Empirical Distribution Approach to the Robustness Measure for Non-stationary Data

This paper proposes 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 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, we apply the geometric methodology to the detection of time varying deterministic signals in imperfectly known dependent non-stationary Gaussian noise.