Passive ranging techniques are used in sonar systems to localize sources that radiate acoustic energy into the underwater environment. Passive ranging by wavefront curvature relies on the spherical expansion of the wavefronts as the acoustic energy propagates outwards from the source. A wide-aperture receiving array is used to sense the curvature of the wavefront by estimating the intersensor time delays as the wavefront traverses the array. The time delay estimates are used to calculate the range (which is equal to the radius of curvature of the wavefront) and hearing of the source. The method assumes that the properties of the sound propagation medium are temporally invariant (or stationary). The wavefront curvature method is applied here to the passive ranging of three different sources of acoustic signals: underwater acoustic transients, high-frequency pulsed sonar transmissions and low-frequency continuous sound wave transmissions in air. In general, the propagation of sound in the underwater medium is found to be temporally invariant. An exception is the sporadic occurrence of nonstationary events during which time-varying bias errors in the source range and bearing estimates are observed over a period of minutes. When the underwater medium is stationary, the source position estimates are randomly distributed about the mean position and are bounded by a range-bearing error (or positional uncertainty) ellipse. When the underwater medium becomes nonstationary, the estimated position of the source falls outside this ellipse. Large passive ranging errors are observed for the in-air source because the atmosphere is a highly nonstationary sound propagation medium. Atmospheric turbulence causes perturbations in the curvature of the acoustic wavefronts; and leads to random fluctuations in the source position estimates on time scales ranging from seconds to minutes. Background noise at each sensor also contributes to the positional uncertainty of the in air source with random fluctuations in the source position estimates occurring on subsecond time scales. Detrending the data removes the effects of atmospheric turbulence and enables the smaller random errors attributed to background noise to be isolated for model validation purposes.
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