Optimal Measurement Policy for Linear Measurement Systems With Applications to UAV Network Topology Prediction

Dynamic network topology can pose important challenges to communication and control protocols in networks of autonomous vehicles. For instance, maintaining connectivity is a key challenge in unmanned aerial vehicle (UAV) networks. However, tracking and computational resources of the observer module might not be sufficient for constant monitoring of all surrounding nodes in large-scale networks. In this article, we propose an optimal measurement policy for network topology monitoring under constrained resources. To this end, We formulate the localization of multiple objects in terms of linear networked systems and solve it using Kalman filtering with intermittent observation. The proposed policy includes two sequential steps. We first find optimal measurement attempt probabilities for each target using numerical optimization methods to assign the limited number of resources among targets. The optimal resource allocation follows a waterfall-like solution to assign more resources to targets with lower measurement success probability. This provides a $\text{10}\%$ to $\text{60}\%$ gain in prediction accuracy. The second step is finding optimal on-off patterns for measurement attempts for each target over time. We show that a regular measurement pattern that evenly distributed resources over time outperforms the two extreme cases of using all measurement resources either in the beginning or at the end of the measurement cycle. Our proof is based on characterizing the fixed-point solution of the error covariance matrix for regular patterns. Extensive simulation results confirm the optimality of the most alternating pattern with up to 10-fold prediction improvement for different scenarios. These two guidelines define a general policy for target tracking under constrained resources with applications to network topology prediction of autonomous systems.