Bayesian learning of random signal distributions in complex environments

This paper describes the coupling of Bayesian learning methods with realistic statistical models for randomly scattered signals. Such a formulation enables efficient learning of signal properties observed at sensors in urban and other complex environments. It also provides a realistic assessment of the uncertainties in the sensed signal characteristics, which is useful for calculating target class probabilities in automated target recognition. In the Bayesian formulation, the physics-based model for the random signal corresponds to the likelihood function, whereas the distribution for the uncertain signal parameters corresponds to the prior. Single and multivariate distributions for randomly scattered signals (as appropriate to single- and multiple-receiver problems, respectively) are reviewed, and it is suggested that the log-normal and gamma distributions are the most useful due to their physical applicability and the availability of Bayesian conjugate priors, which enable efficient refinement of the signal hyperparameters. Realistic simulations for sound propagation are employed to illustrate the Bayesian processing. The processing is found to be robust to mismatches between the simulated signal distributions and the assumed forms of the likelihood functions.