Spectral abundance fraction estimation of materials using kalman filters

Kalman filter has been widely used in statistical signal processing for parameter estimation. Although a Kalman filter approach has been recently developed for spectral unmixing, referred to as Kalman filter-based linear unmixing (KFLU), its applicability to spectral characterization within a single pixel vector has not been explored. This paper presents a new application of Kalman filtering in spectral estimation and quantification. It develops a Kalman filter-based spectral signature estimator (KFSSE) which is different from the KFLU in the sense that the former performs a Kalman filter wavelength by wavelength across a spectral signature as opposed to the latter which implements a Kalman filter pixel vector by pixel vector in an image cube. The idea of the KFSSE is to implement the state equation to characterize the true spectral signature, while the measurement equation is being used to describe the spectral signature to be processed. Additionally, since a Kalman filter can accurately estimate spectral abundance fraction of a signature, our proposed KFSSE can be further used for spectral quantification for subpixel targets and mixed pixel vectors, called Kalman filter-based spectral quantifier (KFSQ). Such spectral quantification is particularly important for chemical/biological defense which requires quantification of detected agents for damage control assessment. Several different types of hyperspectrral data are used for experiments to demonstrate the ability of the KFSSE in estimation of spectral signature and the utility of the KFSQ in spectral quantification.