Sensitivity of scattering function estimates to physical parameter measurement errors with applications to the wavelet transform domain estimator-correlator

A sensitivity analysis of scattering function estimates to errors in the measurement of physical parameters is conducted. The model used is that of a shallow water channel and the application is to the implementation of the wideband estimator-correlator. The estimator-correlator is used for the active detection of multiple moving scatterers in a complex acoustic environment. The transform domain estimator-correlator is derived using group theoretic definitions and is applicable to the Heisenberg and affine groups for either narrowband or wideband processing. The received signal incorporates a narrowband/wideband spreading function. The transform domain estimator-correlator uses a total scattering function in its estimate of the echoed signal. Most of the error occurs from incorrect scattering function information and noise. For the parameter sensitivity analysis, the total scattering function is decomposed into the group convolution of an environment and object scattering function. The error is shown to propagate as the group convolution of the two intermediate scattering functions. The environment scattering function is examined for errors in range and speed both theoretically by differentiation and analytically for multipath returns from a single discrete point scatterer. The errors due to incorrect channel depth, scatterer depth and sound speed are determined. The errors in the peak location of the range and speed for the multipath returns due to the addition of noise are analyzed. The errors in the object scattering function due to ignoring one of two discrete, uncorrelated point scatterers and scatterer positions are studied. Examples of error in the total scattering function due to error in both intermediate scattering functions are given. A discussion on ambiguity function resolution versus the detection statistic is given with an example of error in the total scattering function.