Hyperspectral Data Processing: Algorithm Design and Analysis

28.3 Kalman Filter-Based Spectral Characterization Signal-Processing Techniques

Three KFSCSP techniques are derived and presented in this section, called Kalman filter-based spectral signature estimator (KFSSE), Kalman filter-based spectral signature identifier (KFSSI), and Kalman filter-based spectral signature quantifier (KFSSQ). In KFSSE, the input and output of its measurement equation are specified by a noise-corrupted signature vector and its true signature vector to be estimated, respectively. KFSSE then uses a state equation to predict spectral values of the true signature vector across its spectral coverage via a signal model such as the Gaussian–Markov model. So, the role of KFSSE is to capture spectral signature changes between adjacent spectral bands compared with KFLU, which is developed to capture changes in abundance fractions between two adjacent pixel vectors. Most importantly, as noted previously, KFSSE does not need a linear mixture model as required by KFLU. Therefore, there is no need for KFSSE to find image endmembers to form a linear mixture model. On the other hand, KFSSI is developed to identify a signature vector via a matching signature vector chosen from a known database or spectral library. In doing so, KFSSI is derived from KFSSE by replacing the true signature vector used in KFSSE with an auxiliary signature vector that enables it to capture the matching signature vector in identifying the unknown signature vector. According to functionality, both ...