Variational State Estimation Method Delivers Closed‑Form Gaussian Posteriors for Model‑Free Processes

Global: Variational State Estimation Method Delivers Closed‑Form Gaussian Posteriors for Model‑Free Processes

A new variational state estimation (VSE) technique was introduced in a paper submitted on 29 January 2026 to the arXiv preprint server. The work, authored by Gustav Norén, Anubhab Ghosh, Fredrik Cumlin, and Saikat Chatterjee, proposes a way to infer the hidden state of complex dynamical systems without relying on explicit physics‑based models.

Method Overview

The VSE approach generates a closed‑form Gaussian posterior for the underlying process by employing a recurrent neural network (RNN) during inference. Training leverages a second RNN that operates in the learning phase, allowing the two networks to iteratively improve each other under variational inference principles.

Computational Simplicity

Because the inference stage relies on a single RNN, the method remains computationally lightweight compared with alternatives that require extensive sampling or optimization at run time.

Experimental Validation

To demonstrate the technique, the authors applied VSE to a tracking scenario involving a stochastic Lorenz system—a standard benchmark in chaotic dynamics—observed through a two‑dimensional camera measurement model. The experiment illustrates how VSE can estimate states from noisy, nonlinear observations.

Performance Comparison

Results indicate that VSE performs competitively against a particle filter that has full knowledge of the Lorenz system’s governing equations, as well as against a recently proposed data‑driven estimator that also lacks model information.

Research Context

The paper is classified under the subjects Signal Processing (eess.SP), Machine Learning (cs.LG), and Machine Learning (stat.ML), reflecting its interdisciplinary nature at the intersection of signal processing and statistical learning.

Implications

By delivering accurate state estimates without explicit system models, the VSE framework could broaden the applicability of real‑time monitoring and control in domains where physical modeling is infeasible or prohibitively complex.

Citation Details

The preprint is listed as arXiv:2601.21887 [eess.SP] and can be accessed via the DOI https://doi.org/10.48550/arXiv.2601.21887.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.