Applications of unbiased perturbations towards quantifying robustness with pragmatic geometric methods

Robustness of a system has been defined in various ways, and extensive work has been completed to model the robustness of a system, but quantifying or measuring robustness has always been very difficult. In this research, we consider a simple system of a linear estimator, and then attempt to model the system performance and robustness in a graphical manner, which admits an analysis using the differential geometric concepts of slope. We try to compare two different types of slopes, namely the slope with biased perturbations of a surface and the slope with unbiased perturbations, and observe the values to see which of them can alternately be used in the process of understanding or measuring robustness. In this process, we have worked on two different examples and taken readings for many points to find if there is any consistency in the two slopes.