Distributed $H_\infty$ State and Parameter Estimation over Wireless Sensor Networks under Energy Constraints

This study is aimed at investigating the $H_\infty$ distributed state estimation (DSE) problem for discrete-time systems with unknown parameters subject to state and output nonlinearities over wireless sensor networks (WSNs) under the influence of energy-bounded process disturbances and sensor noise. The study involves the design of a novel distributed estimator for simultaneously estimating the state of the target plant and identifying its unknown parameters in the absence of a fusion center by employing innovations from the sensor itself and its immediate neighbors in the WSN communication topology. A new free-weighting scalar approach is presented; it comprises manipulations of the estimation error, relaxes the requirement regarding global information of connectivity, allows different gains for different estimators, provides less conservative results, and permits an independent design for sensor nodes. The Lyapunov theory and Kronecker product properties are utilized to establish the asymptotic stability of the estimation error dynamics and to satisfy the $H_\infty$ performance constraints regarding disturbance attenuation. The distributed estimator design problem is formulated as a convex optimization problem, which is solved iteratively and autonomously by each sensor node in the WSN topology. Finally, an illustrative example is provided to demonstrate the viability of the suggested estimation strategy.