Distributed Localization with Complemented RSS and AOA Measurements: Theory and Methods
Abstract
:1. Introduction
2. RSSAOA Distributed Localization Problem
2.1. Problem Statement
2.2. Performance Metrics
2.3. Main Sources of Errors
3. Existing Methods
3.1. SecondOrder Cone Programming (SOCP) Method
3.2. Linear Least Squares (LLS) Method
3.3. MCMCMH Method
Algorithm 1 Summary of MCMCMH algorithm 

3.4. Generalized Trust Region SubProblem (GTRS) Method
4. Performance Analysis
4.1. Analysis of Computational Complexity
4.2. Analysis of Localization Accuracy
 (1)
 The network is connected and does not vary during the computational period;
 (2)
 All nodes are suitably equipped to measure RSS of the received radio signal;
 (3)
 Some nodes (anchors) or possibly all of them are conveniently equipped to measure AOA of the received radio signal;
 (4)
 Working order of the nodes is synchronized.
5. Summary and Future Prospects
Author Contributions
Funding
Conflicts of Interest
Appendix A. CRLB Derivation for RSSAOA Localization
References
 Coluccia, A. Reducedbias MLbased Estimators with Low Complexity for Selfcalibrating RSS Ranging. IEEE Trans. Wirel. Commun. 2014, 12, 1220–1230. [Google Scholar] [CrossRef]
 Beko, M. Energybased Localization in Wireless Sensor Networks Using Secondorder Cone Programming Relaxation. Wirel. Pers. Commun. 2014, 77, 1847–1857. [Google Scholar] [CrossRef]
 Coluccia, A.; Ricciato, F. RSSbased Localization via Bayesian Ranging and Iterative Least Squares Positioning. IEEE Commun. Lett. 2014, 18, 836–876. [Google Scholar] [CrossRef]
 Tomic, S.; Beko, M.; Dinis, R. 3D Target Localization in Wireless Sensor Network Using RSS and AoA Measurement. IEEE Trans. Vehic. Technol. 2017, 66, 3197–3210. [Google Scholar] [CrossRef]
 Tomic, S.; Beko, M.; Dinis, R.; Tuba, M.; Bacanin, N. Bayesian Methodology for Target Tracking Using RSS and AoA Measurements. Phys. Commun. 2017, 25, 158–166. [Google Scholar] [CrossRef] [Green Version]
 Correia, S.; Beko, M.; Cruz, L.; Tomic, S. Elephant Herding Optimization for EnergyBased Localization. Sensors 2018, 18, 2849. [Google Scholar]
 Tomic, S.; Beko, M.; Tuba, M.; Correia, V.M.F. Target Localization in NLOS Environments Using RSS and TOA Measurements. IEEE Wirel. Commun. Lett. 2018, 7, 1062–1065. [Google Scholar] [CrossRef] [Green Version]
 Pedro, D.; Tomic, S.; Bernardo, L.; Beko, M.; Oliveira, R.; Dinis, R.; Pinto, P.; Amaral, P. Algorithms for Estimating the Location of Remote Nodes Using Smartphones. IEEE Access 2019, 17, 33713–33727. [Google Scholar] [CrossRef]
 Tomic, S.; Beko, M.; Dinis, R.; Gomes, J.P. Target Tracking with Sensor Navigation Using Coupled RSS and AOA Measurements. Sensors 2017, 17, 2690. [Google Scholar] [CrossRef] [Green Version]
 Bandiera, F.; Coluccia, A.; Ricci, G. A Cognitive Algorithm for Received Signal Strength Based Localization. IEEE Trans. Signal Process. 2015, 63, 1726–1736. [Google Scholar] [CrossRef]
 Tomic, S.; Beko, M. Exact Robust Solution to TWToAbased Target Localization Problem with Clock Imperfections. IEEE Signal Process. Lett. 2018, 25, 531–535. [Google Scholar] [CrossRef] [Green Version]
 Coluccia, A.; Fascista, A. On the Hybrid TOA/RSS Range Estimation in Wireless Sensor Networks. IEEE Trans. Wirel. Commun. 2018, 17, 361–371. [Google Scholar] [CrossRef]
