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 Cramér-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.

[1]  Ulrich Hammes,et al.  Robust Tracking and Geolocation for Wireless Networks in NLOS Environments , 2009, IEEE Journal of Selected Topics in Signal Processing.

[2]  Ismail Güvenç,et al.  Fundamental limits and improved algorithms for linear least-squares wireless position estimation , 2012, Wirel. Commun. Mob. Comput..

[3]  Moe Z. Win,et al.  Cooperative Localization in Wireless Networks , 2009, Proceedings of the IEEE.

[4]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[5]  Xi Chen,et al.  Sequential Monte Carlo for simultaneous passive device-free tracking and sensor localization using received signal strength measurements , 2011, Proceedings of the 10th ACM/IEEE International Conference on Information Processing in Sensor Networks.

[6]  Alfred O. Hero,et al.  Relative location estimation in wireless sensor networks , 2003, IEEE Trans. Signal Process..

[7]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[8]  Carlo Fischione,et al.  A Sensor Fusion Algorithm for Mobile Node Localization , 2011 .

[9]  Jing Liu,et al.  Survey of Wireless Indoor Positioning Techniques and Systems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[10]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[11]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[12]  Maurizio A. Spirito,et al.  On the accuracy of cellular mobile station location estimation , 2001, IEEE Trans. Veh. Technol..

[13]  Jean-Pierre Le Cadre,et al.  Closed-form posterior Cramer-Rao bounds for bearings-only tracking , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[14]  Isaac Skog,et al.  In-Car Positioning and Navigation Technologies—A Survey , 2009, IEEE Transactions on Intelligent Transportation Systems.

[15]  Peter K. Allen,et al.  Localization methods for a mobile robot in urban environments , 2004, IEEE Transactions on Robotics.

[16]  Maurizio Longo,et al.  Posterior Cramér-Rao bound for range-based target tracking in sensor networks , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.

[17]  Soummya Kar,et al.  DILAND: An Algorithm for Distributed Sensor Localization With Noisy Distance Measurements , 2009, IEEE Transactions on Signal Processing.

[18]  Brian D. O. Anderson,et al.  Optimality analysis of sensor-target localization geometries , 2010, Autom..

[19]  Rick S. Blum,et al.  Target Localization and Tracking in Noncoherent Multiple-Input Multiple-Output Radar Systems , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[20]  Alessio De Angelis,et al.  Characterization and Modeling of an Experimental UWB Pulse-Based Distance Measurement System , 2009, IEEE Transactions on Instrumentation and Measurement.

[21]  Carlo Fischione,et al.  A distributed minimum variance estimator for sensor networks , 2008, IEEE Journal on Selected Areas in Communications.

[22]  Alessio De Angelis,et al.  Indoor Positioning by Ultra-Wideband Radio Aided Inertial Navigation , 2009 .

[23]  Soummya Kar,et al.  Distributed Sensor Localization in Random Environments Using Minimal Number of Anchor Nodes , 2008, IEEE Transactions on Signal Processing.

[24]  R.L. Moses,et al.  Locating the nodes: cooperative localization in wireless sensor networks , 2005, IEEE Signal Processing Magazine.

[25]  Moe Z. Win,et al.  Network Experimentation for Cooperative Localization , 2012, IEEE Journal on Selected Areas in Communications.

[26]  Niclas Bergman,et al.  Recursive Bayesian Estimation : Navigation and Tracking Applications , 1999 .

[27]  Stergios I. Roumeliotis,et al.  Performance analysis of multirobot Cooperative localization , 2006, IEEE Transactions on Robotics.

[28]  Erik G. Ström,et al.  TDOA Based Positioning in the Presence of Unknown Clock Skew , 2013, IEEE Transactions on Communications.

[29]  Carlo Fischione,et al.  A distributed information fusion method for localization based on Pareto optimization , 2011, 2011 International Conference on Distributed Computing in Sensor Systems and Workshops (DCOSS).

[30]  Moe Z. Win,et al.  Fundamental Limits of Wideband Localization— Part I: A General Framework , 2010, IEEE Transactions on Information Theory.

[31]  Brian D. O. Anderson,et al.  Cooperative Self-Localization of Mobile Agents , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[32]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[33]  Moe Z. Win,et al.  Fundamental Limits of Wideband Localization— Part II: Cooperative Networks , 2010, IEEE Transactions on Information Theory.

[34]  James H. Taylor The Cramer-Rao estimation error lower bound computation for deterministic nonlinear systems , 1978 .

[35]  Marc Moonen,et al.  Seeing the Bigger Picture: How Nodes Can Learn Their Place Within a Complex Ad Hoc Network Topology , 2013, IEEE Signal Processing Magazine.

[36]  Thomas B. Schon,et al.  Tightly coupled UWB/IMU pose estimation , 2009, 2009 IEEE International Conference on Ultra-Wideband.

[37]  G.B. Giannakis,et al.  Localization via ultra-wideband radios: a look at positioning aspects for future sensor networks , 2005, IEEE Signal Processing Magazine.

[38]  Yan Yu,et al.  Toward Robust Indoor Localization Based on Bayesian Filter Using Chirp-Spread-Spectrum Ranging , 2012, IEEE Transactions on Industrial Electronics.

[39]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[40]  James A. Bucklew,et al.  Robust decentralized source localization via averaging , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[41]  Maria Huhtala,et al.  Random Variables and Stochastic Processes , 2021, Matrix and Tensor Decompositions in Signal Processing.

[42]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[43]  D. Powell,et al.  Land-vehicle navigation using GPS , 1999, Proc. IEEE.

[44]  Alessio De Angelis,et al.  Schedule-based sequential localization in asynchronous wireless networks , 2014, EURASIP J. Adv. Signal Process..

[45]  S. Kay Fundamentals of statistical signal processing: estimation theory , 1993 .

[46]  Carlos H. Muravchik,et al.  Posterior Cramer-Rao bounds for discrete-time nonlinear filtering , 1998, IEEE Trans. Signal Process..

[47]  Branko Ristic,et al.  Tracking a manoeuvring target using angle-only measurements: algorithms and performance , 2003, Signal Process..

[48]  Fredrik Gustafsson,et al.  Statistical Sensor Fusion , 2013 .

[49]  Wing-Kin Ma,et al.  Received signal strength based mobile positioning via constrained weighted least squares , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[50]  Magnus Jobs,et al.  Accurate and reliable soldier and first responder indoor positioning: multisensor systems and cooperative localization , 2011, IEEE Wireless Communications.

[51]  M.Z. Win,et al.  Monte Carlo localization in dense multipath environments using UWB ranging , 2005, 2005 IEEE International Conference on Ultra-Wideband.