Gaussian Variational State Estimation for Nonlinear State-Space Models

Courts, Jarrad; Wills, Adrian; Schön, Thomas B.

doi:10.1109/tsp.2021.3122296

Cited by 12 publications

(3 citation statements)

References 36 publications

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“…Another alternative, which has recently gained attention, is the variational approach to state estimation. This approach aims to minimize some divergence measure, typically the kl divergence, between the true and an assumed posterior [118,119]. This approach has been used to develop variational Gaussian filters [119], but has also recently been extended to Gaussian sum filters [120].…”

Section: Alternative State Estimation Approachesmentioning

confidence: 99%

“…This approach aims to minimize some divergence measure, typically the kl divergence, between the true and an assumed posterior [118,119]. This approach has been used to develop variational Gaussian filters [119], but has also recently been extended to Gaussian sum filters [120]. These approaches are generally applicable to any ssm but typically involve complex high-dimensional optimization problems.…”

Section: Alternative State Estimation Approachesmentioning

confidence: 99%

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Dynamic rEvolution : Adaptive state estimation via Gaussian processes and iterative filtering

Kullberg

2024

Linköping Studies in Science and Technology. Dissertations

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Cover illustration: A Gaussian process model of the lateral acceleration experienced by a car driving around the Nürburgring, Germany. The acceleration profile is illustrated for a part of the track, specifically Kallenhard-Wehrseifen-Ex-Mühle. Title: A play on words relating to the theme of the thesis. Dynamic -the thesis studies dynamical systems; Evolution -dynamical systems evolve over time and the contributions are an evolution of the research field itself; rE(volution) -iterated algorithms are at the core of parts of the contributions.Linköping studies in science and technology. Dissertations.No. 2391

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Section: Alternative State Estimation Approachesmentioning

confidence: 99%

Section: Alternative State Estimation Approachesmentioning

confidence: 99%

Dynamic rEvolution : Adaptive state estimation via Gaussian processes and iterative filtering

Kullberg

2024

Linköping Studies in Science and Technology. Dissertations

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“…(19). In Bayesian statistics, a vital object of learning and inference is the model evidence function p(Y|θ) [54]. For instance, Bayesian learning typically resorts to maximizing the logarithm of the p(Y|θ) w.r.t.…”

Section: A Variational Inference and Approximationsmentioning

confidence: 99%

Towards Flexibility and Interpretability of Gaussian Process State-Space Model

Lin¹,

Yin²

2023

Preprint

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Gaussian process state-space model (GPSSM) has attracted much attention over the past decade. However, the model representation power of GPSSM is far from satisfactory. Most GPSSM works rely on the standard Gaussian process (GP) with a preliminary kernel, such as squared exponential (SE) kernel and Matérn kernel, which limit the model representation power and its application in complex scenarios. To address this issue, this paper proposes a novel class of probabilistic statespace model named TGPSSM that enriches the GP priors in the standard GPSSM through parametric normalizing flow, making the state-space model more flexible and expressive. In addition, by inheriting the advantages of sparse representation of GP models, we propose a scalable and interpretable variational learning algorithm to learn the TGPSSM and infer the latent dynamics simultaneously. By integrating a constrained optimization framework and explicitly constructing a non-Gaussian state variational distribution, the proposed learning algorithm enables the TG-PSSM to significantly improve the capabilities of state space representation and model inference. Experimental results based on various synthetic and real datasets corroborate that the proposed TGPSSM yields superior learning and inference performance compared to several state-of-the-art methods. The accompanying source code is available at https://github.com/zhidilin/TGPSSM.

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Minimalistic estimation with stochastic constraints for closed-type tethered satellite formations

Fang

Zhang

et al. 2023

Aerospace Science and Technology

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Gaussian Variational State Estimation for Nonlinear State-Space Models

Cited by 12 publications

References 36 publications

Dynamic rEvolution : Adaptive state estimation via Gaussian processes and iterative filtering

Dynamic rEvolution : Adaptive state estimation via Gaussian processes and iterative filtering

Towards Flexibility and Interpretability of Gaussian Process State-Space Model

Minimalistic estimation with stochastic constraints for closed-type tethered satellite formations

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