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Kalman Filter-Based Estimation for Hyperspectral Signals
Most popular and widely used approaches in statistical signal estimation are mean squared error (MSE) based approaches among which Kalman filtering (KF) is the most powerful and effective technique that can be implemented in real time under a nonstationary environment. Recently, a Kalman filtering approach to linear spectral unmixing, called Kalman filter-based linear spectral unmixing (KFLU) was developed for mixed pixel classification by Chang and Brumbley (1999a, 1999b). However, its applicability to spectral characterization for spectral estimation, identification, and quantification has not been explored. This chapter presents new applications of KF in spectral estimation, identification, and abundance quantification for which three Kalman filter (KF)-based spectral characterization signal processing (KFSCSP) techniques are developed. These techniques are completely different from KFLU in the sense that the former performs a Kalman filter across a spectral coverage wavelength by wavelength (i.e., band-by-band) as opposed to the latter, which implements a Kalman filter pixel vector by pixel vector throughout an entire image cube. In addition, the proposed Kalman filter-based techniques do not require a linear mixture model as KFLU does. Accordingly, they are not linear spectral unmixing methods but rather spectral signature filters operating as if they are spectral measures. More specifically, the state equation implemented ...
