlinear and nonconvex,the pseudo linear ap-proximation is used to achieve the closed-form solution to weighted least squares(WLS)estimation of the target location.However,the pseudo linear method can not reach CRLB and is very sensitive to measurement noise.In this thesis,the nonconvex constraints be-tween variables are introduced.The nonconvex original problem is relaxed to a semidef-inite programming(SDP)problem,and it is solved by convex optimization tool.The proposed SDP method has stronger resistance against the noise.4.Although SDP positioning method can improve the positioning accuracy,it also increases the algorithm complexity to some extent,which is computationally expensive,time-consuming and difficult to realize in engineering.In order to solve this problem,an alternative iterative algorithm is devised,which can ensure high positioning accuracy and reduce the computational complexity,and the positioning performance do not depend on the selection of the initial position,and can converge after a small number of iterations.At last,the effectiveness of three-dimensional positioning method based on one-dimensional angle measurement is verified by simulation.By comparing the mean square error of WLS,SDP and alternative iterative algorithm with CRLB,it can be seen that when the measurement noise is relatively small,SDP and alternative iterative algorithm can reach CRLB,and the latter greatly reduces the computation load,and can meet the needs of high-precision real-time positioning.