Stochastic performance analysis of visual motion observer and experimental verifications

This paper analyzes an estimation performance of a vision-based observer, presented in one of the authors´ antecessors, when a target object 3-D motion includes stochastic factors. We first formulate time evolution of the error between the actual object motion and its estimate, produced by the visual observer, as a stochastic differential equation (SDE) on SE(3). In order to evaluate the error, we first employ the notion of noise-to-state stability (NSS). By using the notion, it is shown that the error is bounded above in a probabilistic sense. However, the analysis remains qualitative and hence we do not explicitly know the bound. Thus, in order to reveal a quantitative property, we further analyze the estimation performance based on the notion of exponential ultimate boundedness in mean square. Finally, we demonstrate the validity of the results through experiment.