Distributed model-invariant detection of unknown inputs in networked systems

This work considers hypothesis testing in networked systems under severe lack of prior knowledge. In previous work we derived a centralized Uniformly Most Powerful Invariant (UMPI) approach to testing unknown inputs in unknown Linear Time Invariant (LTI) networked dynamics subject to unknown Gaussian noise. The detector was also shown to have Constant False Alarm Rate (CFAR) properties. Nonetheless, in large-scale systems, centralized testing may be infeasible or undesirable. Thus, we develop a distributed testing version of our previous work that utilizes a statistic that is maximally invariant to the unknown parameters and the nonlocal/neighboring measurements. Similar to the centralized approach, the distributed test is shown to have CFAR properties and to have performance that asymptotically approaches that of the centralized test. Simulation results illustrate that the performance of the distributed approach suffers marginal performance degradation in comparison to the centralized approach. Insight to this phenomena is provided through a discussion.