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.

该论文提出了一种基于数据的非线性状态估计方法，使用反复神经网络捕捉模型无自由过程的非线性动态，结合朴素贝叶斯方法进行无监督学习，证明其在模拟线性和非线性模型下具有与传统模型驱动方法相当的性能。