Optimum bearing resolution for a moving towed array and extension of its physical aperture

Abstract

This paper examines the limits of the angular resolution capability of a moving towed array (MTA) by finding the Cramer–Rao lower bounds (CRLB) and provides algorithms that extend the physical aperture of an MTA. The model that is considered for the CRLB estimates assumes that an N-hydrophone towed array is moving at a known constant speed and that in the received signal unknowns are all the parameters for two sources. The estimated CRLBs for this model indicated that an N-hydrophone MTA provides very high angular resolution when the duration T of the received signal is very long. This ability of the moving array to resolve two closely spaced sources is related to the fact that the physical aperture has been extended by the distance traveled by the array during the T seconds of the observation period. Computer-simulation examples using a maximum-likelihood estimator and an extended towed array algorithm to find the bearing of sources are presented. The results of these simulations agree with the CRLB if the signal-to-noise ratio (SNR) is higher than 0 dB at the hydrophone level, which suggests that both of the above techniques are efficient estimators. Real-data applications using the extended towed-array algorithm were successful, and the physical aperture of a 32-hydrophone MTA was extended to an equivalent of a 512-hydrophone fully populated array during 185 s of observation period. These results have also indicated that the performance of the above algorithm is very robust, since it extends the physical aperture of an array by more than one order of magnitude for the case of a very low signal-to-noise ratio (SNR) broadband signal and for a pure tone, even though the source had a speed of 3.6 kn along its bearing.

A generalized Cramér-Rao lower bound for moving arrays

“…Here, it can be seen that when jointly estimating the bearing and source frequency, as opposed to the bearing alone, the moving array underperforms 4 the stationary array. This result was first shown by Stergiopoulos 5 and later, in a more general sense, by Edelson. 6 It is interesting to note that, at early times (i.e., small R), the down-Doppler case underperforms the up-Doppler case.…”

Extended Towed Array Measurement: Beam-domain phase estimation and coherent summation

“…Step 4: Beamforming of full array at snapshot m: In [1], the synthesis of an extended array is achieved by an overlap-correlator which provides the phase correction NA factor by correlating overlapping space samples of the bn(Jo On(s)=~Xn,m(f0)ep|j (nAl)6cosOsI| (4) acoustic signal received at successive moments by the moving J= towed array. The correlation is performed in the time-domain, [2] and [3].…”

An improved phase correction algorithm in extended towed array method for passive synthetic aperture

“…Besides, Nuttall et al proposed a maximum likelihood estimation method 11 (ML). It was shown 12 that the ETAM method has performance comparable to that of a maximum likelihood estimator, which provides bearing estimates comparable to the ones of a fully populated array, when SNR higher than 0 dB is received at the hydrophone. ETAM, FFTSA, ML are the three most important PASA algorithms so far.…”