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

2024-07-10

arXiv.org

AI Summary

This work addresses the underdetermined Bayesian state estimation problem where no prior dynamical model is available and the measurement dimension is lower than the state dimension. We propose SemiDANSE—the first semi-supervised learning framework for model-free state inversion. SemiDANSE integrates variational inference, temporal modeling, and a novel semi-supervised loss, jointly leveraging a small set of labeled (measurement–state pair) data and abundant unlabeled measurements to enforce regularization. This overcomes performance bottlenecks inherent to purely unsupervised methods in compressed sensing settings. Experiments on three chaotic systems demonstrate that, compared to DANSE and deep state-space models (DSSMs), SemiDANSE reduces state estimation error by 32%–57% under high compression ratios. Its accuracy matches or surpasses that of KalmanNet and classical nonlinear Kalman filters (EKF/UKF), significantly improving estimation precision and robustness in model-free, low-dimensional observation regimes.

Technology Category

• Machine Learning: Semi-Supervised Learning
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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).

Problem

• Data-Driven Methods
• State Estimation
• Limited Measurement Information

Innovation

• SemiDANSE
• semi-supervised learning
• state estimation