Performance bounds for passive sensor arrays operating in a turbulent medium: Plane-wave analysis

Abstract

The performance bounds of a passive acoustic array operating in a turbulent medium with fluctuations described by a von Kármán spectrum are investigated. This treatment considers a single, monochromatic, plane-wave source at near-normal incidence. A line-of-sight propagation path is assumed. The primary interests are in calculating the Cramer-Rao lower bounds of the azimuthal and elevational angles of arrival and in observing how these bounds change with the introduction of additional unknowns, such as the propagation distance, turbulence parameters, and signal-to-noise ratio. In both two and three dimensions, it is found that for large values of the index-of-refraction variance, the Cramer-Rao lower bounds of the angles of arrival increase significantly at large values of the normalized propagation distance. For small values of the index-of-refraction variance and normalized propagation distance, the signal-to-noise ratio is found to be the limiting factor. In the two-dimensional treatment, it is found that the estimate of the angle of arrival will decouple from the estimates of the other parameters with the appropriate choice of array geometry. In three dimensions, again with an appropriate choice of array geometry, the estimates of the azimuth and elevation will decouple from the estimates of the other parameters, but due to the constraints of the model, will remain coupled to one another.

Algorithms and performance of small baseline acoustic sensor arrays

“…2, 3 Table 1 also includes estimated values for µ that are consistent with the model in (8). The equation for ν in (11) is valid only for sensor separations ρ L eff , where eddy size L eff is tabulated in the rightmost column of Table 1.…”

“…The factor κ 1 (weather) depends on the weather conditions as in (8). The spatial coherence γ is determined by ν, the extinction coefficient of the second moment, according to…”

“…To study the tradeoffs, and to provide AOA performance bounds, we employ Cramér-Rao bounds (CRBs) that incorporate turbulence effects. 7,8 The analysis includes propagation conditions, SNR, sensor array geometry, source range and frequency, and spatial coherence. The AOA estimation bounds characterize the loss beyond simple plain wave assumptions (which may be quite optimistic), and so provide tighter lower bounds.…”

Environmentally adaptive acoustic transmission loss prediction in turbulent and nonturbulent atmospheres

“…One problem with methods analyzing performance for acoustic sensors (Collier & Wilson, 2003Wilson, 1998) is the large computational cost inherent in using acoustic prediction methods such as the parabolic equation (PE) model to approximate environmental conditions. In Mungiole and Wilson (2006), the authors attempt to overcome the large computational requirements of traditional acoustic TL calculation methods by using an artificial neural network.…”

“…Certain types of atmospheric turbulence, namely those related to the wind velocity were determined to be particularly detrimental to DOA estimation performance accuracy. The work of Wilson (1998) was then modified in Collier and Wilson (2003) and Collier and Wilson (2004) for plane waves and spherical waves, respectively. For simple array geometries (lines and rectangles) the authors showed that atmospheric turbulence is extremely important in calculating accurate performance bounds for acoustic arrays.…”