Brief Paper - Distributed input and state estimation for non-linear discrete-time systems with direct feedthrough

This study investigates the problem of distributed estimation for non-linear system of sensor networks with unknown inputs affecting both the system state and outputs. A novel `information filtering algorithm´ is derived by reconstructing the non-linear version of the extended recursive three-step filter (NERTSF) into the information filter architecture, which simultaneously estimates the state and the unknown input, denoted as non-linear version of the extended recursive three-step information filter (NERTSIF). Afterwards the information filter is extended to the `derivative-free´ version with the help of the cubature Kalman filter (CKF) according to the linear error propagation methodology. A distributed filtering algorithm, based on the derivative-free version of the NERTSIF is proposed in which each sensor node only fuses the local observation instead of the global information and updates the local information state and matrix from its neighbours´ estimates using the dynamic average-consensus strategy. The efficacy of the proposed distributed algorithm is demonstrated by simulation examples on target tracking problem and is compared with existing algorithms such as centralised fusion filter and distributed CKF, which lack in tracking the true dynamics of the unknown input.