Robustness measures for signal detection in non-stationary noise using differential geometric tools

Abstract

We propose the study of robustness measures for signal detection in non-stationary noise using differential geometric tools in conjunction with empirical distribution analysis. Our approach shows that the gradient can be viewed as a random variable and therefore used to generate sample densities allowing one to draw conclusions regarding the robustness. As an example, one can apply the geometric methodology to the detection of time varying deterministic signals in imperfectly known dependent nonstationary Gaussian noise. We also compare stationary to non-stationary noise and prove that robustness is barely reduced by admitting non-stationarity. In addition, we show that robustness decreases with larger sample sizes, but there is a convergence in this decrease for sample sizes greater than 14. We then move on to compare the effect on robustness for signal detection between non-Gaussian tail effects and residual dependency. The work focuses on robustness as applied to tail effects for the noise distribution, affecting discrete-time detection of signals in independent non-stationary noise. This approach makes use of the extension to the generalized Gaussian case allowing the comparison in robustness between the Gaussian and Laplacian PDF. The obtained results are contrasted with the influence of dependency on robustness for a fixed tail category and draws consequences on residual dependency versus tail uncertainty.