Measures of unobservability

An observed nonlinear dynamics is observable if the mapping from initial condition to output trajectory is one to one. The standard tool for checking observability is the observability rank condition but this only gives a yes or no answer. It does not measure how observable or unobservable the system is. Moreover it requires the ability to differentiate the dynamics and the observations. We introduce new tools, the local unobservability index and the local estimation condition number, to measure the degree of observability or unobservability of a system. To compute these one only needs the ability to simulate the system. We apply these tools to find the best location to put a sensor to observe the flow induced by two point vortices.