VSE: Variational state estimation of complex model-free process

2026-01-29

AI Summary

This work addresses the challenge of accurately estimating states in complex dynamical systems lacking explicit physical models, particularly from noisy nonlinear observations. The authors propose a model-free variational state estimation method that uniquely integrates a dual recurrent neural network (RNN) architecture with variational inference to directly learn a Gaussian approximation of the state posterior. This approach enables closed-form, efficient online inference without requiring knowledge of the underlying system dynamics. Evaluated on state tracking in a stochastic Lorenz system, the method achieves performance comparable to a particle filter with full model knowledge, despite operating entirely in a data-driven manner, and significantly outperforms existing model-free alternatives. These results demonstrate its effectiveness and robustness in highly nonlinear, non-Gaussian environments.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

We design a variational state estimation (VSE) method that provides a closed-form Gaussian posterior of an underlying complex dynamical process from (noisy) nonlinear measurements. The complex process is model-free. That is, we do not have a suitable physics-based model characterizing the temporal evolution of the process state. The closed-form Gaussian posterior is provided by a recurrent neural network (RNN). The use of RNN is computationally simple in the inference phase. For learning the RNN, an additional RNN is used in the learning phase. Both RNNs help each other learn better based on variational inference principles. The VSE is demonstrated for a tracking application - state estimation of a stochastic Lorenz system (a benchmark process) using a 2-D camera measurement model. The VSE is shown to be competitive against a particle filter that knows the Lorenz system model and a recently proposed data-driven state estimation method that does not know the Lorenz system model.

Problem

• state estimation
• model-free
• nonlinear measurements
• complex dynamical process
• Gaussian posterior

Innovation

• Variational State Estimation
• Model-free
• Recurrent Neural Network
• Closed-form Gaussian Posterior
• Variational Inference