System-orthogonal functions for sound speed profile perturbation

Empirical orthogonal functions (EOFs) are typically derived from direct measurements of the sound speed profile (SSP) and they are orthogonal in regard to the statistics of the SSP uncertainty. Viewed from the output end of a particular sonar system, however, the effect of an error in one EOF is usually coupled with the effect of the error in another due to the strongly nonlinear relation between the SSP parameters and the system response. In this paper, a new set of basis functions, orthogonal in regard to sonar performance measure, is developed to characterize SSP perturbations. The performance measure used is the Cramer-Rao bound (CRB) for SSP expansion coefficients derived from a full-field random Gaussian signal model; a closed-form, analytical solution is obtained for both the range-independent and adiabatically range-dependent environments. The derived functions make the CRB matrix diagonal, decoupling the errors in the estimation of the expansion coefficients. Compared to the EOFs, the new set of basis functions depends on both the statistics of the sound speed uncertainty and the sound waveguide propagation property; it incorporates the measurement noise as well. The development makes possible the investigation of the relative significance of the individual basis functions in system response; it also provides a novel framework for optimum acoustic parameterization in adaptive rapid environmental assessment.