Optimal sensor placement for parametric model identification of electrical networks, Part II: Estimation under output feedback

In this paper we present an algorithm for choosing optimal measurement points on the edges of a network of dynamic electrical oscillators such that the noise-corrupted electrical signals measured by sensors at that point can be used for generating the most accurate estimates for the network model. Assuming that the measured outputs are fed back to the network nodes to increase system damping we show that the Cramer-Rao bounds for the model estimates are functions of the sensor locations on every edge in the network. We finally state the condition for finding the optimal sensor locations to achieve the tightest Cramer-Rao bounds. An interesting observation is that unlike the algorithm derived in Part-I of this paper, where the open-loop configuration of the system allows us to optimize the bounds in a distributed fashion for each individual edge, here the problem no longer has that decoupled structure under the influence of feedback and must be carried out in a centralized way.