pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements
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arXiv
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| Natura: | Preprint |
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2025
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| author | Ghosh, Anubhab Eldar, Yonina C. Chatterjee, Saikat |
| author_facet | Ghosh, Anubhab Eldar, Yonina C. Chatterjee, Saikat |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements Ghosh, Anubhab Eldar, Yonina C. Chatterjee, Saikat Signal Processing Machine Learning 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. |
| title | pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements |
| topic | Signal Processing Machine Learning |
| url | https://arxiv.org/abs/2510.27503 |