{"ID":2847630,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.27503","arxiv_id":"2510.27503","title":"pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements","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 secondorder statistics of the state posterior are computed using the nonlinear measurements observed at the time point. We address the nonlinear measurements using a reparameterization trickbased 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 cameramodel nonlinearity where unsupervised learning is used; then we explore half-wave rectification nonlinearity and Cartesian-tospherical nonlinearity where semi-supervised learning is used. Additionally, we also show the performance of pDANSE for the stochastic Lorenz-96 system with a half-wave, rectified measurement system. The performance of state estimation is shown to be competitive vis-a-vis model-driven methods that have complete knowledge of the STM of the dynamical system.","short_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 Ga...","url_abs":"https://arxiv.org/abs/2510.27503","url_pdf":"https://arxiv.org/pdf/2510.27503v2","authors":"[\"Anubhab Ghosh\",\"Yonina C. Eldar\",\"Saikat Chatterjee\"]","published":"2025-10-31T14:26:48Z","proceeding":"eess.SP","tasks":"[\"eess.SP\",\"cs.LG\"]","methods":"[]","has_code":false}