ABSTRACT
Due to constraints in cost, power, and communication, losses often arise in large sensor networks. The sensor can be modeled as an output of a linear stochastic system with random losses of the sensor output samples. This paper considers the general problem of state estimation for jump linear systems where the discrete transitions are modeled as a Markov chain. Among other applications, this rich model can be used to analyze sensor networks. The sensor loss events are then modeled as Markov processes. Under the jump linear system model, many types of underlying losses can be easily considered, and the optimal estimator to be performed at the receiver in the presence of missing sensor data samples is given by a standard time-varying Kalman filter.We show that the asymptotic average estimation error variance converges and is given by a Linear Matrix Inequality, which can be easily solved. Under this framework, any arbitrary Markov loss process can be modeled, and its average asymptotic error variance can be directly computed. We include a few illustrative examples including .xed-length burst errors, a two-state model,and partial losses due to multiple SNR states. Our analysis encompasses modeling discrete changes not only in the received data as stated above, but also in the underlying system. In the context of the lossy sensor model, the former allows for variation in sensor positioning, power control, and loss of data communications; the latter could allow for discrete changes in the dynamics of the variable monitored by the sensor. This freedom in modeling yields a tool that is potentially valuable in various scenarios in which entities that share information are subjected to challenging and time-varying network conditions.
- C. Andrieu,M. Davy,and A. Doucet.Efficient particle filtering for jump Markov systems. application to time-varying autoregressions. IEEE Trans. Signal Proc.51(7):1762--1770, July 2003. Google ScholarDigital Library
- S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory SIAM, Philadelphia, PA, 1994.Google Scholar
- H. J. Chizeck, A. S. Willsky, and D. Castano. Discrete-time Markovian jump linear quadratic optimal control. Int. J. Contr. 43:213--31, 1986.Google ScholarCross Ref
- O. L. V. Costa. Optimal linear filtering for discrete-time Markovian jump linear systems. In Proc. IEEE Conf. Dec. & Contr. volume 3, pages 2761--2762, Dec. 1991.Google ScholarCross Ref
- O. L. V. Costa and M. D. Fragaso. Stability results for discrete-time linear systems with Markovian jumping parameters. Int. J. Contr. 66:557--579, 1993.Google ScholarCross Ref
- O. L. V. Costaand R. P. Marques. Robust H 2 control for discrete-time Markovian jump linear systems. Int. J. Contr. 73(1):11--21, 2000.Google ScholarCross Ref
- C. E. de Souza and M. D. Fragoso. On the existence of a maximal solution for generalized algebraic Riccati equation arising in the stochastic control. Sys. & Contr. Letters 14:233--39,1990. Google ScholarDigital Library
- P. Dorato. Theoretical developments in discrete-time control. Automatica 19:395--400, 1993.Google ScholarDigital Library
- A. Doucet and C. Andrieu. state estimation of jump Markov linear systems. IEEE Trans. Signal Proc. 49(6):1216--1226, June 2001. Google ScholarDigital Library
- A. Doucet, A. Logothetis, and V. Krishnamurthy. Stochastic sampling algorithms for state estimation of jump Markov linear systems. IEEE Trans. Automat. Control 45(1):188--202, Jan. 2000. Google ScholarDigital Library
- J. S. Evans and R. J. Evans. State estimation for Markov switching systems with modal observations. In Proc. IEEE Conf. Dec. & Contr. pages 1688--1693, Dec.1997.Google ScholarCross Ref
- A. K. Fletcher, S. Rangan, V. K. Goyal, and K. Ramchandran. Robust predictive quantization: A new analysis and optimization framework. In Proc. IEEE Int. Symp. Inform. Th.Chicago, IL, June--July 2004. To appear.Google ScholarCross Ref
- M. Gastpar and M. Vetterli. Scaling laws for homogeneous sensor networks. In Proc. 41st Ann. Allerton Conf. on Commun., Control and Comp. Monticello, IL, Oct. 2003.Google Scholar
- N. N. Krasovskii and E. A. Lidskii. Analytical design of controllers in systems with random attributes I, II, III.Automation Remote Contr. 22:1021--1025, 1141--1146, 1289--1294, 1961.Google Scholar
- V. Krishnamurthy and G. G. Lin. Recursive algorithms for estimation of hidden Markov models and autoregressive models with Markov regime. IEEE Trans. Inform. Th.48(2):458--476, Feb. 2002. Google ScholarDigital Library
- P. R. Kumar and P. Varaiya. Stochastic Systems: Estimation, Identification, and Adaptive Control Prentice-Hall, Englewood Cliffs, NJ, 1986. Google ScholarDigital Library
- A. Logothetis and V. Krishnamurthy. Estimation maximization algorithms for MAP estimation of jump Markov linear systems. IEEE Trans. Signal Proc. 47(8):2139--2156, Aug. 1999. Google ScholarDigital Library
- M. A. Rami and L. El Ghaoui. LMI optimization for nonstandard Riccati equations arising in stochastic control. IEEE Trans. Automat. Control 41:1666--1671, 1996.Google ScholarCross Ref
- P. Seiler and R. Sengupta. Analysis of communication losses in vehicle control problems. In Proc. IEEE Amer. Contr. Conf. pages 25--27, June 2001.Google ScholarCross Ref
- B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan,and S. S. Sastry. Kalman .ltering with intermittent observations. In Proc. IEEE Conf. Dec. & Contr. Maui, Hawaii, Dec. 2003. to appear.Google Scholar
- S. C. Smith and P. Seiler. Optimal pseudo-steady-state estimators with Markovian intermittent measurements. In Proc. IEEE Amer. Contr. Conf. pages 3021--3027, May 2002.Google ScholarCross Ref
- D. D. Sworder. Feedback control of a class of linear systems with jump parameters. IEEE Trans. Automat. Control AC-14:60--63, 1969.Google Scholar
- W. M. Wonham. On a matrix Riccati equation of stochastic control. SIAM J. Contr.6(4):681--697, 1968.Google ScholarCross Ref
- F. Zhao and L. J .Guibas, editors. Information Processing in Sensor Networks, Second International Workshop, IPSN 2003, Palo Alto, CA, USA, April 22-23, 2003 volume 2634 of Lecture Notes in Computer Science Springer, 2003. Google ScholarDigital Library
Index Terms
- Estimation from lossy sensor data: jump linear modeling and Kalman filtering
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