Kalman particle filtering algorithm and its comparison to Kalman based linear unmixing

Spectral Unmixing is a challenging and absorbing problem. Unmixning allows us to break down a pixel's composition into its material components. Many avenues of spectral unmixing have been attempted with considerable success. One such avenue is to frame the spectral unmixing problem as an Estimation-Measurement problem and avail the use of the well-known Kalman Filter (KF) technique. Two such recent work has been the KF based Linear Unmixing (KFLU) approach and the KF approach for Hyperspectral Signature Estimation, Identification and Abundance Quantification (KFHSE/I/AQ). The above techniques aim to address the spectral unmixing and the spectral signature identification problems respectively. This work extends the above formulation by the use of the Particle Filter (PF) based filtering approach. The particle filter is a recent development in the KF framework. It addresses two major improvements over the KF. It enables use of nonlinearity in the estimation process and further allows fusion of multiple information sources. Additionally, by the use of distributed setup using particles, measurement errors are more efficiently reduced. The above enhancements are the primary motivation to create the proposed Kalman Particle Filter (KPF) in this paper. A major disadvantage in the use of Kalman Filter is the selection of the estimation matrix which can be efficiently resolved using the Kalman Particle Filter as described in this paper. Experiments performed using this new algorithm demonstrate the utility of the proposed approach as a better new tool to solve the spectral unmixing problem as compared to prior Kalman linear unmixing approach.