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DANSE: Data-Driven Non-Linear State Estimation of Model-Free Process in Unsupervised Learning Setup
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering. (Digital Futures)ORCID iD: 0000-0001-6612-6923
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering. (Digital Futures)ORCID iD: 0000-0003-0166-1356
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering. (Digital Futures)ORCID iD: 0000-0003-2638-6047
2024 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 72, p. 1824-1838Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE) , 2024. Vol. 72, p. 1824-1838
Keywords [en]
State estimation, Computational modeling, Training, Bayes methods, Noise measurement, Supervised learning, Unsupervised learning, Bayesian state estimation, forecasting, neural networks, recurrent neural networks
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:kth:diva-346102DOI: 10.1109/TSP.2024.3383277ISI: 001200035500017Scopus ID: 2-s2.0-85189517590OAI: oai:DiVA.org:kth-346102DiVA, id: diva2:1855839
Note

QC 20240503

Available from: 2024-05-03 Created: 2024-05-03 Last updated: 2024-05-03Bibliographically approved

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Ghosh, AnubhabHonore, AntoineChatterjee, Saikat

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