State Variance Estimation in Large-Scale Network Systems

State variance of a network system is a nonlinear functional computed as the squared deviation of the network's state vector. Such a quantity is useful to monitor how much the states of network nodes are spread around their average mean. Estimating state variance is crucial when the full state estimation of a network system is not possible due to limited computational and sensing resources. We propose a novel methodology to estimate the state variance in a computationally efficient way. First, clusters are identified in the network such that the state variance can be approximated from the average states of the clusters. Then, the approximated state variance is estimated from the average state observer.