Measurements and models of the correlation of redundant spatial coherence measurements for the incoherently scattered field

Sonar systems that exploit correlation for navigation, such as correlation velocity logs and micronavigation for synthetic aperture sonar, often make redundant estimates of the spatial coherence of the scattered field at several spatial lags. Two models for the correlation of these redundant measurements are described. First, an analytical model is derived using the assumption of stationary Gaussian statistics. Next, a numerical model is described that accounts for non-stationary processes present in measurements of seafloor scattering. These models are compared to normal-incidence scattering data collected at Seneca Lake, NY. Both models show good agreement with the measurements when the spatial separation between redundant hydrophone pairs is less than the coherence length. At greater spatial separation, the analytical model diverges from the measurements. This disagreement is explained by a lack of stationarity in the measured data which is captured by the numerical model. Finally, spatial variations in the volume scattering strength of the sediment are identified as a source of the non-stationarity in the measurements.