Multivariate probability model for 3-layer remote sensing

In this paper we develop a multivariate probability model for a 3-layer radiative transfer equation, which can be used to predict the stochastic nature of measured signals for multispectral and hyperspectral remote sensing applications. A multivariate 3-layer model is particularly important because the remote sensing problem is typically clutter limited, meaning that variability from the scene - temporal or spatial changes in environmental parameters collectively called “clutter” - is greater than sensor noise and thus is the limiting factor in determining whether a particular target of interest can be detected. Our model is derived from physical considerations regarding expected statistics for blackbody radiation, transmission, and radiance, and is described by the Johnson system of distributions. With the model we obtain pdfs of the target radiance, background radiances, and thermal contrast, and obtain new physical insights on the remote sensing scenario.