The path optimisation problem of mobile sensor networks for arrival-of-angle (AOA) target localisation, using the consensus-based extended information filter is considered, in this study. A new idea of equipping sensors with informationdriven mobility to improve the estimation accuracy with respect to a stationary target is proposed by the authors. A gradient descent method is used for mobile sensors, which are subject to geometric constraints, to choose the next optimal waypoints. The corresponding optimisation problem is solved in a distributed manner, by selecting a proper cost function for each mobile sensor. It is shown that the boundedness of the estimation error is guaranteed. Moreover, they find that the mobility of sensors does decrease the estimation error bounds compared with the static sensor networks, which is beneficial for the localisation performance. Simulation is carried out to show the effectiveness of the proposed method.