DNS: Data-driven Nonlinear Smoother for Complex Model-free Process

2026-02-09

AI Summary

This work proposes a data-driven nonlinear smoother (DNS) for complex nonlinear dynamical systems with unknown models. Leveraging only noisy linear observations, DNS employs a recurrent neural network to directly learn a closed-form posterior distribution over latent states in an unsupervised manner, without requiring an explicit state transition model. By circumventing the need for prior knowledge of system dynamics, the method overcomes a fundamental limitation of conventional smoothers and is applicable to arbitrary nonlinear processes. Benchmark evaluations on systems such as Lorenz demonstrate that DNS significantly outperforms existing approaches—including the deep Kalman smoother (DKS) and iDANSE—in both state estimation accuracy and generalization capability.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

We propose data-driven nonlinear smoother (DNS) to estimate a hidden state sequence of a complex dynamical process from a noisy, linear measurement sequence. The dynamical process is model-free, that is, we do not have any knowledge of the nonlinear dynamics of the complex process. There is no state-transition model (STM) of the process available. The proposed DNS uses a recurrent architecture that helps to provide a closed-form posterior of the hidden state sequence given the measurement sequence. DNS learns in an unsupervised manner, meaning the training dataset consists of only measurement data and no state data. We demonstrate DNS using simulations for smoothing of several stochastic dynamical processes, including a benchmark Lorenz system. Experimental results show that the DNS is significantly better than a deep Kalman smoother (DKS) and an iterative data-driven nonlinear state estimation (iDANSE) smoother.

Problem

• model-free
• state estimation
• nonlinear smoother
• hidden state sequence
• noisy measurements

Innovation

• data-driven
• model-free
• nonlinear smoother
• unsupervised learning
• recurrent architecture