Sensitivity Analysis of an Estimator-Correlator for the Detection of Spread Targets with Multiple Discrete Highlights

摘要

The maximum-likelihood sense optimum detector for the detection of randomly fluctuating multiple highlight objects in Gaussian reverberation and noise is an Estimator-Correlator (EC). If a large time-bandwidth product signal is used, a conventional matched-filter detector can spread scattered energy into multiple detector bins, resulting in lower output in each bin than if all the energy had been concentrated in just one. The wideband, or Wavelet Transform Domain EC (WTD-EC) recombines the detection statistics from discrete highlights into a single detection statistic, possibly dramatically improving detector performance as characterized by the Receiver Operating Characteristics (ROC). Implementation of the estimator branch of the EC requires an a priori estimate of the second order statistics of the echo, i.e., the covariance function or scattering function. Scattering functions are used as prior statistics because they are physically meaningful, robust statistical characterizations of distributed scatterers. A critical issue in the implementation of the WTD-EC is the sensitivity of its performance to the errors in the a priori statistical models. This thesis analyzes the sensitivity of the WTD-EC to errors in the assumed scattering functions. Analytic expressions and verified numerical code are developed for the computation of ROC curves for arbitrary target scattering functions, reverberant scattering functions, and wideband transmitted signals. The sensitivity of the detector is found by deriving an expression for the ROC when the assumed scattering function is not the correct scattering function. It is demonstrated that the WTD-EC cannot be characterized by a scalar figure of merit, and that only a ROC curve is adequate to characterize the performance of the detector.