“ 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 array. 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 asymptotic 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 estimates provided that the noise is Gaussian and spatially uncorrected and that the time delay estimator achieves the CRLB as well. Moreover, with the suggested algorithm no constrains 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 constraints the CRLB is achieved as well. The TDDF algorithm offers several advantages over the beamforming approach. First, it is more efficient in terms of computational load. Secondly, the azimuth estimator does not require the a-priory knowledge of the wave propagation velocity. Thirdly, the TDDF algorithm is suitable for applications where the arrival time is the only measured input, in contrast to the beamformer, which is not applicable in this case.