Recursive Estimation of Proportions in Earth Observations

In Earth observations problems, we usually have the situation of knowing accurately the probability density functions of the several classes of interest, and we need to classify a set of observations with unknown class proportions. The observations are in n-dimensional space, where n is the number of spectral bands. Two recursive algorithms for classifying the observations and estimating the prior probabilities are described. The first one achieves simultaneous classification of pixels and estimation of prior probabilities (or proportions) and the second one estimates the proportions in a recursive fashion. There is a similarity of the second approach to maximum likelihood estimation, but the proposed method requires less computer time.