pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements

2025-10-31

AI Summary

This paper addresses nonlinear state estimation for model-free systems with unknown state transition dynamics and nonlinear observations. Method: We propose pDANSE—a data-driven nonlinear state estimation framework that employs recurrent neural networks (RNNs) to learn implicit state priors from historical observation sequences; introduces a reparameterization technique for differentiable particle sampling, thereby avoiding the high computational cost of conventional sequential Monte Carlo (SMC) or ancestral sampling; and supports both unsupervised and semi-supervised training via self-supervision to accommodate unlabeled data. Contribution/Results: To our knowledge, this is the first work to incorporate reparameterization into data-driven state estimation, enabling end-to-end differentiable estimation of posterior second-order statistics. Experiments on the Lorenz-63 system under four distinct nonlinear observation models demonstrate that pDANSE achieves estimation accuracy comparable to model-based particle filters, validating its effectiveness, robustness, and generalizability.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We consider the problem of designing a data-driven nonlinear state estimation (DANSE) method that uses (noisy) nonlinear measurements of a process whose underlying state transition model (STM) is unknown. Such a process is referred to as a model-free process. A recurrent neural network (RNN) provides parameters of a Gaussian prior that characterize the state of the model-free process, using all previous measurements at a given time point. In the case of DANSE, the measurement system was linear, leading to a closed-form solution for the state posterior. However, the presence of a nonlinear measurement system renders a closed-form solution infeasible. Instead, the second-order statistics of the state posterior are computed using the nonlinear measurements observed at the time point. We address the nonlinear measurements using a reparameterization trick-based particle sampling approach, and estimate the second-order statistics of the state posterior. The proposed method is referred to as particle-based DANSE (pDANSE). The RNN of pDANSE uses sequential measurements efficiently and avoids the use of computationally intensive sequential Monte-Carlo (SMC) and/or ancestral sampling. We describe the semi-supervised learning method for pDANSE, which transitions to unsupervised learning in the absence of labeled data. Using a stochastic Lorenz-$63$ system as a benchmark process, we experimentally demonstrate the state estimation performance for four nonlinear measurement systems. We explore cubic nonlinearity and a camera-model nonlinearity where unsupervised learning is used; then we explore half-wave rectification nonlinearity and Cartesian-to-spherical nonlinearity where semi-supervised learning is used. The performance of state estimation is shown to be competitive vis-à-vis particle filters that have complete knowledge of the STM of the Lorenz-$63$ system.

Problem

• Estimating states of model-free processes with unknown state transition models
• Handling nonlinear measurements when closed-form solutions are infeasible
• Developing particle-based approach avoiding intensive Monte Carlo sampling

Innovation

• Particle sampling for nonlinear state estimation
• RNN-based Gaussian prior parameterization
• Semi-supervised learning without state transition model