 Carlino, L.; Bandiera, F.; Coluccia, A.; Ricci, G. Improving Localization by Testing Mobility. IEEE Trans. Signal Process. 2019, 67, 3412–3423. [Google Scholar] [CrossRef]
 Tomic, S.; Beko, M.; Dinis, R.; Tuba, M.; Bacanin, N. RSSAOAbased Target Localization and Tracking in Wireless Sensor Networks, 1st ed.; River Publishers: Delft, The Netherlands, 2017. [Google Scholar]
 Tomic, S.; Beko, M.; Tuba, M. A Linear Estimator for Network Localization Using Integrated RSS and AOA Measurements. IEEE Signal Process. Lett. 2019, 26, 405–409. [Google Scholar] [CrossRef] [Green Version]
 Coluccia, A.; Fascista, A. Hybrid TOA/RSS RangeBased Localization with SelfCalibration in Asynchronous Wireless Networks. J. Sens. Actuator Netw. 2019, 8, 31. [Google Scholar] [CrossRef] [Green Version]
 Tomic, S.; Beko, M. A Bisectionbased Approach for Exact Target Localization in NLOS Environments. Signal Process. 2018, 143, 328–335. [Google Scholar] [CrossRef] [Green Version]
 Tomic, S.; Beko, M.; Dinis, R.; Montezuma, P. A Robust Bisectionbased Estimator for TOAbased Target Localization in NLOS Environments. IEEE Commun. Lett. 2017, 21, 2488–2491. [Google Scholar] [CrossRef] [Green Version]
 Safavi, S.; Khan, U.A.; Kar, S.; Moura, J.M.F. Estimating Directional Data From Network Topology for Improving Tracking Performance. Proc. IEEE 2018, 106, 1204–1223. [Google Scholar] [CrossRef]
 Tomic, S.; Beko, M.; Dinis, R.; Bernardo, L. On Target Localization Using Combined RSS and AoA Measurements. Sensors 2018, 18, 1266. [Google Scholar] [CrossRef] [Green Version]
 Tomic, S.; Beko, M. A Robust NLOS Bias Mitigation Technique for RSSTOAbased Target Localization. IEEE Signal Process. Lett. 2019, 26, 64–68. [Google Scholar] [CrossRef]
 Pahlavan, K.; Krishnamurthy, P.; Geng, Y. Localization Challenges for the Emergence of the Smart World. IEEE Access 2015, 3, 3058–3067. [Google Scholar] [CrossRef]
 Yang, Z.; Wu, C.; Zhou, Z.; Zhang, X.; Wang, X.; Liu, Y. A Review of Advanced Localization Techniques for Crowdsensing Wireless Sensor Networks. ACM Comput. Surv. 2015, 47, 1–34. [Google Scholar] [CrossRef]
 Han, G.; Jiang, J.; Zhang, C.; Duong, T.Q.; Guizani, M.; Karagiannidis, G.K. A Survey on Mobile Anchor Node Assisted Localization in Wireless Sensor Networks. IEEE Commun. Surv. Tutorials 2016, 18, 2220–2243. [Google Scholar] [CrossRef]
 Coluccia, A.; Fascista, A. A Review of Advanced Localization Techniques for Crowdsensing Wireless Sensor Networks. Sensors 2019, 19, 988. [Google Scholar] [CrossRef] [PubMed] [Green Version]
 CamarinhaMatos, L.M.; Afsarmanesh, H. Roots of Collaboration: NatureInspired Solutions for Collaborative Networks. IEEE Access 2018, 6, 30829–30843. [Google Scholar] [CrossRef]
 Witrisal, K.; Meissner, P.; Leitinger, E.; Shen, Y.; Gustafson, C.; Tufvesson, F.; Haneda, K.; Dardari, D.; Molisch, A.F.; Conti, A.; et al. HighAccuracy Localization for Assisted Living: 5G systems will turn multipath channels from foe to friend. IEEE Signal Process. Mag. 2016, 33, 59–70. [Google Scholar] [CrossRef]
 AbuShaban, Z.; Zhou, X.; Abhayapala, T.; SecoGranados, G.; Wymeersch, H. Error Bounds for Uplink and Downlink 3D Localization in 5G Millimeter Wave Systems. IEEE Trans. Wirel. Commun. 2018, 17, 4939–4954. [Google Scholar]
