Mobile Node Localization via Pareto Optimization: Algorithm and Fundamental Performance Limitations

Accurate estimation of the position of network nodes is essential, e.g., in localization, geographic routing, and vehicular networks. Unfortunately, typical positioning techniques based on ranging or on velocity and angular measurements are inherently limited. To overcome the limitations of specific positioning techniques, the fusion of multiple and heterogeneous sensor information is an appealing strategy. In this paper, we investigate the fundamental performance of linear fusion of multiple measurements of the position of mobile nodes, and propose a new distributed recursive position estimator. The Cram\'er-Rao lower bounds for the parametric and a-posteriori cases are investigated. The proposed estimator combines information coming from ranging, speed, and angular measurements, which is jointly fused by a Pareto optimization problem where the mean and the variance of the localization error are simultaneously minimized. A distinguished feature of the method is that it assumes a very simple dynamical model of the mobility and therefore it is applicable to a large number of scenarios providing good performance. The main challenge is the characterization of the statistical information needed to model the Fisher information matrix and the Pareto optimization problem. The proposed analysis is validated by Monte Carlo simulations, and the performance is compared to several Kalman-based filters, commonly employed for localization and sensor fusion. Simulation results show that the proposed estimator outperforms the traditional approaches that are based on the extended Kalman filter when no assumption on the model of motion is used. In such a scenario, better performance is achieved by the proposed method, but at the price of an increased computational complexity.