Generalized Information Representation and Compression Using Covariance Union

Abstract

In this paper we consider the use of Covariance Union (CU) with multi-hypothesis techniques (MHT) and Gaussian mixture models (GMMs) to generalize the conventional mean and covariance representation of information. More specifically, we address the representation of multi-modal information using multiple mean and covariance estimates. A significant challenge is to define a rigorous fusion algorithm that can bind the complexity of the filtering process. This requires a mechanism for subsuming subsets of modes into single modes so that the complexity of the representation satisfies a specified upper bound. We discuss how this can be accomplished using CU. The practical challenge is to develop efficient implementations of the CU algorithm. Because of the novelty of the CU algorithm, there are no existing real-time codes for use in real applications. In this paper we address this deficiency by considering a general-purpose implementation of the CU algorithm based on general nonlinear optimization techniques. Computational results are reported