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In this paper, a constrained cooperative Kalman filter is developed to estimate field values and gradients along trajectories of mobile robots collecting measurements. We assume the underlying field is generated by a polynomial partial differential equation with unknown time-varying parameters. A long short-term memory (LSTM) based Kalman filter, is applied for the parameter estimation leveraging the updated state estimates from the constrained cooperative Kalman filter. Convergence for the constrained cooperative Kalman filter has been justified. Simulation results in a 2-dimensional field are provided to validate the proposed method.
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Real-time variational method for learning neural trajectory and its dynamics
Latent variable models have become instrumental in computational neuroscience for reasoning about neural computation. This has fostered the development of powerful offline algorithms for extracting latent neural trajectories from neural recordings. However, despite the potential of real-time alternatives to give immediate feedback to experimentalists, and enhance experimental design, they have received markedly less attention. In this work, we introduce the exponential family variational Kalman filter (eVKF), an online recursive Bayesian method aimed at inferring latent trajectories while simultaneously learning the dynamical system generating them. eVKF works for arbitrary likelihoods and utilizes the constant base measure exponential family to model the latent state stochasticity. We derive a closed-form variational analog to the predict step of the Kalman filter which leads to a provably tighter bound on the ELBO compared to another online variational method. We validate our method on synthetic and real-world data, and, notably, show that it achieves competitive performance.
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- Award ID(s):
- 1845836
- PAR ID:
- 10482092
- Publisher / Repository:
- OpenReview
- Date Published:
- Journal Name:
- The Eleventh International Conference on Learning Representations
- Subject(s) / Keyword(s):
- neural dynamics neural trajectory online variational inference
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Proceeding:
- The DOI is not currently available.
