ON STATISTICAL MODELS FOR SIGNAL DETECTION

A thesis on developing statistical models that will aid in predicting signal detection at an infrasound sensor given a noise model for the sensor. The thesis aims first to provide a means to sample from a set of atmospheric profiles effectively using a statistical model, so we can have a smaller sample space to generate transmission loss values, saving time for running propagation models. And secondly, it aims to provide a formalism for a signal detection criterion using signal-to-noise ratio. The statistical model is developed using Empirical Orthogonal Function Analysis also known as Principal Component Analysis, and Inverse Transform Sampling. Further, we find the optimal sample size using a Cauchy criterion that indicates sampling optimally, which is the sample size the probability distribution converges. A joint probability density function is used to get the expectation value for the signal detection criterion and a measure of confidence in the expectation value. This thesis also presents probability distributions for transmission loss at different times and locations, majorly periods with a good ground duct and periods with a very bad ground duct. The probability distributions are produced using the Kernel Density Estimation approach. The probability distributions reveal the nature of the available ducts by showing high probability or low probability for a range of transmission loss values. Also, the atmospheric profiles used to generate the transmission loss for which we get probability distributions are those sampled from a large set of atmospheric profiles using the statistical model. This thesis has application in estimating what a source signal should be so detection can be made. It will be applied in the development of early warning systems for tornadoes