Distributed parameter estimation in sensor networks: Nonlinear observation models and imperfect communication

IEEE Transactions on Information Theory

Volumn 58, Issue 6, 2012, Pages 3575-3605

  Kar, Soummya ^a   Moura, José M F ^a   Ramanan, Kavita ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b BROWN UNIVERSITY   (United States)

Author keywords

Asymptotic normality; consensus; consensus + innovations; consistency; distributed parameter estimation; estimable; Laplacian; separable; spectral graph theory; stochastic approximation; unbiasedness

Indexed keywords

ASYMPTOTIC NORMALITY; CONSENSUS; CONSISTENCY; DISTRIBUTED PARAMETER ESTIMATION; ESTIMABLE; LAPLACIANS; SEPARABLE; SPECTRAL GRAPH THEORY; STOCHASTIC APPROXIMATIONS; UNBIASEDNESS;

ALGORITHMS; APPROXIMATION THEORY; COMMUNICATION; ESTIMATION; GRAPH THEORY; OBSERVABILITY; PARAMETER ESTIMATION; SENSOR NETWORKS;

NONLINEAR ANALYSIS;

EID: 84861357379     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2012.2191450     Document Type: Article

References (59)

1. R. Olfati-Saber and R. M. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Trans. Automat. Contr., vol. 49, no. 9, pp. 1520-1533, Sep. 2004.
2. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Trans. Autom. Control, vol. 48, no. 6, pp. 988-1001, Jun. 2003.
3. L. Xiao and S. Boyd, "Fast linear iterations for distributed averaging," Syst. Contr. Lett., vol. 53, pp. 65-78, 2004.
4. S. Kar and J. M. F. Moura, "Sensor networks with random links: Topology design for distributed consensus," IEEE Trans. Signal Process., vol. 56, no. 7, pp. 3315-3326, Jul. 2008.
5. S. Kar and J.M. F.Moura, "Distributed consensus algorithms in sensor networkswith communication channel noise and randomlink failures," presented at the 41st Asilomar Conf. Signals, Systems, and Computers, Pacific Grove, CA, Nov. 2007.
6. S. Kar and J. M. F. Moura, "Distributed average consensus in sensor networks with quantized inter-sensor communication," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., Las Vegas, NV, Apr. 1-4, 2008, pp. 2281-2284.
7. Y. Hatano and M. Mesbahi, "Agreement over random networks," in Proc. 43rd IEEE Conf. Decis. Control, Dec. 2004, vol. 2, pp. 2010-2015. (Pubitemid 40291253)
8. T. C. Aysal, M. Coates, and M. Rabbat, "Distributed average consensus using probabilistic quantization," in IEEE/SP 14th Workshop Statist. Signal Process. Workshop, Maddison, WI, Aug. 2007, pp. 640-644.
9. M. E. Yildiz and A. Scaglione, "Differential nested lattice encoding for consensus problems," in Proc. 6th Int. Symp. Inf. Process. Sens. Netw., Cambridge, MA, Apr. 2007, pp. 89-98. (Pubitemid 47582139)
10. A. Kashyap, T. Basar, and R. Srikant, "Quantized consensus," Automatica, vol. 43, pp. 1192-1203, Jul. 2007. (Pubitemid 46802442)
11. P. Frasca, R. Carli, F. Fagnani, and S. Zampieri, "Average consensus on networks with quantized communication," Int. J. Robust Nonlinear Control, vol. 19, pp. 1787-1816, 2008.
12. A. Nedic, A. Olshevsky, A. Ozdaglar, and J. N. Tsitsiklis, On distributed averaging algorithms and quantization effects 2007, Tech. Rep. 2778, LIDS-MIT.
13. M. Huang and J. Manton, "Stochastic approximation for consensus seeking: Mean square and almost sure convergence," in Proc. 46th IEEE Conf. Decis. Control, New Orleans, LA, Dec. 12-14, 2007, pp. 306-311. (Pubitemid 351277170)
