Neural-Network-Based State Estimation for Nonlinear Systems with Measurement Outliers and Amplify-and-Forward Relays

This paper is concerned with the state estimation problem for a class of nonlinear systems subject to amplify-and-forward (AF) relays and measurement outliers. The AF relay is implemented between the sensors and the estimator, which amplifies and forwards the measurement signals. A novel algorithm is proposed to detect measurement outliers based on historical measurement data. For the nonlinear system, a neural network based method is used to approximate the general nonlinearity. By solving matrix recursive equations, upper bounds are first derived on the estimation error covariance and the neural network weight estimation error covariance, and then the derived upper bounds are minimized through designing adequate estimator gain and tuning scalar. Finally, the validity of the proposed estimation approach is confirmed by an example.