Kalman filter-based approaches to hyperspectral signature similarity and discrimination

Kalman filter has been widely used in statistical signal processing for parameter estimation. Recently, a Kalman filter-based approach to spectral unmixing, referred to as Kalman filter-based linear unmixing (KFLU) was also developed for mixed pixel classification. However, its applicability to estimation and discrimination for hyperspectral signature characterization has not been explored where a hyperspectral signature is defined as a vector on a range of contiguous optical wavelengths of interest. This paper presents a new application of Kalman filtering in hyperspectral signature similarity and discrimination. In particular, it develops a Kalman filter-based signature estimator from which two Kalman filter-based discriminators can be derived for signature similarity and discrimination. The developed Kalman filter-based discriminators utilize a state equation to characterize a hyperspectral signature and a measurement equation to describe another hyperspectral signature, while the developed Kalman filter-based estimator makes use of state and measurement equations to describe the true signature and the observable signature respectively. The least squares error resulting from the Kalman filter-estimated hyperspectral signature is then used as the power for hyperspectral signature similarity and discrimination. Experimental results demonstrate that such Kalman filter-based discriminators are more effective than commonly used spectral similarity measures such as spectral angle mapper (SAM) or Euclidean distance.