Data fusion based on convex optimization

A distributed fusion problem is addressed where cross-covariance matrices of estimated variables are unknown. We first try to estimate the cross-covariances, and then calculate the weighting coefficients to combine the estimates linearly. We consider two approaches, one where we do not use priors for the covariance matrices of the model and another, where we use priors and engage the Bayesian machinery. For the former, we exploit the maximum-entropy principle in finding the optimal cross-covariance estimate and for the latter, we employ Wishart distributions as priors and search for the maximum a posteriori estimate. Both problems turn out to require convex optimization which can be solved by existing techniques. When the cross-covariance estimates are obtained, the weighting coefficients can easily be calculated so that fusion can take place. Simulation results that demonstrate the performance of the proposed methods are provided.