Optimal placement of mobile sensors for data assimilations

We explore the theoretical framework as well as the associated algorithms for the problem of optimally placing mobile observation platforms to maximise the improvement of estimation accuracy. The approach in this study is based on the concept of observability, which is a quantitative measure of the information provided by sensor data and user-knowledge. To find the optimal sensor locations, the observability is maximised using a gradient projection method. The Burgers equation is used to verify this approach. To prove the optimality of the sensor locations, Monte Carlo experimentations are carried out using standard 4D-Var algorithms based on two sets of data, one from equally spaced sensors and the other from the optimal sensor locations. The results show that, relative to equally spaced sensors, the 4D-Var data assimilation achieves significantly improved estimation accuracy if the sensors are placed at the optimal locations. A robustness study is also carried out in which the error covariance matrix is varied by 50% and the sensor noise covariance is varied by 100%. In addition, both Gaussian and uniform probability distributions are used for the sensor noise and initial estimation errors. In all cases, the optimal sensor locations result in significantly improved estimation accuracy.