State-oriented evaluation of observability and sensor placement for mechanical estimation applications

Optimal sensor selection and placement are of paramount importance in estimation and control applications. In this article, we exploit observability metrics based on the observability Gramian to effectively determine sensor locations that contribute significantly to the individual observability of a limited number of states of importance. In particular, the ellipsoid representation of the observability Gramian is utilized to ensure optimal sensor placement in conjunction with a state-based observability evaluation. The method is demonstrated on a numerical example of a mechanical linear time-invariant system. The results show that the method can highlight states with particularly good observability and place a set of sensors in such a way that the observability is maximised for an arbitrary set of interested states.