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Compensation strategy for distributed tracking in wireless sensor networks with packet losses

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Abstract

Packet loss is inevitable in wireless sensor networks (WSNs). On the basis of the distributed Kalman filter (DKF) and consensus filter, we propose both biased and unbiased compensation strategies to improve tracking accuracy and reliability for WSNs’ packet dropout problem. In the biased compensation strategy, undelivered data from neighbours is compensated by the data of node itself; and in the unbiased compensation strategy, weights of all nodes are updated when packet dropout happens. With these two compensation strategies, DKF can be valid under both mild and poor connectivity conditions. Furthermore, sufficient condition is given to guarantee the convergence of estimation error system. Simulation results show that statistics average estimation errors of the biased and unbiased compensation strategies reduce 37.541 and 37.542 % of state estimation respectively compared to the DKF when the packet loss rate reaches 33.3 %, which demonstrates that the proposed algorithms perform better in filtering packet dropout than the DKF.

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Abbreviations

k :

Simulation iteration

A :

System matrix of moving target

x(k):

Target states

B :

Noise matrix

w(k):

Process noise (independent)

z i (k):

Observation of target from the ith sensor

H i :

Measurement matrix (reversible)

v i (k):

Measurement noise of the ith sensor (independent)

P i (k):

Priori estimation of gain matrix of the ith sensor

\(\hat{x}_{i} (k)\) :

State estimation of target from the ith sensor

\(\bar{x}_{i} (k)\) :

Mean state estimation of target from the ith sensor

N i (k):

The nodes that is connected to the Node i

J i (k):

The nodes which can deliver information to the Node i

u i (k):

Measurement aggregated by sensor data from the ith sensor

U i (k):

Covariance aggregated by covariance data from the ith sensor

y i (k):

Fused sensor data

S i (k):

Fused inverse-covariance matrices

ε:

Step-size

\(M_{i} (k)\) :

Defined as \((P_{i}^{ - 1} (k) + S_{i} (k))^{ - 1}\)

\(\hat{A} = \{ a_{ij} \}\) :

Adjacency matrix

L :

Laplacian matrix

\(\hat{P}_{ij}\) :

A matrix defined as \(\hat{P}_{ij} = I - \epsilon \cdot L_{ij}\)

γ ij k :

A binary variable to mark whether packet drop happens

e i (k):

Estimation error of the ith sensor

v(k):

Measurement noise vector in the k iteration

ρ(A) = α :

Spectral radius of system matrix of system matrix A

\(\hat{D}\) :

A matrix defined by \(\hat{D} = \hat{A} \cdot diag(H_{i}^{T} R_{i}^{ - 1} H_{i} )\)

\(\Xi\) :

A covariance matrix defined by lim k→∞ E(e(k) · e T(k))

References

  1. Akyildiz, I. F., Su, W., Sankarasubramaniam, Y., et al. (2002). A survey on sensor networks. Communications Magazine, IEEE, 40(8), 102–114.

    Article  Google Scholar 

  2. Akyildiz, I. F., Su, W., Sankarasubramaniam, Y., et al. (2002). Wireless sensor networks: A survey. Computer Networks, 38(4), 393–422.

    Article  Google Scholar 

  3. Stankovic, J. A. (2008). Wireless sensor networks. IEEE Computer, 41(10), 92–95.

    Article  Google Scholar 

  4. Rao, B. S. Y., Durrant-Whyte, H. F., & Sheen, J. A. (1993). A fully decentralized multi-sensor system for tracking and surveillance. The International Journal of Robotics Research, 12(1), 20–44.

    Article  Google Scholar 

  5. Chong, C. Y., & Kumar, S. P. (2003). Sensor networks: evolution, opportunities, and challenges. Proceedings of the IEEE, 91(8), 1247–1256.

    Article  Google Scholar 

  6. Chen, W. P., Hou, J. C., & Sha, L. (2004). Dynamic clustering for acoustic target tracking in wireless sensor networks. Mobile Computing, IEEE Transactions on, 3(3), 258–271.

