Distributed cooperative Kalman filter constrained by advection-diffusion equation for mobile sensor networks

Ziqiao Zhang; Scott T Mayberry; Wencen Wu; Fumin Zhang

doi:10.3389/frobt.2023.1175418

Distributed cooperative Kalman filter constrained by advection-diffusion equation for mobile sensor networks

Front Robot AI. 2023 Jun 7:10:1175418. doi: 10.3389/frobt.2023.1175418. eCollection 2023.

Authors

Ziqiao Zhang¹, Scott T Mayberry², Wencen Wu³, Fumin Zhang^{1

4}

Affiliations

¹ School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, United States.
² George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, United States.
³ Computer Engineering Department of San Jose State University, San Jose, CA, United States.
⁴ Cheng Kar-Shun Robotics Institute, Hong Kong University of Science and Technology, Hong Kong, Hong Kong SAR, China.

Abstract

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.

Keywords: Kalman filter; cooperative control; distributed parameter systems; formation control; mobile sensor networks.

Grants and funding

The research work is supported by ONR grants N00014-19-1-2556 and N00014-19-1-2266; AFOSR grant FA9550-19-1-0283; NSF grants GCR-1934836, CNS-2016582, ITE-2137798, CMMI-1917300, and RINGS-2148353; and NOAA grant NA16NOS0120028.