 Fascista, A.; Coluccia, A.; Wymeersch, H.; SecoGranados, G. MillimeterWave Downlink Positioning With a SingleAntenna Receiver. IEEE Trans. Wirel. Commun. 2019, 18, 4479–4490. [Google Scholar] [CrossRef] [Green Version]
 Singh, Y.; Saha, S.; Chugh, U.; Gupt, C. Distributed Event Detection in Wireless Sensor Networks for Forest Fires. In Proceedings of the 2013 UKSim 15th International Conference on Computer Modelling and Simulation, Cambridge, UK, 10–12 April 2013; pp. 634–639. [Google Scholar]
 Madeira, R.; Paulino, N. Analysis and Implementation of a Power Management Unit with a Multiratio Switched Capacitor DC–DC Converter for a Supercapacitor Power Supply. Int. J. Circuit Theory Appl. 2016, 44, 2018–2034. [Google Scholar] [CrossRef]
 Nowacki, B.; Paulino, N.; Goes, J. A ThirdOrder MASH ΣΔ Modulator Using Passive Integrators. IEEE Trans. Circuits Syst. Regul. Pap. 2017, 64, 2871–2883. [Google Scholar] [CrossRef]
 Tahat, A.; Kaddoum, G.; Yousefi, S.; Valaee, S.; Gagnon, F. A Look at the Recent Wireless Positioning Techniques With a Focus on Algorithms for Moving Receivers. IEEE Access 2016, 4, 6652–6680. [Google Scholar] [CrossRef]
 Tomic, S.; Beko, M.; Dinis, R.; Montezuma, P. Distributed Algorithm for Target Localization in Wireless Sensor Networks Using RSS and AoA Measurements. Pervasive Mob. Comput. 2017, 37, 63–77. [Google Scholar] [CrossRef] [Green Version]
 Zamiri, M.; CamarinhaMatos, L.M. Mass Collaboration and Learning: Opportunities, Challenges, and Influential Factors. Appl. Sci. 2019, 9, 2620. [Google Scholar] [CrossRef] [Green Version]
 Vafaei, N.; Ribeiro, R.A.; CamarinhaMatos, L.M.; Valera, L.R. Normalization Techniques for Collaborative Networks. Kybernetes 2019, X, X–Z. [Google Scholar] [CrossRef]
 Vaghefi, R.M.; Buehrer, R.M. Cooperative Localization in NLOS Environments Using Semidefinite Programming. IEEE Commun. Lett. 2015, 19, 1382–1385. [Google Scholar] [CrossRef]
 Khan, M.W.; Salman, N.; Kemp, A.H. Optimised Hybrid Localisation with Cooperation in Wireless Sensor Networks. IET Signal Process. 2017, 11, 341–348. [Google Scholar] [CrossRef]
 Tomic, S.; Beko, M. Target Localization via Integrated and Segregated Ranging Based on RSS and TOA Measurements. Sensors 2019, 19, 230. [Google Scholar] [CrossRef] [Green Version]
 Tomic, S.; Beko, M.; Dinis, R. Distributed RSSBased Localization in Wireless Sensor Networks Based on SecondOrder Cone Programming. Sensors 2014, 14, 18410–18432. [Google Scholar] [CrossRef] [Green Version]
 Patwari, N. Location Estimation in Sensor Networks. Ph.D. Thesis, University of Michigan, Ann Arbor, MI, USA, 2005. [Google Scholar]
 Rappaport, T.S. Wireless Communications: Principles and Practice, 1st ed.; Prentice Hall: Upper Saddle River, NJ, USA, 1996. [Google Scholar]
 Sichitiu, M.L.; Ramadurai, V. Localization of Wireless Sensor Networks with a Mobile Beacon. In Proceedings of the 2004 IEEE International Conference on Mobile Adhoc and Sensor Systems, Fort Lauderdale, FL, USA, 25–27 October 2004; pp. 174–183. [Google Scholar]
 Tomic, S.; Beko, M.; Dinis, R. RSSbased Localization in Wireless Sensor Networks Using Convex Relaxation: Noncooperative and Cooperative Schemes. IEEE Trans. Veh. Technol. 2015, 64, 2037–2050. [Google Scholar] [CrossRef] [Green Version]
