Data-driven Bayesian State Estimation with Compressed Measurement of Model-free Process using Semi-supervised Learning

• URL: http://arxiv.org/abs/2407.07368v2
• Date: Tue, 14 Jan 2025 07:28:06 GMT
• Title: Data-driven Bayesian State Estimation with Compressed Measurement of Model-free Process using Semi-supervised Learning
• Authors: Anubhab Ghosh, Yonina C. Eldar, Saikat Chatterjee,
• Abstract summary: The research topic is: data-driven Bayesian state estimation with compressed measurement. The underlying dynamical model of the states is assumed to be unknown. Two existing unsupervised learning-based data-driven methods fail to address the BSCM problem.
• Score: 57.04370580292727
• License:
• Abstract: The research topic is: data-driven Bayesian state estimation with compressed measurement (BSCM) of model-free process, say for a (causal) tracking application. The dimension of the temporal measurement vector is lower than the dimension of the temporal state vector to be estimated. Hence the state estimation problem is an underdetermined inverse problem. The underlying dynamical model of the states is assumed to be unknown and hence, we use the terminology 'model-free process'. In absence of the dynamical model, we can not employ traditional model-driven methods like Kalman Filter (KF) and Particle Filter (PF), and instead require data-driven methods. We first experimentally show that two existing unsupervised learning-based data-driven methods fail to address the BSCM problem for model-free process; they are - data-driven nonlinear state estimation (DANSE) method and deep Markov model (DMM) method. The unsupervised learning uses unlabelled data comprised of only noisy, linear measurements. While DANSE provides a good predictive / forecasting performance to model the temporal measurement data as time-series, its unsupervised learning lacks a regularization for state estimation. We then investigate the use of a semi-supervised learning approach, and develop a semi-supervised learning-based DANSE method, referred to as SemiDANSE. In SemiDANSE, we use a limited amount of labelled data along-with a large amount of unlabelled data, and that helps to bring the desired regularization for addressing the BSCM problem. The labelled data means pairwise measurement-and-state data. Using three chaotic dynamical systems (or processes) with nonlinear dynamical models as benchmark, we show that the data-driven SemiDANSE provides competitive performance for BSCM against a hybrid method called KalmanNet and two model-driven methods -- an extended KF (EKF) and an unscented KF (UKF).

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