    Article  Google Scholar 

  7. Bhargavi, R, Ganesh, K. S., Sekar, M. R., et al. (2011). An integrated system of complex event processing and Kalman filter for multiple people tracking in WSN. Recent Trends in Information Technology (ICRTIT), Chennai, 2011 International Conference on IEEE, pp. 890–895.

  8. Speyer, J. L. (1979). Computation and transmission requirements for a decentralized linear-quadratic-gaussian control problem. IEEE Transactions on Automatic Control, 24(2), 266–269.

    Article  Google Scholar 

  9. Rao, B. S. Y., Durrant-Whyte, H. F., & Sheen, J. A. (1993). A fully decentralized multi-sensor system for tracking and surveillance. International Journal of Robotics Research, 12(1), 20–44.

    Article  Google Scholar 

  10. Distributed Kalman Filtering. (2013). A bibliographic review. IET Control Theory and Applications, 7(4), 483–501.

    Article  MathSciNet  Google Scholar 

  11. Hatano, Y., & Mesbahi, M. (2005). Agreement over random networks. IEEE Transactions on Automatic Control, 50(11), 1867–1872.

    Article  MathSciNet  Google Scholar 

  12. Zhang, W.-A., Feng, G., & Li, Y. (2012). Multi-rate distributed fusion estimation for sensor networks with packet losses. Automatica, 48(9), 2016–2028.

    Article  MathSciNet  Google Scholar 

  13. Ren, W., & Beard, R. W. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), 655–661.

    Article  MathSciNet  Google Scholar 

  14. Cortes, J., Martinez, S., Karatas, T., et al. (2002). Coverage control for mobile sensing networks. Robotics and automation, 2002. In Proceedings. ICRA’02. IEEE International Conference on. IEEE, 2002, vol. 2, pp. 1327–1332.

  15. Matei, I., Baras, J. S., & Somarakis, C. (2013). Convergence results for the linear consensus problem under Markovian random graphs. SIAM Journal on Control and Optimization, 51(2), 1574–1591.

  16. Fagnani, F., & Zampieri, S. (2009). Average consensus with packet drop communication. SIAM Journal on Control and Optimization, 48(1), 102–133.

    Article  MathSciNet  Google Scholar 

  17. Olfati-Saber, R. (2005). Distributed Kalman filter with embedded consensus filters. 44th IEEE conference on decision and control, 2005 and 2005 European control conference (CDC-ECC’05), pp. 8179–8184, Dec. 2005.

  18. Olfati-Saber, R., & Shamma, J. S. (2005). Consensus filters for sensor networks and distributed sensor fusion. 44th IEEE conference on decision and control, 2005 and 2005 European control conference (CDC-ECC’05), pp. 6698–6703, Dec. 2005.

  19. Spanos, D., Olfati-Saber, R., & Murray, R. M. (2005). Dynamic consensus on mobile networks. The 16th IFAC World Congress, Prague, Czech, 2005.

  20. Yonggui, Liu, & Bugong, X. (2011). Filter designing with finite packet losses and its application for stochastic systems. IET Control Theory Applications, V5, 775–784.

    Google Scholar 

  21. Sahebsara, M., Chen, T., & Shah, S. L. (2007). Optimal filtering with random sensor delay, multiple packet dropout and uncertain observations. International Journal of Control, 80(2), 292–301.

    Article  MathSciNet  Google Scholar 

  22. Yu, M., Wang, L., Chu, T., et al. (2004). Stabilization of networked control systems with data packet dropout and network delays via switching system approach. Decision and control, 2004. CDC. 43rd IEEE conference on. IEEE, 2004, Vol. 4, pp. 3539–3544

  23. Chu, M., Haussecker, H., & Zhao, F. (2002). Scalable information-driven sensor querying and routing for ad hoc heterogeneous sensor networks. International Journal of High Performance Computing Applications, 16(3), 293–313.

