This paper proposes cooperative Kalman filters for distributed mobile sensor networks where the mobile sensors are organized into cells that resemble a mesh grid to cover a spatial area. The mobile sensor networks are deployed to map an underlying spatial-temporal field modeled by the Poisson equation. After discretizing the Poisson equation with finite volume method, we found that the cooperative Kalman filters for the cells are subjected to a set of distributed constraints. The field value and gradient information at each cell center can be estimated by the constrained cooperative Kalman filter using measurements within each cell and information from neighboring cells. We also provide convergence analysis for the distributed constrained cooperative Kalman filter. Simulation results with a five cell network validates the proposed distributed filtering method.
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Cooperative Filtering and Parameter Estimation for Polynomial PDEs using a Mobile Sensor Network
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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- NSF-PAR ID:
- 10359105
- Date Published:
- Journal Name:
- Proceedings of the 2022 American Control Conference
- Page Range / eLocation ID:
- 982 to 987
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC53348.2022.9867676
