Statistical signal processing and its applications to detection, model order selection, and classification
This dissertation has focused on topics in statistical signal processing including detection and estimation theory, information fusion, model order selection, as well as their applications to standoff detection. Model order selection is a very common problem in statistical signal processing. In composite multiple hypothesis testing, the maximum likelihood rule will always choose the hypothesis with the largest order if the parameters in each candidate hypothesis are hierarchically nested. Hence, many methods have been proposed to offset this overestimating tendency by introducing a penalty term. Two popular methods are the minimum description length (MDL) and the Akaike information criterion (AIC). It has been shown that the MDL is consistent and the AIC tends to overestimate the model as the sample size goes to infinity. In this dissertation, we show that for a fixed sample size, the MDL and the AIC are inconsistent as the noise variance goes to zero. The result is surprising since intuitively, a good model order selection criterion should choose the correct model when the noise is small enough. Moreover, it is proved that the embedded exponentially family (EEF) criterion is consistent as the noise variance goes to zero. Standoff detection aims to detect hazardous substances in an effort to keep people away from potential damage and danger. The work in standoff detection has been on developing algorithms for detection and classification of surface chemical agents using Raman spectra. We use an autoregressive model to fit the Raman spectra, develop an unsupervised detection algorithm followed by a classification scheme, and manage to control the false alarm rate to a low level while maintaining a very good detection and classification performance. In information fusion and sensor integration, multiple sensors of the same or different types are deployed in order to obtain more information to make a better decision than with a single sensor. A common and simple method is to assume that the measurements of the sensors are independent, so that the joint probability density function (PDF) is the product of the marginal PDFs. However, this assumption does not hold if the measurements are correlated. We have proposed a novel method of constructing the joint PDF using the exponential family. This method combines all the available information in a multi-sensor setting from a statistical standpoint. It is shown that this method is asymptotically optimal in minimizing Kullback-Leibler divergence, and it attains comparable detection/classification performance as existing methods. The maximum likelihood estimator (MLE) is the most popular method in parameter estimation. It is asymptotically optimal in that it approximates the minimum variance unbiased (MVU) estimator for large data records. Under a misspecified model, it is well known that the MLE still converges to a well defined limit as the sample size goes to infinity. We have proved that under some regularity conditions, the MLE under a misspecified model also converges to a well defined limit at high signal-to-noise ratio (SNR). This result provides important performance analysis of the MLE under a misspecified model.
"Statistical signal processing and its applications to detection, model order selection, and classification"
Dissertations and Master's Theses (Campus Access).