An N-D Technique for Coherent Wave Doa Estimation

of propagation. The signal phase difference between any two adjacent sensors in radians Dimensional Direction of Arrival (N-D DOA) estimated by measuring the phase difference technique is based between the signal values at each sensor, or mulation was motivated by previous work in tained in a “snapshot” of data from all the sensors. which the Cram& Rao Bound (CRB) for coherent wave N-D DOA was developed. Means formance for low SNR are also presented. rithm which is Our target application [3] generates a set of values corresponding to samples from an N-dimensional lattice of senIntroduction sors, the plane wave frequency components of The DOA problem involves estimation of which are the parameters revealing the object plane wave frequency components from data identity and pose. This motivates an extencollected by a uniformly spaced grid of sension of the DOA algorithm to N-D. sors. One and two-dimensional versions of There are a variety of techniques for perthe DOA problem arise in sonar and radar forming 1D DOA estimation, c.f. [4, 5 , 61; direction finding and target tracking applicaone such method, the state space technique, tions [l, 21; the need for an N-D DOA techwas chosen for this extension to N-D. The nique arises in a recently developed object state space DOA method involves determirecognition algorithm [3]. Figure 1 shows a nation of a system, the impulse response of plane wave impinging at an angle t9 on a 1which would produce the sensor data. Once D array of linearly spaced sensors. The dissuch a system is found, we may perform an tance between each sensor is I , The waveeigenvalue decomposition of the system malength of the plane wave is X = c/fo, where trix in order to determine the modes of the c is the speed of propagation of the wave system. These modes are the estimated freand fo is its spatial frequency. The plane quency components of the plane wave along wave is constant along a front perpendicuthe direction of the array of sensors. Given lar to the vectors that indicate the direction the distance 1 between each sensor, we can In this paper, we describe a to the Nis (2T1 sin e)/X. Thus the parameter 8 can be The N-D On a state ‘pace and its forequivalently by estimating the frequency confor improving the N-D DOA estimation perThe model based object recognition alga-