 Kulas, L. RSSBased DoA Estimation Using ESPAR Antennas and Interpolated Radiation Patterns. IEEE Antennas Wirel. Propag. Lett. 2018, 17, 25–28. [Google Scholar] [CrossRef]
 Niculescu, D.; Nath, B. VOR Base Stations for Indoor 802.11 Positioning. In Proceedings of the 10th annual international conference on Mobile computing and networking, Philadelphia, PA, USA, 26 September–1 October 2004; pp. 58–69. [Google Scholar]
 Ferreira, M.B.; Gomes, J.; Costeira, J.P. A Unified Approach for Hybrid Source Localization Based on Ranges and Video. In Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, QLD, Australia, 19–24 April 2015; pp. 2879–2883. [Google Scholar]
 Tomic, S.; Beko, M.; Dinis, R.; Montezuma, P. Estimating Directional Data From Network Topology for Improving Tracking Performance. J. Sens. Actuator Netw. 2019, 8, 30. [Google Scholar] [CrossRef] [Green Version]
 Schmidt, R. Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 1986, 34, 276–280. [Google Scholar] [CrossRef] [Green Version]
 Roy, R.; Kailath, T. ESPRITestimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process. 1989, 37, 984–995. [Google Scholar] [CrossRef] [Green Version]
 Yu, K. 3D Localization Error Analysis in Wireless Networks. IEEE Trans. Wirel. Commun. 2007, 6, 3473–3481. [Google Scholar]
 Fascista, A.; Ciccarese, G.; Coluccia, A.; Ricci, G. Angle of ArrivalBased Cooperative Positioning for Smart Vehicles. IEEE Trans. Intell. Transp. Syst. 2018, 19, 2880–2892. [Google Scholar] [CrossRef]
 Tomic, S.; Beko, M.; Dinis, R.; Montezuma, P. A Closedform Solution for RSS/AoA Target Localization by Spherical Coordinates Conversion. IEEE Wirel. Commun. Lett. 2016, 5, 680–683. [Google Scholar] [CrossRef] [Green Version]
 Mardia, K.V. Statistics of Directional Data, 1st ed.; Academic Press, Inc.: London, UK, 1972. [Google Scholar]
 Forbes, C.; Evans, M.E.; Hastings, N.; Peacock, B. Statistical Distributions, 4th ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2011. [Google Scholar]
 Kay, S.M. Fundamentals of Statistical Signal Processing: Estimation Theory, 1st ed.; Prentice Hall: Upper Saddle River, NJ, USA, 1993. [Google Scholar]
 Li, X.R.; Zhao, Z. Measures of Performance for Evaluation of Estimators and Filters. In Signal and Data Processing of Small Targets 2001; Drummond, O., Ed.; SPIE: San Diego, CA, USA, 2001; Volume 4473, pp. 1–12. [Google Scholar]
 Dardari, D.; Closas, P.; Djuric, P.M. Indoor Tracking: Theory, Methods, and Technologies. IEEE Trans. Veh. Technol. 2016, 64, 1263–1278. [Google Scholar] [CrossRef] [Green Version]
 Patwari, N.; Ash, J.N.; Kyperountas, S.; Hero, A.O., III; Moses, R.L.; Correal, N.S. Locating the Nodes: Cooperative Localization in Wireless Sensor Networks. IEEE Signal Process. Mag. 2005, 22, 54–69. [Google Scholar] [CrossRef]
 Hashemi, H. The Indoor Radio Propagation Channel. Proc. IEEE 1993, 81, 943–968. [Google Scholar] [CrossRef]
 Tomic, S.; Beko, M.; Dinis, R. Distributed RSSAoA Based Localization with Unknown Transmit Powers. IEEE Wirel. Commun. Lett. 2016, 5, 392–395. [Google Scholar] [CrossRef]
 Boyd, S.; Vandenberghe, L. Convex Optimization, 1st ed.; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]
