Time-varying spatial spectrum estimation with a maneuverable towed array

Abstract

This paper addresses the problem of field directionality mapping (FDM) or spatial spectrum estimation in dynamic environments with a maneuverable towed acoustic array. Array processing algorithms for towed arrays are typically designed assuming the array is straight, and are thus degraded during tow-ship maneuvers. In this paper, maneuvering the array is treated as a feature allowing for left and right disambiguation as well as improved resolution toward endfire. The Cramér-Rao lower bound is used to motivate the improvement in source localization which can be theoretically achieved by exploiting array maneuverability. Two methods for estimating time-varying field directionality with a maneuvering array are presented: (1) Maximum likelihood (ML) estimation solved using the expectation maximization algorithm and (2) a non-negative least squares (NNLS) approach. The NNLS method is designed to compute the field directionality from beamformed power outputs, while the ML algorithm uses raw sensor data. A multi-source simulation is used to illustrate both the proposed algorithms' ability to suppress ambiguous towed array backlobes and resolve closely spaced interferers near endfire which pose challenges for conventional beamforming approaches especially during array maneuvers. Receiver operating characteristics are presented to evaluate the algorithms' detection performance versus signal-to-noise ratio. The results indicate that both FDM algorithms offer the potential to provide superior detection performance when compared to conventional beamforming with a maneuverable array.

Maximum-likelihood spatial spectrum estimation in dynamic environments with a short maneuverable array

“…The second step is maximizing the result with respect to the unknown parameters. As described in previous array processing work using EM algorithms, 14,17,23 define the complete data as the hidden source and noise signals, C N ðkÞ ¼ fsðkÞ; gðkÞ; …; sðk À N þ 1Þ; gðk À N þ 1Þg, while the incomplete data is XðnÞ. The likelihood function with the complete data is given as…”

“…[14][15][16] More recently, an approach for time-varying spatial spectrum estimation with long maneuverable towed arrays using the expectation-maximation algorithm was presented by Rogers and Krolik. 17 In this paper, the work of Rogers and Krolik is extended for field directionality mapping with short maneuvering arrays. The additional challenge with short arrays is that their inherently poor spatial resolution limits the usable bearing space fraction available for weak target detection, i.e., performance is significantly degraded toward endfire.…”

Adaptive Selective Sidelobe Canceller Beamformer With Applications to Interference Mitigation in Radio Astronomy

“…The MVDR weights are given by (5) where is the measured correlation matrix, is the array steering vector, defined in (4) and stands for the Hermitian conjugate.…”

“…This problem appears for instance in radar imaging, [1], [2], sonar, [3], towed array sonar, [4], [5], and radio astronomy, [6] and becomes more complex when the number of signals is much larger that the number of physical sensors used for each measurement (see [7] for example).…”

“…(Minimum-Variance-Distortionless-Response) and MUSIC (Multiple-Signal-Classification) was proposed by [8] and [9]; the maximum likelihood, least-square and non-negative least square generalization have been developed and discussed by various authors (see [10], [11] and [5]) and the Cramér-Rao Lower Bound (CRLB) analysis for the moving array has been established (see for example [12], [13] and [4]). …”