Physics-Informed Data-Driven Autoregressive Nonlinear Filter

State estimation for nonlinear models has been a longstanding challenge in the field of signal processing. Classical nonlinear filters, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), and particle filter (PF), often struggle to balance accuracy and computational cost in highly nonlinear models. Inspired by the property that data-driven methods trained offline in advance are generally efficient during inference phrase, we propose a physics-informed Data-driven Autoregressive nonlinear Filter (DAF) based on the Transformer architecture. During inference phrase, the DAF relies entirely on the neural network and does not retain any structure from classical nonlinear filters. Simulation results demonstrate that the DAF not only achieves higher accuracy than classical nonlinear filters without requiring access to ground-truth state values but also offers competitive computational efficiency.