14. R. Olfati-Saber, J. A. Fax, and R. M. Murray, "Consensus and cooperation in networked multi-agent systems," Proc. IEEE, vol. 95, no. 1, pp. 215-233, Jan. 2007.
15. A. Das and M. Mesbahi, "Distributed linear parameter estimation in sensor networks based on Laplacian dynamics consensus algorithm," in 3rd Annu. IEEE Commun. Soc. Sens. Ad Hoc Commun. Netw., Reston, VA, Sep. 28-28, 2006, vol. 2, pp. 440-449.
16. R. Olfati-Saber, "Distributed Kalman filter with embedded consensus filters," in Proc. 44th IEEE Conf. Decis. Control and 2005 Eur. Control Conf., 2005, pp. 8179-8184.
17. I. D. Schizas, A. Ribeiro, and G. B. Giannakis, "Consensus in Ad Hoc WSNs with noisy links: Part I. Distributed estimation of deterministic signals," IEEE Trans. Signal Process., vol. 56, no. 1, pp. 350-364, Jan. 2008.
18. U. A. Khan and J. M. F. Moura, "Distributing the Kalman filter for large-scale systems," IEEE Trans. Signal Process., vol. 56, no. 10, pp. 4919-4935, Oct. 2008.
19. R. Carli, A. Chiuso, L. Schenato, and S. Zampieri, "Distributed Kalman filtering using consensus strategies," IEEE J. Sel. Areas Commun., vol. 26, no. 4, pp. 622-633, Sep. 2008. (Pubitemid 351658778)
20. D. Bajovic, D. Jakovetic, J. Xavier, B. Sinopoli, and J. M. F. Moura, "Distributed detection via Gaussian running consensus: Large deviations asymptotic analysis," IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4381-4396, Sep 2011.
21. D. Jakovetic, J. M. F. Moura, and J. Xavier, "Distributed detection over noisy networks: Large deviations analysis," IEEE Trans. Signal Process., vol. 60, 2012, to be published.
22. C.G. Lopes and A. H. Sayed, "Diffusion least-mean squares over adaptive networks: Formulation and performance analysis," IEEE Trans. Signal Process., vol. 56, no. 7, pp. 3122-3136, Jul. 2008.
23. S. Stankovic, M. Stankovic, and D. Stipanovic, "Decentralized parameter estimation by consensus based stochastic approximation," in Proc. 46th IEEE Conf. Decis. Control, New Orleans, LA, Dec. 12-14, 2007, pp. 1535-1540. (Pubitemid 351277371)
24. I. Schizas, G. Mateos, and G. Giannakis, "Stability analysis of the consensus-based distributed LMS algorithm," in Proc. 33rd Int. Conf. Acoust., Speech, Signal Process., Las Vegas, NV, Apr. 1-4, 2008, pp. 3289-3292.
25. S. Ram, V. Veeravalli, and A. Nedic, "Distributed and recursive parameter estimation in parametrized linear state-space models," IEEE Trans. Automat. Control, vol. 55, no. 2, pp. 488-492, Feb. 2010.
26. S. Kar and J. M. F. Moura, "Convergence rate analysis of distributed gossip (linear parameter) estimation: Fundamental limits and tradeoffs," IEEE J. Sel. Top. Signal Process., vol. 5, no. 4, pp. 674-690, Aug. 2011.
27. S. Kar and J. M. F. Moura, "Gossip and distributed Kalman filtering: Weak consensus under weak detectability," IEEE Trans. Signal Process., vol. 59, no. 4, pp. 1766-1786, Apr 2011.
28. D. Jakovetic, J. Xavier, and J. M. F. Moura, "Weight optimization for consenus algorithms with correlated switching topology," IEEE Trans. Signal Process., vol. 58, no. 7, pp. 3788-3801, Jul. 2010.
29. J. N. Tsitsiklis, "Problems in decentralized decision making and computation," Ph.D. dissertation, Massachusetts Inst. Technol., Cambridge, MA, 1984.
30. J. N. Tsitsiklis, D. P. Bertsekas, and M. Athans, "Distributed asynchronous deterministic and stochastic gradient optimization algorithms," IEEE Trans. Autom. Control, vol. AC-31, no. 9, pp. 803-812, Sep. 1986. (Pubitemid 16629805)
