Likelihood updating for Gauss-Gauss detection

This paper investigates the effects of incrementally adding new data to the classical Gauss-Gauss detector for testing between the known covariance matrices in competing multivariate models. We show that updating the likelihood ratio and J-divergence as a result of general data augmentation inherently involves linearly estimating the new data from the old. Using the change in divergence and the eigenstructure of a whitened error covariance matrix, a reduced-rank version of the update is built. A simulation example of a single narrow-band source in the sensing environment of multiple uniform linear arrays (ULA's) is given showing the practicality of adding data in multi-static sonar applications.