Performance bounds for robust estimation using the H∞ filter

A key concern in network observability is to quantify performance and robustness limitations for state estimation from noisy sensors in terms of its dynamical properties and sensor architecture. We develop performance bounds for the robust H-infinity filter, a generalization of the Kalman filter. Utilizing an eigenvalue bound on the observability Gramian, we derive a related eigenvalue bound on the estimation error covariance matrix from the generalized Riccati equation of the H-infinity filter. As a special case, we obtain estimation performance bounds on the Kalman Filter. The bounds reflect the cardinality of the network and sensor set, the stability of the network, and the number and specific set of states to be estimated. We illustrate our results with numerical analysis on a regular network showing how the bounds change with system parameters.