Distributed Motion Tomography for Reconstruction of Flow Fields

This paper considers a group of mobile sensing agents in a flow field and presents a distributed method for motion tomography (MT) that estimates the underlying flow field. MT formulates an underdetermined nonlinear system of equations as an inverse problem. Inspired by the Kaczmarz method which is an optimization approach for solving a linear system of equations, our previous work developed a nonlinear Kaczmarz method that solves the system of equations associated with MT. Considering distributed multi-agent systems for MT, this paper extends the nonlinear Kaczmarz method into a distributed framework. The distributed nonlinear Kaczmarz method is developed by formulating a constrained consensus problem that belongs to a class of projected consensus algorithms. To study the convergence and consensus for the method, its linear case is analyzed first and then its nonlinear case is discussed. The nonlinear case of the method is further validated through simulations by estimating a gyre flow field using mobile sensor networks with different numbers of neighboring agents. Resulting estimated flow fields are compared with a flow field estimated by its centralized counterpart.