Parametric techniques for adaptive detection of Gaussian signals

Two parametric techniques are presented for detection of Gaussian signals with unknown statistics in white Gaussian noise. The first method models the signal as an autoregressive process, while the second models the sum of the signal and the noise as an autoregressive moving-average process. For each model a test statistic (likelihood ratio) is proposed, based on the limiting properties of the likelihood ratios used in the case of known statistics. Approximate distributions of the likelihood ratio are derived to predict the performance of these adaptive detection schemes. Some numerical examples are presented to validate the analysis.