Geoffrey S. Edelson

On the ability to estimate narrow-band signal parameters using towed arrays

Using the Cramer-Rao lower bound (CRLB) as an indicator of potential performance, the limits on the estimation and resolution capabilities of a towed line array of uniformly spaced hydrophones to provide frequency and bearing information about narrowband signals are examined. It is assumed that a monochromatic plane wave arrives at the array for each source. Several versions of the bounds are computed using different assumptions about which parameters have known values and about the way in which the samples are taken in space and in time. It is shown that the CRLB values for different situations can be compared to provide information about the effective use of a moving aperture for estimation of the parameters of narrowband signals arriving at the array. It is also shown that adding at least one hydrophone occupying a fixed position in space can improve the bearing estimates of a towed array by supplying additional frequency information if both the bearings and frequencies of the sources are unknown. >

Limitations on the overlap-correlator method imposed by noise and signal characteristics

Limitations on the performance of the overlap-correlator method of forming a passive synthetic aperture are derived. The technique uses the overlap of the array in sequential positions to estimate a series of phase correction factors that compensate for the motion of the array over time. It is of primary interest to optimize this overlap with respect to the effects of random noise. By minimizing the variance of the estimates of the set of phase correction factors, it is found that the optimal overlap is one-half the length of the physical array. Using this optimal overlap, the bounds on the usable spatial response are then determined as a function of signal-to-noise ratio and the number of hydrophones in the physical array. The ability of the overlap-correlator algorithm to synthesize a coherent aperture is investigated for the case of multiple sources in the absence of noise. >

Maximum Likelihood Estimation Of The Location Of A Narrow-band Acoustic Source Using A Spatially-referenced Towed Array

We invehgate the maximum likelihood esti- mate (MLE) of the location of an acoustic narrow-band source using dat,a from a spatially-referenced towed array (SPARTA). A SPARTA consists of both a conventional towed line subarray and a fixed-position line subarray of passive equispaced hydrophones. It is assumed that the towed subarray moves in a straight line with known speed and that an acoustic signal with a spherical wavefront ar- rives at both subarrays from a non-moving source. We fur- ther assume that the signal component of the data received at the hydrophones differs only in the phase produced by differential propagation delay. The MLEs of the range, cross-range, and frequency are found from a three-dimensional search over a function of these parameters and the observed data. The bearing MLE can be computed directly from the MLE of t.he two local- ization parameters. Some MLE results for the SPARTA are compared to their corresponding Cram&-Rao lower bounds and to the MLE results for conventional t,owed arrays. We confirm that adding at least one reference hydrophone can improve the source 1ocat.ion estimates of a towed array.

On the performance of the overlap‐correlator synthetic‐aperture technique

The overlap‐correlator technique of passive synthetic‐aperture array processing [S. Stergiopoulos and E. J. Sullivan, J. Acoust. Soc. Am. 86, 158–171 (1989)] is investigated. This method of providing an effective aperture greater than that of the physical array utilizes phase correction factors that are calculated by correlating overlapping space samples of the acoustic signal from successive measurements of the moving towed array. Given the criterion of minimizing the effect of the signal‐to‐noise ratio (SNR) on the phase correction factor error while achieving a fixed effective aperture length, the optimal overlap in number of hydrophones between these two successive measurements is derived. The conditions under which the calculated phase correction factor is equivalent to that of the desired phase correction factor are also studied.

Multiple source behavior of passive synthetic aperture algorithms

Generally speaking, passive synthetic aperture algorithms involve the calculation of a single phase correction factor from snapshot to snapshot in order to compensate for the spatial movement of the array over time. Within a given frequency bin and for sources in the far field, this approach is shown to be sufficient for the case of any single source and for the case of two completely deterministic (fully coherent) sources. However, for any other scenario, such as one deterministic and one stochastic source, this technique is shown not to result in the desired phase correction factor. This is a direct consequence of the algorithms used in the various passive synthetic aperture techniques. After reviewing these techniques, an approach to the resolution of this problem, which is based on the multivariate maximum likelihood method, is presented.

