Scalar field estimation with mobile sensor networks

In this article, we consider the problem of estimating a scalar field using a network of mobile sensors which can measure the value of the field at their instantaneous location. The scalar field to be estimated is assumed to be represented by positive definite radial basis kernels and we use techniques from adaptive control and Lyapunov analysis to prove the stability of the proposed estimation algorithm. The convergence of the estimated parameter values to the true values is guaranteed by planning the motion of the mobile sensors to satisfy persistence-like conditions. Two kinds of estimation algorithms are proposed: (1) where each mobile sensor estimates the entire parameter vector, (2) where each mobile sensor estimates only part of the parameter vector. Simulations are used for validating the algorithms. We find that the algorithm in case (1) gives more accurate parameter estimates but can be computationally expensive, whereas the algorithm in case (2) performs much faster though the parameter estimates are less accurate. A modification to the second algorithm can be seen to perform fast while providing good accuracy.