Performance limitation in multi-agent estimation with limited sensor measurements

This paper studies the problem of performance limitations in state estimation of multi-agent systems with limited sensor measurement. We model the agents as LTV systems with erasure in output. We first look to design a state observer for a single agent with output measurement erasure, which guarantees a required performance criterion on the error dynamics. The main result shows that fundamental performance limitation arises in state observation of the agent dynamics when we use exponential mean square stability of the estimation error as the performance metric. This limitation is expressed in terms of the characteristic Lyapunov exponents of the agent dynamics and the uncertainty in the measurement. We then apply this result to the multi-agent estimation problem with limited sensor measurements. Separate cases for cooperative and noncooperative behavior among sensors is studied. Simulation results comparing these cases are given.