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Information fusion strategies and performance bounds in packet-drop networks. (English) Zbl 1219.93121
Summary: We discuss suboptimal distributed estimation schemes for stable stochastic discrete time linear systems under the assumptions that (i) distributed sensors have computation capabilities, (ii) the communication between the sensors and the estimation center is subject to random packet loss, and (iii) there is no communication between sensors. We consider strategies which are based on raw Measurement Fusion (MF) as well as on fusing local estimates, such as local Kalman filters or other pre-processing rules. We show that the optimal mean square estimation error that can be achieved under packet loss, referred as the Infinite Bandwidth Filter (IBF), cannot be reached using a limited bandwidth channel; we also compare these strategies under specific noise regimes. We also propose novel mathematical tools to derive analytical upper and lower bounds for the expected estimation error covariance of the MF and the IBF strategies assuming identical sensors. The theoretical findings are complemented by simulation results.

93E10 Estimation and detection in stochastic control theory
93E11 Filtering in stochastic control theory
93E15 Stochastic stability in control theory
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
Full Text: DOI
[1] Agnoli, A., Chiuso, A., D’Errico, P., Pegoraro, A., & Schenato, L. (2008). Sensor fusion and estimation strategies for data traffic reduction in rooted wireless sensor networks. In Proc. of IEEE ISCCSP’08 (pp. 677-682). La Valletta, Malta.
[2] Anderson, B.D.O.; Moore, J.B., Optimal filtering, (1979), Prentice Hall · Zbl 0758.93070
[3] Bar-Shalom, Y.; Chen, H.; Mallick, M., One-step solution for the general out-of-sequence measurement problem in tracking, IEEE transactions on aerospace and electronics systems, 40, 1, 27-37, (2004)
[4] Bar-Shalom, Y.; Li, X.R.; Kirubarajan, T., Estimation with applications to tracking and navigation, (2001), John Wiley & Sons, Inc.
[5] Chiuso, A., & Schenato, L. (2008). Information fusion strategies from distributed filters in packet-drop networks. In Proc. of CDC 08 (pp. 1079-1084).
[6] Chiuso, A., & Schenato, L. (2009). Performance bounds for information fusion strategies in packet-drop networks. In Proc. of ECC 09 (pp. 4326-4331). · Zbl 1219.93121
[7] Gupta, V.; Martins, N.C.; Baras, J.S., Stabilization over erasure channels using multiple sensors, IEEE transactions on automatic control, 57, 7, 1463-1476, (2009) · Zbl 1367.93504
[8] Gupta, V.; Spanos, D.; Hassibi, B.; Murray, R.M., Optimal LQG control across a packet-dropping link, Systems and control letters, 56, 6, 439-446, (2007) · Zbl 1137.90379
[9] Hespanha, J.P.; Naghshtabrizi, P.; Xu, Y., A survey of recent results in networked control systems, Proceedings of the IEEE, 95, 1, 138-162, (2007), [special issue]
[10] Levy, B.C.; Castañon, D.A.; Verghese, G.C.; Willsky, A.S., A scattering framework for decentralized estimation problems, Automatica, 19, 4, 373-384, (1983) · Zbl 0518.93055
[11] Matveev, A.S.; Savkin, A.V., The problem of state estimation via asynchronous communication channels with irregular transmission times, IEEE transactions on automatic control, 48, 4, 670-676, (2003) · Zbl 1364.93779
[12] Robinson, C., & Kumar, P. R. (2007). Sending the most recent observation is not optimal in networked control: linear temporal coding and towards the design of a control specific transport protocol. In Proc. of IEEE conf. on decision and control (pp. 334-339). New Orleans, USA.
[13] Schenato, L. (2007). Optimal sensor fusion for distributed sensors subject to random delay and packet loss. In Proc. of IEEE conf. on decision and control (pp. 1547-1552). New Orleans, USA.
[14] Shi, L., Johansson, K. H., & Murray, R. M. (2008). Estimation over wireless sensor networks: tradeoff between communication, computation and estimation qualities. In Proc. of IFAC world congressVol. 17. Seoul, Korea.
[15] Sinopoli, B.; Schenato, L.; Franceschetti, M.; Poolla, K.; Jordan, M.I.; Sastry, S.S., Kalman filtering with intermittent observations, IEEE transactions on automatic control, September, 1453-1464, (2004) · Zbl 1365.93512
[16] Willsky, A.S.; Bello, M.G.; Castanon, D.A.; Levy, B.C.; Verghese, G.C., Combining and updating of local estimates and regional maps along sets of one-dimensional tracks, IEEE transactions on automatic control, 27, 4, 799-813, (1982) · Zbl 0605.93051
[17] Wolfe, J. D., & Speyer, J. L. (2003). A low-power filtering scheme for distributed sensor networks. In Proceeding of IEEE conference on decision and control (CDC’03) (pp. 6325-6326).
[18] Zhang, K.S.; Li, X.R.; Zhu, Y.M., Optimal update with out-of-sequence observations for distributed filtering, IEEE transactions on signal processing, 53, 6, 1992-2004, (2005) · Zbl 1370.93192
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