On direction finding of an emitting source from time delays

This paper presents a statistically and computationally efficient-algorithm for direction finding of a single far-field source using a multi-sensor ar ray. The algorithm extracts the azimuth and elevation angles directly from the estimated time delays between the array elements. Hence, it is referred to herein as the time delay direction finding (TDDF) algorithm. An asympto tic performance analysis, using a small error assumption, is conducted. For any 1-D and 2-D array configurations, it is shown that the TDDF algorithm achieves the Cramer Rao lower bound (CRLB) for the azimuth and elevation es timates provided that the noise is Gaussian and spatially uncorrected and t hat the time delay estimator achieves the CRLB as well. Moreover, with the suggested algorithm no constraints on the array geometry are required. For the general 3-D case the algorithm does not achieve the CRLB for a general array. However, it is shown that for array geometries which obey certain co nstraints the CRLB is achieved as well. The TDDF algorithm offers several a dvantages over the beamforming approach. First, it is more efficient in ter ms of computational load. Second, the azimuth estimator does not require th e a priori knowledge of the wave propagation velocity. Third, the TDDF algo rithm is suitable for applications where the arrival time is the only measu red input, in contrast to the beamformer, which is not applicable in this c ase. (C) 1999 Acoustical Society of America. [S0001-4966(99)05106-1].