High-resolution wave-number-frequency methods for towed arrays

Abstract

In passive narrow-band or broadband target detection sonars, line arrays are used to enhance performance. In large towed arrays, wave-number-frequency (k-ω) data analysis methods have been used on an experimental basis to detect and identify the presence of noise generators. The noise sources are composed of acoustically radiating sources located in the ocean, vibrational energy within the array, and pressure disturbances along the array. In this paper, a hybrid autoregressive (AR) technique is presented that will generate k-ω solutions having better spatial resolution than is currently possible with methods that make use of a two-dimensional fast Fourier transform (FFT). The hybrid AR method is implemented by applying a one-dimensional FFT on the sampled time series data and using this result to obtain an averaged array cross-spectral density matrix. The AR method is now applied to the spatial cross spectral density matrix to obtain a wave-number-frequency spectrum. For the hybrid AR method, equations are presented for calculating the spatial wave-number resolution as a function of signal-to-noise ratio (SNR), array size, and time-bandwidth product (T-BW). The equations for resolution and array gain are useful for determining when to apply the hybrid AR method. In addition to the hybrid AR development, a modification of the FFT–FFT method is introduced that provides efficient and rapid computation of a standard wave-number-frequency spectrum. Comparisons for various SNR, AR order, and T-BW conditions using computer simulated, and actual at-sea data are made between the k-ω solutions obtained using this modified FFT method and our proposed hybrid AR technique.