Online Detection and Parameter Estimation With Correlated Observations

We present an online expectation maximization (EM) based algorithm for the problem of model parameter estimation and hypothesis testing based on observations from a network of heterogeneous sensors. The sensors' measurements are assumed to be correlated and copula theory is used to model this correlation. Moreover, it is assumed that the statistical model for the sensors' data is not completely known. We first develop the batch-mode EM to estimate the parameters of the underlying distributions of the sensors' measurements and to detect the hypothesis. Next, we develop an online EM-based method that processes the data on a sample-by-sample basis. Numerical results are presented for both simulation data and two different real-world datasets. These results demonstrate the efficacy of the proposed method showing significant improvements for both parameter estimation and hypothesis testing compared to the method that ignores the correlation in sensors' measurements. Hypothesis testing results from the real-world data are also compared with several unsupervised and supervised learning methods. It is shown that the proposed methods outperform the unsupervised and even some supervised methods.