Joint estimation of DOA and time-delay in underwater localization

Joint estimation of direction of arrival (DOA) and time delay plays a great role in source localization, which attracts many researchers not only in the areas of radar, sonar, geological exploration but also in wireless communication. [1][2][3][4] M. Wax applies approximate MLE with iteration algorithm , which convert a 2-D search into two or three 1-D search. A.J.van der Veen use 2-D ESPRIT to conduct joint estimation . Both of them show good performance at a cost of large computation. And both of them require deconvolution in frequency domain to transfer time-delay into phase. The deconvolution leads to two problems. One is blowing up noise, the other is leading to spurious peak if the emitted signal is non-minimum phase. In this paper, a simple method using 1-D ESPRIT is presented to complete joint estimation of DOA and time-delay, which requires no deconvolution. It is suitable for active underwater localization where non-minimum phase signal is frequently employed. The method can estimate parameters of three reflectors with big difference between amplitudes as large as 12dB. The statistical performance of new estimators and the probability of correct pairing are given by computer simulations. It shows that better performance of the new method can be achieved for multiple source localization even in low SNR. 1 Modeling The emit signal is a sine wave with an envelop s(t). An Melement d-spaced uniform linear sensor array is employed as a receiver. Assume that there are p reflectors in water. If a single echo wave is sampled with N points in time domain, the complex envelop of received echo can be written as a N M matrix: X s t b j a N i i i T i i p = − + = ∑ ( ) exp( ) ( ) τ φ θ