This work details how to obtain additional information to find a unique solution to model-based polarimetric decompositions. In general, polarimetric target decomposition methods decompose the multi-look covariance or coherency matrix, a second-order statistic, into a mixture of components. These complex matrices only have five distinct elements that equates to five distinct expressions for the model-based decomposition. However, virtually all models involve more than five physical parameters, making the decomposition underdetermined and hence does not have a single unique solution. The general approach to solve this problem is to make certain assumptions, thus fixing one or more parameters, allowing the other free parameters to be solved from the set of expressions. This work describes how to obtain new, independent expressions from higher order statistical moments to obtain a unique solution and presents preliminary results.