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

• URL: http://arxiv.org/abs/2510.27503v1
• Date: Fri, 31 Oct 2025 14:26:48 GMT
• Title: pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements
• Authors: Anubhab Ghosh, Yonina C. Eldar, Saikat Chatterjee,
• Abstract summary: We consider the problem of designing a data-driven nonlinear state estimation (DANSE) method that uses (noisy) nonlinear measurements.<n>A recurrent neural network (RNN) provides parameters of a Gaussian prior that characterize the state of the model-free process.<n>The second-order statistics of the state posterior are computed using the nonlinear measurements observed at the time point.
• Score: 55.95348868409957
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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-\`a-vis particle filters that have complete knowledge of the STM of the Lorenz-$63$ system.

Related papers

• VSE: Variational state estimation of complex model-free process [10.460885341690664]
  We present a variational state estimation (VSE) method that provides a closed-form Gaussian posterior of an underlying complex dynamical process from (noisy) nonlinear measurements.<n>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.
  arXiv  Detail & Related papers  (2026-01-29T15:47:28Z)
• Bayesian Model Parameter Learning in Linear Inverse Problems: Application in EEG Focal Source Imaging [49.1574468325115]
  Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly.<n>We studied a linear inverse problem that included an unknown non-linear model parameter.<n>We utilized a Bayesian model-based learning approach that allowed signal recovery and subsequently estimation of the model parameter.
  arXiv  Detail & Related papers  (2025-01-07T18:14:24Z)
• Semi-Supervised Model-Free Bayesian State Estimation from Compressed Measurements [57.04370580292727]
  We consider data-driven Bayesian state estimation from compressed measurements.<n>The dimension of the temporal measurement vector is lower than that of the temporal state vector to be estimated.<n>The underlying dynamical model of the state's evolution is unknown for a'model-free process'
  arXiv  Detail & Related papers  (2024-07-10T05:03:48Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setup [10.160595990346627]
  We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup.<n>A data-driven recurrent neural network (RNN) is used in DANSE to provide the parameters of a prior of the state.<n>We show that the proposed DANSE, without knowledge of the unscented process model and without supervised learning, provides a competitive performance against model-driven methods.
  arXiv  Detail & Related papers  (2023-06-04T15:03:39Z)
• Distributed Nonlinear State Estimation in Electric Power Systems using Graph Neural Networks [1.1470070927586016]
  This paper introduces an original graph neural network based SE implementation over the augmented factor graph of the nonlinear power system SE. The proposed regression model has linear computational complexity during the inference time once trained, with a possibility of distributed implementation.
  arXiv  Detail & Related papers  (2022-07-23T08:54:24Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Concurrent Learning Based Tracking Control of Nonlinear Systems using Gaussian Process [2.7930955543692817]
  This paper demonstrates the applicability of the combination of concurrent learning as a tool for parameter estimation and non-parametric Gaussian Process for online disturbance learning. A control law is developed by using both techniques sequentially in the context of feedback linearization. The closed-loop system stability for the nth-order system is proven using the Lyapunov stability theorem.
  arXiv  Detail & Related papers  (2021-06-02T02:59:48Z)
• Active Learning for Nonlinear System Identification with Guarantees [102.43355665393067]
  We study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs. We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data. We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression.
  arXiv  Detail & Related papers  (2020-06-18T04:54:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.