High-Precision State Estimator Design for the State of Gaussian Linear Systems Based on Deep Neural Network Kalman Filter

Kalman filter (KF) is highly valued in engineering for its simplicity, small storage, and real-time processing. However, KF is optimal for linear filters and not as effective for nonlinear ones. In this article, we propose a high-precision nonlinear filter, the deep neural network Kalman filter (DKF), which combines KF and a neural network model. DKF's estimation process follows the Kalman filter approach. To maximize the use of model information, we establish DKF by merging the Kalman prediction and update outcomes as neural network input features and training the input–output nonlinear mapping model online. We also introduce a fusion filter, FDKF, based on KF and DKF. Simulation results demonstrate that, for linear Gaussian systems, DKF outperforms KF, and FDKF outperforms both DKF and KF in offline iterative prediction.