This paper is concerned with the problem of distributed estimation fusion over peer-to-peer asynchronous sensor networks with random packet dropouts. A distributed asynchronous fusion algorithm is proposed via the covariance intersection method. First, local estimator is developed in an optimal batch fashion by constructing augmented measurement equations. Then the fusion estimator is designed to fuse local estimates in the neighborhood. Both local estimator and fusion estimator are developed by taking into account the random packet losses. The presented estimation method improves local estimates and reduces the estimate disagreement. Simulation results validate the effectiveness of the proposed distributed asynchronous fusion algorithm. 1. Introduction Distributed fusion and estimation problem over peer-to-peer sensor networks has attracted significant interest in the research community, because of its variety of applications, such as environmental monitoring, surveillance, and target tracking, [1–10]. In these applications, every sensor in the network does not only take measurements in a parallel manner but also acquires information from neighbors and processes it to get an estimate. Compared with the centralized fusion fashion, the main advantage of distributed fusion estimation is the computation burden alleviation and robustness enhancement. In general, two main approaches are presented in the literature to solve the distributed fusion and estimation problem. The first approach is the consensus approach. The consensus approach was proposed in [11, 12], where local measurements are exchanged among neighbors to get local estimates, and then by using average consensus algorithms among neighbors every sensor in the network gets the same estimate in steady-state. In order to obtain the same estimate at every sensor in the network, the consensus approach may iterate several times for each new measurement. This is highly undesired when estimating the state of dynamic systems where new measurements need to be processed in a timely manner. The second approach is the diffusion approach. The diffusion approach was presented in [13], in which the estimates of local filters are calculated individually at each sensor by using the data from the neighborhood, and then the local estimates from the neighborhood are fused locally by a convex combination. Therefore, the diffusion approach is well suited for estimating the state of dynamic systems where new measurements are being taken in real time. Though the adaptive weights for the diffusion algorithm were presented
References
[1]
C. Chong, S. Mori, and K. Chang, “Adaptive distributed estimation,” in Proceedings of the IEEE Conference on Decision Control,, vol. 26, pp. 2233–2238, 1987.
[2]
K. C. Chang, R. K. Saha, and Y. Bar-Shalom, “On optimal track-to-track fusion,” IEEE Transactions on Aerospace and Electronic Systems, vol. 33, no. 4, pp. 1271–1276, 1997.
[3]
X. Li, K. Zhang, J. Zhao, and Y. Zhu, “Optimal linear estimation fusion—part V: relationships,” in Proceedings of the 5th International Conference on Information Fusion, pp. 497–504, 2002.
[4]
S. Mori, W. H. Barker, C.-Y. Chong, and K.-C. Chang, “Track association and track fusion with nondeterministic target dynamics,” IEEE Transactions on Aerospace and Electronic Systems, vol. 38, no. 2, pp. 659–668, 2002.
[5]
Y. Zhu, E. Song, J. Zhou, and Z. You, “Optimal dimensionality reduction of sensor data in multisensor estimation fusion,” IEEE Transactions on Signal Processing, vol. 53, no. 5, pp. 1631–1639, 2005.
[6]
S. Marano, V. Matta, and P. Willett, “Distributed estimation in large wireless sensor networks via a locally optimum approach,” IEEE Transactions on Signal Processing, vol. 56, no. 2, pp. 748–756, 2008.
[7]
I. D. Schizas, G. B. Giannakis, and Z.-Q. Luo, “Distributed estimation using reduced-dimensionality sensor observations,” IEEE Transactions on Signal Processing, vol. 55, no. 8, pp. 4284–4299, 2007.
[8]
F. S. Cattivelli, C. G. Lopes, and A. H. Sayed, “Diffusion recursive least-squares for distributed estimation over adaptive networks,” IEEE Transactions on Signal Processing, vol. 56, no. 5, pp. 1865–1877, 2008.
[9]
R. Carli, A. Chiuso, L. Schenato, and S. Zampieri, “Distributed Kalman filtering based on consensus strategies,” IEEE Journal on Selected Areas in Communications, vol. 26, no. 4, pp. 622–633, 2008.
[10]
S. Kar and J. M. F. Moura, “Gossip and distributed Kalman filtering: weak consensus under weak detectability,” IEEE Transactions on Signal Processing, vol. 59, no. 4, pp. 1766–1784, 2011.
[11]
R. Olfati-Saber, “Distributed Kalman filtering for sensor networks,” in Proceedings of the 46th IEEE Conference on Decision and Control (CDC '07), pp. 5492–5498, December 2007.
[12]
R. Olfati-Saber, “Distributed Kalman filter with embedded consensus filters,” in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC '05), pp. 8179–8184, December 2005.
[13]
F. S. Cattivelli and A. H. Sayed, “Diffusion strategies for distributed Kalman filtering and smoothing,” IEEE Transactions on Automatic Control, vol. 55, no. 9, pp. 2069–2084, 2010.
[14]
F. Cattivelli and A. H. Sayed, “Diffusion distributed Kalman filtering with adaptive weights,” in Proceedings of the 43rd Asilomar Conference on Signals, Systems and Computers, pp. 908–912, November 2009.
[15]
S. J. Julier and J. K. Uhlmann, “Non-divergent estimation algorithm in the presence of unknown correlations,” in Proceedings of the American Control Conference, vol. 4, pp. 2369–2373, June 1997.
[16]
S. Julier and J. Uhlmann, General Decentralized Data Fusion with Covariance Intersection, Handbook of Multisensor Data Fusion, 2001.
[17]
J. Hu, L. Xie, and C. Zhang, “Diffusion Kalman filtering based on covariance intersection,” IEEE Transactions on Signal Processing, vol. 60, no. 2, pp. 891–902, 2012.