Resolution performance of the overlap‐correlator synthetic aperture technique

The resolution capabilities of the overlap‐correlator technique for passive acoustic synthetic aperture array processing are considered. The overlap‐correlator method [S. Stergiopoulos and E. J. Sullivan, J. Acoust. Soc. Am. 86, 158–171 (1989)] can successfully lengthen the effective aperture of a towed array in the passive mode. In this present work, previously reported results on the performance bounds of the overlap‐correlator bearing error variance for a single acoustic source as a function of signal‐to‐noise ratio, the number of elements in the physical army, and the size and number of the overlaps [J. Acoust. Soc. Am. Suppl. 1 87, S155 (1990)] are extended. In addition, the performance of the technique in resolving multiple sources is investigated. This performance is compared to the corresponding Cramer‐Rao bounds for static line arrays and towed synthetic aperture line arrays. Results using simulated data are presented.

Model‐based broadband towed‐array processing

Conventional broadband towed array processors operate in the frequency domain and exploit the phases of the frequency components from a DFT to extract the bearing estimate. In this process, the fact that the array is moving is not taken into consideration. In fact, to first order, the effect of the motion is negligible. However, it has been shown that, in the narrow‐band case, the effect of the motion on the variance of the bearing estimate is not negligible. This is due to the fact that the Doppler incurred by the motion itself carries bearing information. In this work, it is shown that a recursive bearing estimation scheme, based on sequential DFT’s, can produce the so‐called synthetic aperture effect, where the Cramer–Rao lower bound on the bearing estimate progressively decreases, as compared to the case where the motion is not explicitly included in the processing scheme. Examples of this effect are shown based on simulated data, and the capabilities and limitations of the technique are discussed.

Matched image processing for undersampled synthetic aperture sonar

An approach conceptually similar to matched field processing that mitigates the effects of aliasing in undersampled synthetic aperture sonar images is presented. This pattern matching technique is performed in the complex image domain and reduces the strength of the aliases by cross-correlating replica sub-images with an aliased undersampled synthetic aperture sonar image. The issue of mitigating multipath effects is not addressed but matched image processing could be combined with a more conventional range/depth matched field processing algorithm to achieve even greater image improvements in multipath environments.

Performance analysis of an underwater acoustic communications time diversity receiver

One method for introducing time diversity into a decision feedback equalizer (DFE) spatial diversity communications receiver operating in an underwater acoustic environment is presented and analyzed. Time diversity refers to the repetition of transmitted packets and the subsequent batch processing of these packets by an appropriately modified multichannel receiver. To overcome the effects of the time‐varying nature of the channel, the modifications made to the spatial diversity‐based multichannel DFE (SD‐DFE) include appropriate Doppler shift compensation for each received packet and determination of the proper alignment among the time‐displaced packets to allow for successful equalization. The proposed time diversity DFE (TD‐DFE) receiver is shown to achieve a high rate of packet success under a variety of channel conditions. More significantly, the TD‐DFE algorithm is able to equalize packets when a comparable SD‐DFE might fail. The packet‐to‐packet coherence of a series of transmissions is analyzed to ...

Mid‐frequency synthetic aperture sonar imaging

A detailed review of many temporal stability and spatial coherence experiments is used to develop a reasonable model for the temporal and spatial limitations on mid‐frequency synthetic aperture sonar (SAS) in shallow water. A comparison of deep‐ versus shallow‐water coherence experiments is made based on an extensive review of the literature. This comparison reveals that the spatial limits for arrays often dominate over temporal limits. The upper bounds on real or synthesized array lengths in shallow water that result from this analysis are presented. The feasibility of mid‐frequency SAS imaging in shallow water is shown, and the predicted resolution in range, azimuth, and depth is compared to the theoretical values for a perfectly stable ocean and precise motion compensation. As a first step to validate the spatial and temporal limitation analysis, a mid‐frequency surface sonar is modeled to create artificial data for SAS imaging in shallow water. The modeled environment includes a time varying ocean sur...