Distributed Bayesian Detection Under Unknown Observation Statistics

In this paper, distributed Bayesian detection problems with unknown prior probabilities of hypotheses are considered. The sensors obtain observations which are conditionally dependent across sensors and their probability density functions (pdf) are not exactly known. The observations are quantized and are sent to the fusion center. The fusion center fuses the current quantized observations and makes a final decision. It also designs (updated) quantizers to be used at the sensors and the fusion rule based on all previous quantized observations. Information regarding updated quantizers is sent back to the sensors for use at the next time. In this paper, the conditional joint pdf is represented in a parametric form by using the copula framework. The unknown parameters include dependence parameters and marginal parameters. Maximum likelihood estimation (MLE) with feedback based on quantized data is proposed to estimate the unknown parameters. These estimates are iteratively used to refine the quantizers and the fusion rule to improve distributed detection performance by using feedback. Numerical examples show that the new detection method based on MLE with feedback is much better than the usual detection method based on the assumption of conditionally independent observations.