Improving Localization Accuracy under Constrained Regions in Wireless Sensor Networks through Geometry Optimization.

In addition to various estimation algorithms, the target localization accuracy in wireless sensor networks (WSNs) can also be improved from the perspective of geometry optimization. Note that existing placement strategies are mainly aimed at unconstrained deployment regions, i.e., the positions of sensors are arbitrary. In this paper, considering factors such as terrain, communication, and security, the optimal range-based sensor geometries under circular deployment region and minimum safety distance constraints are proposed. The geometry optimization problem is modeled as a constrained optimization problem, with a D-optimality-based (maximizing the determinant of FIM matrix) scalar function as the objective function and the irregular feasible deployment regions as the constraints. We transform the constrained optimization problem into an equivalent form using the introduced maximum feasible angle and separation angle, and discuss the optimal geometries based on the relationship between the minimum safety distance and the maximum feasible angle. We first consider optimal geometries for two and three sensors in the localization system, and then use their findings to extend the study to scenarios with arbitrary numbers of sensors and arbitrarily shaped feasible regions. Numerical simulation results are included to verify the theoretical conclusions.