    Article  Google Scholar 

  24. Epstein, L. M., Shi, L., Tiwari, A., et al. (2008). Probabilistic performance of state estimation across a lossy network. Automatica, 44, 3046–3053.

    Article  MathSciNet  Google Scholar 

  25. Sun, S. L., Xie, L. H., Xiao, W. D., et al. (2008). Optimal filtering for systems with multiple packet DROPOUTS. IEEE Transactions on Circuits and Systems: Express Briefs, 55, 695–699.

    Article  Google Scholar 

  26. Sun, S. L., Xie, L. H., Xiao, W. D., et al. (2008). Optimal linear estimation for systems with multiple packet dropouts. Automatica, 44, 1333–1342.

    Article  MathSciNet  Google Scholar 

  27. Sun, S. L., & Xiao, W. D. (2008). Optimal full- order and reduced order estimators for discrete-time systems with multiple packet dropouts. IEEE Transactions on Signal Processing, 56, 4031–4038.

    Article  MathSciNet  Google Scholar 

  28. Sinopoli, B., Schenato, L., Franceschetti, M., Poola, K., Jordan, M. I., & Sastry, S. S. (2004). Kalman filtering with intermittent observations. IEEE Transactions on Automatic Control, 49(9), 1453–1464.

    Article  Google Scholar 

  29. Gupta, V., Spanos, D., Hassibi, B., & Murray, R. M. (2005). On LQG control across a stocjastic packet-dropping link. In Proceedings of the 2005 automatic control conference, pp. 360–365, June 2005.

  30. Schenato, L., Sinopoli, B., Franceschetti, M., Poola, K., & Sastry, S. S. (2007). Foundations of control and estimation over lossy networks. Proceedings of the IEEE, 95(1), 163–187.

    Article  Google Scholar 

  31. Mahmoud, M. S., Khalid, Haris M., & Sabih, Muhammad. (2013). Improved distributed estimation method for environmental physical variables in static sensor networks. IET Wireless Sensor Systems, 3(3), 216–232.

    Article  Google Scholar 

  32. Mahmoud, M. S., & Matasm, M. H. M. (2014). Distributed estimation for adaptive sensor selection in wireless sensor networks. International Journal of General Systems, 43(3–4), 267–281.

    Article  MathSciNet  Google Scholar 

  33. Sinopoli, B., Schenato, L., Franceschetti, M., et al. (2004). Kalman filtering with intermittent observations. Automatic Control, IEEE Transactions on, 49(9), 1453–1464.

    Article  MathSciNet  Google Scholar 

  34. Olfati-Saber, R. (2007). Distributed tracking for mobile sensor networks with information-driven mobility. In Proceedings of the American Control Conference, New York, 2007, pp. 4606–4612.

  35. Matei, I., & Baras, J. S. (2012). Consensus-based linear distributed filtering. Automatica, 48(8), 1776–1782.

    Article  MathSciNet  Google Scholar 

  36. Olfati-Saber, R., & Shamma, J. S. (2005). Consensus filters for sensor networks and distributed sensor fusion. Decision and control, 2005 and 2005 European control conference. CDC-ECC’05. 44th IEEE conference on. IEEE, pp. 6698–6703.

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Acknowledgments

This work was supported by Key Project of Chinese National Programs for Fundamental Research and Development (973 program) under Grant (2012CB720003), the National Natural Science Foundation of China (Nos. 91016004, 61004023, 61127007, 61174069) and the International S&T Cooperation Program of China (No. 2013DEE13040).

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Authors and Affiliations

  1. School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191, People’s Republic of China

    Yan Wang, Chen Qian & Xiangyu Liu

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  1. Yan Wang
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  2. Chen Qian
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Correspondence to Yan Wang.

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Wang, Y., Qian, C. & Liu, X. Compensation strategy for distributed tracking in wireless sensor networks with packet losses. Wireless Netw 21, 1925–1934 (2015). https://doi.org/10.1007/s11276-014-0884-x

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