Bayesian Modeling and Estimation of Linear Time-Variant Systems using Neural Networks and Gaussian Processes

• URL: http://arxiv.org/abs/2507.12878v1
• Date: Thu, 17 Jul 2025 07:55:34 GMT
• Title: Bayesian Modeling and Estimation of Linear Time-Variant Systems using Neural Networks and Gaussian Processes
• Authors: Yaniv Shulman,
• Abstract summary: This work introduces a unified Bayesian framework that models the system's impulse response, $h(t, tau)$, as a process.<n>We decompose the response into a posterior mean and a random fluctuation term, which naturally defines a new, useful system class we term Linear Time-Invariant in Expectation (LTIE)<n>We demonstrate through a series of experiments that our framework can robustly infer the properties of an LTI system from a single noisy observation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The identification of Linear Time-Variant (LTV) systems from input-output data is a fundamental yet challenging ill-posed inverse problem. This work introduces a unified Bayesian framework that models the system's impulse response, $h(t, \tau)$, as a stochastic process. We decompose the response into a posterior mean and a random fluctuation term, a formulation that provides a principled approach for quantifying uncertainty and naturally defines a new, useful system class we term Linear Time-Invariant in Expectation (LTIE). To perform inference, we leverage modern machine learning techniques, including Bayesian neural networks and Gaussian Processes, using scalable variational inference. We demonstrate through a series of experiments that our framework can robustly infer the properties of an LTI system from a single noisy observation, show superior data efficiency compared to classical methods in a simulated ambient noise tomography problem, and successfully track a continuously varying LTV impulse response by using a structured Gaussian Process prior. This work provides a flexible and robust methodology for uncertainty-aware system identification in dynamic environments.

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