We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup. In the seminar, we discuss our new method called DANSE -- Data-driven Nonlinear State Estimation method. DANSE provides a closed-form posterior of the state of the model-free process, given linear measurements of the state. In addition it provides a closed-form posterior for forecasting. We show how data-driven recurrent neural networks (RNNs) are used in the DANSE to provide closed-form prior of the state and posterior. The training of DANSE, mainly learning the parameters of RNN, is executed in unsupervised learning approach. In the unsupervised learning, we have access to a training dataset comprising of only a set of measurement data trajectories, but we do not have any access to the state trajectories. Therefore, DANSE does not have access to state information in training data and can not use supervised learning. Using simulated linear and non-linear process models (Lorenz attractor and Chen attractor), we evaluate the unsupervised learning-based DANSE. We show that the proposed DANSE, without knowledge of the process model and without supervised learning, provides a competitive performance against model-driven methods, such as Kalman filter (KF), extended KF (EKF) and unscented KF (UKF), and a recently proposed hybrid method called KalmanNet.