[18]
H. Dong, Z. Wang, and H. Gao, “Distributed H∞ filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks,” IEEE Transactions on Industrial Electronics, vol. 60, no. 10, pp. 4665–4672, 2013.
[19]
L. Ma, Z. Wang, Y. Bo, and Z. Guo, “Robust sliding mode control for nonlinear stochastic systems with multiple data packet losses,” International Journal of Robust and Nonlinear Control, vol. 22, no. 5, pp. 473–491, 2012.
[20]
L. Ma, Z. Wang, Y. Bo, and Z. Guo, “Finite-horizon control for a class of nonlinear Markovian jump systems with probabilistic sensor failures,” International Journal of Control, vol. 84, no. 11, pp. 1847–1857, 2011.
[21]
D. Ding, Z. Wang, H. Dong, and H. Shu, “Distributed state estimation with stochastic parameters and nonlinearities through sensor networks: the finite-horizon case,” Automatica, vol. 48, no. 8, pp. 1575–1585, 2012.
[22]
H. Dong, Z. Wang, and H. Gao, “Distributed filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks,” IEEE Transactions on Industrial Electronics, vol. 60, no. 10, pp. 4665–4672, 2013.
[23]
H. Dong, Z. Wang, and H. Gao, “Distributed filtering for a class of time-varying systems over sensor networks with quantization errors and successive packet dropouts,” IEEE Transactions on Signal Processing, vol. 60, no. 6, pp. 3164–3173, 2012.
[24]
N. E. Nahi, “Optimal recursive estimation with uncertain observation,” IEEE Transactions on Information Theory, vol. 15, no. 4, pp. 457–462, 1969.
[25]
S. Kar, B. Sinopoli, and J. M. F. Moura, “Kalman filtering with intermittent observations: weak convergence to a stationary distribution,” IEEE Transactions on Automatic Control, vol. 57, no. 2, pp. 405–420, 2012.
[26]
S. Nakamori, R. Caballero-águila, A. Hermoso-Carazo, and J. Linares-Pérez, “Linear recursive discrete-time estimators using covariance information under uncertain observations,” Signal Processing, vol. 83, no. 7, pp. 1553–1559, 2003.
[27]
Z. Wang, D. W. C. Ho, and X. Liu, “Robust filtering under randomly varying sensor delay with variance constraints,” IEEE Transactions on Circuits and Systems, vol. 51, no. 6, pp. 320–326, 2004.
[28]
L. Schenato, “Optimal estimation in networked control systems subject to random delay and packet loss,” in Proceedings of the 45th IEEE Conference on Decision and Control (CDC '06), pp. 5615–5620, December 2006.
[29]
B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan, and S. S. Sastry, “Kalman filtering with intermittent observations,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1453–1464, 2004.
[30]
M. Sahebsara, T. Chen, and S. L. Shah, “Optimal filtering with random sensor delay, multiple packet dropout and uncertain observations,” International Journal of Control, vol. 80, no. 2, pp. 292–301, 2007.
[31]
S. L. Sun, “Optimal linear estimation for networked systems with one-step random delays and multiple packet dropouts,” Acta Automatica Sinica, vol. 38, no. 3, pp. 349–356, 2012.
[32]
J. Ma and S. Sun, “Centralized fusion estimators for multisensor systems with random sensor delays, multiple packet dropouts and uncertain observations,” IEEE Transactions on Signal Processing, vol. 13, no. 4, 2013.
[33]
A. T. Alouani and T. R. Rice, “On optimal asynchronous track fusion,” in Proceedings of the 1st Austalian Data Fusion Symposium, pp. 147–152, November 1996.
[34]
A. T. Alouani and T. R. Rice, “Asynchronous fusion of correlated tracks,” in Acquisition, Tracking and Pointing XII, Proceedings of SPIE, pp. 113–118, April 1998.
[35]
G. A. Watson, T. R. Rice, and A. T. Alouani, “Optimal track fusion with feedback for multiple asynchronous measurements,” in Aquisition, Tracking, and Pointing XIV, Proceedings of SPIE, pp. 20–33, April 2000.
[36]
A. T. Alouani, J. E. Gray, and D. H. McCabe, “Theory of distributed estimation using multiple asynchronous sensors,” IEEE Transactions on Aerospace and Electronic Systems, vol. 41, no. 2, pp. 717–722, 2005.
[37]
L. P. Yan, B. S. Liu, and D. H. Zhou, “Asynchronous multirate multisensor information fusion algorithm,” IEEE Transactions on Aerospace and Electronic Systems, vol. 43, no. 3, pp. 1135–1146, 2007.
[38]
H. Yanyan, D. Zhansheng, and H. Chongzhao, “Optimal batch asynchronous fusion algorithm,” in Proceedings of the IEEE International Conference on Vehicular Electronics and Safety, pp. 237–240, October 2005.
[39]
Y. Hu, Z. Duan, and D. Zhou, “Estimation fusion with general asynchronous multi-rate sensors,” IEEE Transactions on Aerospace and Electronic Systems, vol. 46, no. 4, pp. 2090–2102, 2010.
[40]
D. Simon, Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches, Wiley-Interscience, Hoboken, NJ, USA, 2006.
[41]
P. O. Arambel, C. Rago, and R. K. Mehra, “Covariance intersection algorithm for distributed spacecraft state estimation,” in Proceedings of the American Control Conference, pp. 4398–4403, June 2001.
[42]
Y. Wang and X. R. Li, “A fast and fault-tolerant convex combination fusion algorithm under unknown cross-correlation,” in Proceedings of the 12th International Conference on Information Fusion (FUSION '09), pp. 571–578, July 2009.
