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.