Arthur J. Krener

Department of Applied Mathematics

Naval Postgraduate School

**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 a new tool, the local observability gramian, to measure the degree of observability or unobservability of a system. To compute the local observability gramian, one only needs the ability to simulate the system. We apply this tool to find the best location to put a sensor to observe the flow induced by two point vortices. (This is joint work with K. Ide of the University of Maryland.)

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