 Grant, M.; Boyd, S. CVX: MATLAB Software for Disciplined Convex Programming; CVX Research, Inc.: Austin, TX, USA, 2003. [Google Scholar]
 Coluccia, A.; Ricciato, F.; Ricci, G. Positioning Based on Signals of Opportunity. IEEE Commun. Lett. 2014, 18, 356–359. [Google Scholar] [CrossRef]
 Naseri, H.; Koivunen, V. A Bayesian Algorithm for Distributed Network Localization Using Distance and Direction Data. IEEE Trans. Signal Inf. Process. Over Netw. 2019, 5, 290–304. [Google Scholar] [CrossRef]
 Robert, C.; Casella, G. Introducing Monte Carlo Methods with R, 1st ed.; Springer: Berlin, Germany, 2009. [Google Scholar]
 Koller, D.; Friedman, N. Probabilistic Graphical Models: Principles and Techniques, 1st ed.; MIT Press: Cambridge, MA, USA, 2009. [Google Scholar]
 Tomic, S.; Beko, M. A Geometric Approach for Distributed Multihop Target Localization in Cooperative Networks. Accept. Publ. IEEE Trans. Veh. Technol. 2019, X, X–Y. [Google Scholar] [CrossRef]
 Moré, J.J. Generalization of the Trust Region Problem. Optim. Meth. Soft. 1993, 2, 189–209. [Google Scholar] [CrossRef]
 Beck, A.; Stoica, P.; Li, J. Exact and Approximate Solutions of Source Localization Problems. IEEE Trans. Signal Process. 2008, 56, 1770–1778. [Google Scholar] [CrossRef]
 Ergen, S.C.; Varaiya, P. TDMA Scheduling Algorithms for Wireless Sensor Networks. Wirel. Netw. 2010, 16, 985–997. [Google Scholar] [CrossRef] [Green Version]
 Mota, J.F.C.; Xavier, J.M.F.; Aguiar, P.M.Q.; Püschel, M. DADMM: A CommunicationEfficient Distributed Algorithm for Separable Optimization. Wirel. Netw. 2013, 61, 2718–2723. [Google Scholar] [CrossRef] [Green Version]
 Singh, M.; Leu, P.; Abdou, A.R.; Capkun, S. UWBED: Distance Enlargement Attack Detection in UltraWideband. In Proceedings of the 28th USENIX Security Symposium (USENIX Security 19), Santa Clara, CA, USA, 14–16 August 2019; pp. 73–88. [Google Scholar]
Algorithm  RSS  AOA  ${\mathit{P}}_{\mathit{T}}$  Noise STD 

SOCP  All nodes  Anchors  Not known/Known  Unknown 
LLS  All nodes  All nodes  Known  Known 
MCMCMH  All nodes  All nodes  Known  Known 
GTRS  All nodes  Anchors  Known  Unknown 
Algorithm  Complexity  Time (sec) 

SOCP  $\mathcal{O}\left({\mathcal{E}}_{i}{}^{3.5}\right)$  0.66 
LLS  $\mathcal{O}\left({\mathcal{E}}_{i}\right)$  0.004 
MCMCMH  $\mathcal{O}\left({C}_{\mathrm{max}}\times {T}_{\mathrm{max}}\times \left{\mathcal{E}}_{i}\right\right)$  1.2 
GTRS  $\mathcal{O}\left({S}_{\mathrm{max}}\times \left{\mathcal{E}}_{i}\right\right)$  0.005 
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Tomic, S.; Beko, M.; CamarinhaMatos, L.M.; Oliveira, L.B. Distributed Localization with Complemented RSS and AOA Measurements: Theory and Methods. Appl. Sci. 2020, 10, 272. https://doi.org/10.3390/app10010272
Tomic S, Beko M, CamarinhaMatos LM, Oliveira LB. Distributed Localization with Complemented RSS and AOA Measurements: Theory and Methods. Applied Sciences. 2020; 10(1):272. https://doi.org/10.3390/app10010272
Chicago/Turabian StyleTomic, Slavisa, Marko Beko, Luís M. CamarinhaMatos, and Luís Bica Oliveira. 2020. "Distributed Localization with Complemented RSS and AOA Measurements: Theory and Methods" Applied Sciences 10, no. 1: 272. https://doi.org/10.3390/app10010272