Cramer‐Rao bound characterization of equivalent horizontal aperture achieved from environmental asymmetry

The Cramer‐Rao bound is a well‐accepted lower bound on the mean‐square error of estimated values. Applied to estimation of source position parameters as measured by a hydrophone array, it will give the least achievable mean‐square errors of source position. As is also well known, estimation accuracy of a source's angular transverse to the line of propagation between source and array. By application of the classical optics limit of the Cramer‐Rao bound [A. B. Baggeroer et al., J Acoust. Soc. Am. 83, 571–587 (1988)] it becomes possible to transform a computed lower bound on angular uncertainty into an equivalent array aperture. It has recently been demonstrated [J. S. Perkins and W. A. Kuperman, J. Acoust. Soc. Am. 87, 1553–1556 (1990)] that a vertical array deployed in an azimuthally assymetric environment will achieve angular resolution. Hence, the quantification of this relation between the environment and equivalent horizontal aperture via Cramer‐Rao bounds is desired. Numerical modeling results indicat...