Semi-Supervised Model-Free Bayesian State Estimation from Compressed Measurements
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| Format: | Preprint |
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2024
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| _version_ | 1866918466817097728 |
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| author | Ghosh, Anubhab Eldar, Yonina C. Chatterjee, Saikat |
| author_facet | Ghosh, Anubhab Eldar, Yonina C. Chatterjee, Saikat |
| contents | 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 {benchmark chaotic dynamical systems}, we {empirically} show that the data-driven SemiDANSE provides competitive state estimation performance for BSCM {using a handful of different measurement systems}, against a hybrid method called KalmanNet and two model-driven methods (extended Kalman filter and unscented Kalman filter) that know the dynamical models exactly. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_07368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semi-Supervised Model-Free Bayesian State Estimation from Compressed Measurements Ghosh, Anubhab Eldar, Yonina C. Chatterjee, Saikat Signal Processing Machine Learning 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 {benchmark chaotic dynamical systems}, we {empirically} show that the data-driven SemiDANSE provides competitive state estimation performance for BSCM {using a handful of different measurement systems}, against a hybrid method called KalmanNet and two model-driven methods (extended Kalman filter and unscented Kalman filter) that know the dynamical models exactly. |
| title | Semi-Supervised Model-Free Bayesian State Estimation from Compressed Measurements |
| topic | Signal Processing Machine Learning |
| url | https://arxiv.org/abs/2407.07368 |