Error and Energy Aware Sensor Deployment for RSS Localization—A Linear Quadratic Regulator Formulation

In network localization, sensor deployment positions relative to the points of interest (PoIs) and the fusion center (FC) greatly affect the overall localization error and energy performance. To account for both aspects, sensor deployment is formulated as an optimization problem in which the cost function combines both error and energy terms. Given a set of candidate positions, the problem is then to determine where sensors should be deployed such that the cost function is minimized. One of the challenges associated with this problem is NP-hardness, nonlinearity, and nonconvexity. Moreover, the localization error is submodular in relation to the number of deployed sensors. Thus, in addition to deployment positions, the order of deployment is an important factor to consider. To solve this problem, two suboptimal sequential low-complexity deployment algorithms are proposed. In the first algorithm, deployment is modeled as a constrained linear quadratic regulator (LQR) problem. Using this formulation, deployment is formulated as a constrained convex quadratic optimization problem that can be easily solved. To further reduce computational complexity, a second greedy algorithm is proposed. In this algorithm, a local cost function combining a sensor’s transmission energy and the localization errors at the PoIs is used to make the deployment decision. Simulation results show the effectiveness of the proposed algorithms in comparison to other methods.