Hyperspectral Data Processing: Algorithm Design and Analysis

28.1 Introduction

Kalman filtering (KF) has been widely used in statistical signal processing for the purpose of parameter estimation (Poor, 1994). It makes use of a measurement equation (input/output equation) and a state equation (process equation) to recursively estimate parameters of the state. A new application of KF in linear spectral unmixing, called Kalman filter-based linear spectral unmixing (KFLU), was recently developed by Chang and Brumbley (1999a, 1999b) for mixed pixel classification. When a Kalman filter is implemented for linear spectral unmixing as a mixed pixel classifier, the state vector x in the state equation is specified by the abundance vector α present in an image, and the pixel vector r is specified by another equation called measurement equation from which α can be estimated. With the measurement equation, a Kalman filter takes advantage of a linear mixture model commonly used in linear spectral unmixing to describe how a pixel vector r is linearly mixed via a measurement equation. By recursively implementing these two equations, KFLU generally produces better estimates of abundance fractions than other linear spectral unmixing methods (Chang and Brumbley, 1999a, 1999b). Several advantages resulting from the use of a Kalman filter are obvious for remote sensing image analysis. One is its ability to deal with nonstationary data, which are generally true in remotely sensed imagery. Another is its recursive structure that makes real-time processing feasible. ...