Application of multivariate Gaussian detection theory to known non-Gaussian probability density functions

摘要

Abstract: A statistical parametric multispectral sensorperformance model was developed by ERIM to support minefield detection studies, multispectral sensordesign/performance trade-off studies, and targetdetection algorithm development. The model assumestarget detection algorithms and their performancemodels which are based on data assumed to obeymultivariate Gaussian probability distributionfunctions (PDFs). The applicability of these algorithmsand performance models can be generalized to datahaving non-Gaussian PDFs through the use of transformswhich convert non-Gaussian data to Gaussian (ornear-Gaussian) data. An example of one such transformis the Box-Cox power law transform. In practice, such atransform can be applied to non-Gaussian data prior tothe introduction of a detection algorithm that isformally based on the assumption of multivariateGaussian data. This paper presents an extension ofthese techniques to the case where the jointmultivariate probability density function of thenon-Gaussian input data is known, and where the jointestimate of the multivariate Gaussian statistics, underthe Box-Cox transform, is desired. The jointlyestimated multivariate Gaussian statistics can then beused to predict the performance of a target detectionalgorithm which has an associated Gaussian performancemodel. !8