🤖 AI Summary
This paper addresses Bayesian state estimation and prediction for nonlinear dynamical systems with unknown dynamics and no access to ground-truth state labels. Method: We propose a fully model-free, unsupervised framework that derives a closed-form analytical solution for the posterior state distribution directly from raw measurement data—without requiring system equations or labeled states. By integrating a data-driven RNN to implicitly encode the dynamics prior and coupling it with analytical Bayesian updating, our approach bypasses explicit modeling assumptions. A linear observation model ensures tractability while preserving theoretical rigor and computational feasibility. Results: Experiments on high-dimensional chaotic systems (e.g., Lorenz and Chen) demonstrate estimation and prediction accuracy competitive with KF, EKF, UKF, KalmanNet, and DMM—significantly extending the applicability of Bayesian filtering to scenarios where the underlying dynamics are entirely unknown.
📝 Abstract
We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup. For a model-free process, we do not have any a-priori knowledge of the process dynamics. In the article, we propose DANSE – a 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. A data-driven recurrent neural network (RNN) is used in DANSE to provide the parameters of a prior of the state. The prior depends on the past measurements as input, and then we find the closed-form posterior of the state using the current measurement as input. The data-driven RNN captures the underlying non-linear dynamics of the model-free process. The training of DANSE, mainly learning the parameters of the RNN, is executed using an unsupervised learning approach. In unsupervised learning, we have access to a training dataset comprising only a set of (noisy) measurement data trajectories, but we do not have any access to the state trajectories. Therefore, DANSE does not have access to state information in the 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 the Kalman filter (KF), extended KF (EKF), unscented KF (UKF), a data-driven deep Markov model (DMM) and a recently proposed hybrid method called KalmanNet. In addition, we show that DANSE works for high-dimensional state estimation.
