We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup. 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 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), and a recently proposed hybrid method called KalmanNet.

Multichannel processing is widely used for speech enhancement but several limitations appear when trying to deploy these solutions to the real-world. Distributed sensor arrays that consider several devices with a few microphones is a viable alternative that allows for exploiting the multiple devices equipped with microphones that we are using in our everyday life. In this context, we propose to extend the distributed adaptive node-specific signal estimation approach to a neural networks framework. At each node, a local filtering is performed to send one signal to the other nodes where a mask is estimated by a neural network in order to compute a global multi-channel Wiener filter. In an array of two nodes, we show that this additional signal can be efficiently taken into account to predict the masks and leads to better speech enhancement performances than when the mask estimation relies only on the local signals.