An Optimization Framework for Resilient Batch Estimation in Cyber-Physical Systems

This article proposes a class of resilient state estimators for linear time-varying discrete-time systems. The dynamic equation of the system is assumed to be affected by a bounded process noise. As to the available measurements, they are potentially corrupted by a noise of both dense and impulsive natures. The latter, in addition to being arbitrary in its form, need not be strictly bounded. In this setting, we construct the estimator as the set-valued map, which associates with the measurements the minimizing set of some appropriate performance functions. We consider a family of such performance functions, each of which yielding a specific instance of the proposed general estimation framework. It is then shown that the proposed class of estimators enjoys the property of resilience, i.e., it induces an estimation error, which, under certain conditions, is independent of the extreme values of the (impulsive) measurement noise. Hence, the estimation error may be bounded, while the measurement noise is virtually unbounded. Moreover, we provide several error bounds (in different configurations), whose expressions depend explicitly on the degree of observability of the system being observed and on the considered performance function. Finally, a few simulation results are provided to illustrate the resilience property.