Semi-Supervised Model-Free Bayesian State Estimation from Compressed Measurements

• URL: http://arxiv.org/abs/2407.07368v3
• Date: Fri, 04 Apr 2025 13:38:45 GMT
• Title: Semi-Supervised Model-Free Bayesian State Estimation from Compressed Measurements
• Authors: Anubhab Ghosh, Yonina C. Eldar, Saikat Chatterjee,
• Abstract summary: We consider data-driven Bayesian state estimation from compressed measurements.<n>The dimension of the temporal measurement vector is lower than that of the temporal state vector to be estimated.<n>The underlying dynamical model of the state's evolution is unknown for a'model-free process'
• Score: 57.04370580292727
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider data-driven Bayesian state estimation from compressed measurements (BSCM) of a model-free process. The dimension of the temporal measurement vector is lower than that of the temporal state vector to be estimated, leading to an under-determined inverse problem. The underlying dynamical model of the state's evolution is unknown for a 'model-free process.' Hence, it is difficult to use traditional model-driven methods, for example, Kalman and particle filters. Instead, we consider data-driven methods. We experimentally show that two existing unsupervised learning-based data-driven methods fail to address the BSCM problem in a model-free process. The methods are -- data-driven nonlinear state estimation (DANSE) and deep Markov model (DMM). While DANSE provides good predictive/forecasting performance to model the temporal measurement data as a time series, its unsupervised learning lacks suitable regularization for tackling the BSCM task. We then propose a semi-supervised learning approach and develop a semi-supervised learning-based DANSE method, referred to as SemiDANSE. In SemiDANSE, we use a large amount of unlabelled data along with a limited amount of labelled data, i.e., pairwise measurement-and-state data, which provides the desired regularization. Using three benchmark dynamical systems, we show that the data-driven SemiDANSE provides competitive state estimation performance for BSCM against a hybrid method called KalmanNet and two model-driven methods (extended Kalman filter and unscented Kalman filter) that know the dynamical models exactly.

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