On a quadratic information measure for data assimilation

Data Assimilation is central to Dynamic Data Driven Applications (DDDAS). The limitations of current techniques in the presence of nonlinearity and dimensionality can, in principle, be ameliorated by effective non-Gaussian high-dimensional inference in many areas within DDDAS, but particularly environmental applications. This paper presents an inference algorithm based on maximization of a quadratic form of mutual information that provides an optimization approach to filtering non-Gaussian nonlinear systems. In particular, this is accomplished by using Kapur's mutual information between model predictions and measurements based on Renyi entropy, and using ensemble-based kernel representations of probability mass functions. The effectiveness of the algorithm is demonstrated using the Lorenz-95 model where it is seen outperforming contemporary ensemble filtering.