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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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On Neural Network Training from Noisy Data using a Novel Filtering Framework
We discuss a novel method to train a neural network from noisy data, using Optimal Transport based filtering. We show a comparative study of this methodology with three other filters: the Extended Kalman filter, the Ensemble Kalman filter, and the Unscented Kalman filter, that can also be used for the purpose of training a neural network. We empirically establish that Optimal Transport based filter performs better than the other three filters with respect to root mean square error measure, for non-Gaussian noise in the output. We demonstrate the efficacy of utilizing the Optimal Transport based filtering for neural network training in the context of predicting Mackey-Glass chaotic time series data.
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- Award ID(s):
- 1762825
- PAR ID:
- 10288120
- Date Published:
- Journal Name:
- SciTech 2020 Forum
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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In this paper, a distributed cooperative filtering strategy for state estimation has been developed for mobile sensor networks in a spatial–temporal varying field modeled by the advection–diffusion equation. Sensors are organized into distributed cells that resemble a mesh grid covering a spatial area, and estimation of the field value and gradient information at each cell center is obtained by running a constrained cooperative Kalman filter while incorporating the sensor measurements and information from neighboring cells. Within each cell, the finite volume method is applied to discretize and approximate the advection–diffusion equation. These approximations build the weakly coupled relationships between neighboring cells and define the constraints that the cooperative Kalman filters are subjected to. With the estimated information, a gradient-based formation control law has been developed that enables the sensor network to adjust formation size by utilizing the estimated gradient information. Convergence analysis has been conducted for both the distributed constrained cooperative Kalman filter and the formation control. Simulation results with a 9-cell 12-sensor network validate the proposed distributed filtering method and control law.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.2514/6.2020-1869