31. D. Bertsekas, J. Tsitsiklis, and M. Athans, "Convergence theories of distributed iterative processes: A survey" Tech. Rep. Information and Decision Systems, Massachusetts Inst. Technol.. Cambridge,MA, 1984.
32. H. Kushner and G. Yin, "Asymptotic properties of distributed and communicating stochastic approximation algorithms," SIAM J. Control Optim., vol. 25, no. 5, pp. 1266-1290, Sep. 1987.
33. S. Kar, S. A. Aldosari, and J. M. F. Moura, "Topology for distributed inference on graphs," IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2609-2613, Jun. 2008. (Pubitemid 351795911)
34. A. H. Sayed, Fundamentals of Adaptive Filtering, ser. Wiley-Interscience. Hoboken, NJ: Wiley, 2003.
35. V. Solo and X. Kong, Adaptive Signal Processing Algorithms: Stability and Performance. Upper Saddle River, NJ: Prentice-Hall, 1995.
36. L. Ljung, System Identification: Theory for the User. UpperSaddle River, NJ: Prentice-Hall, 1999.
37. V. S. Borkar, Stochastic Approximation: A Dynamical Systems Viewpoint. Cambridge, U.K.: Cambridge Univ. Press, 2008.
38. S. B. Gelfand and S. K. Mitter, "Recursive stochastic algorithms for global optimization in ," SIAM J. Control Optim., vol. 29, no. 5, pp. 999-1018, Sep. 1991.
39. F. R. K. Chung, Spectral Graph Theory. Providence, RI: American Mathematical Society, 1997.
40. B. Mohar, "The Laplacian spectrumof graphs," in Graph Theory, Combinatorics, and Applications, Y. Alavi, G. Chartr, O. R. Oellermann, andA. J. Schwenk, Eds. NewYork:Wiley, 1991, vol. 2, pp. 871-898.
41. B. Bollobas,ModernGraph Theory. New York,NY: SpringerVerlag, 1998.
42. L. Schuchman, "Dither signals and their effect on quantization noise," IEEE Trans. Commun. Technol., vol. COMM-12, pp. 162-165, Dec. 1964.
43. S. P. Lipshitz, R. A. Wannamaker, and J. Vanderkooy, "Quantization and dither: A theoretical survey," J. Audio Eng. Soc., vol. 40, pp. 355-375, May 1992.
44. A. B. Sripad and D. L. Snyder, "A necessary and sufficient condition for quantization errors to be uniform and white," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-25, pp. 442-448, Oct. 1977.
45. R. M. Gray and T. G. Stockham, "Dithered quantizers," IEEE Trans. Inf. Theory, vol. 39, no. 3, pp. 805-811, May 1993.
46. S. Kar and J. M. F. Moura, "Distributed consensus algorithms in sensor networks: Quantized data and random link failures," IEEE Trans. Signal Process., vol. 58, no. 3, pp. 1383-1400, Mar. 2010.
47. E. Lehmann, Theory of Point Estimation. New York: Wiley, 1983.
48. H.-F. Chen and L. Guo, Identification and Stochastic Adaptive Control. Boston, MA: Birkhauser, 1991.
49. S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, "Randomized gossip algorithms," IEEE/ACM Trans. Netw., vol. 14, no. SI, pp. 2508-2530, Jun. 2006. (Pubitemid 43898906)
50. O. Kallenberg, Foundations of Modern Probability, 2nd ed. New York: Springer, 2002.
51. S. Kar, "Large scale networked dynamical systems: Distributed inference," Ph.D. dissertation, Carnegie Mellon Univ., Pittsburgh, PA, 2010.
52. N. Krasovskii, Stability of Motion. Stanford, CA: Stanford Univ. Press, 1963.
53. A. V. Oppenheim and R.W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
54. M. D. Ilic and J. Zaborszky, Dynamics and Control of Large Electric Power Systems. New York: Wiley, 2000.
55. J. S. Thorp, A. G. Phadke, and K. J. Karimi, "Real time voltage-phasor measurements for static state estimation," IEEE Trans. Power App. Syst., vol. 104, no. 11, pp. 3098-3106, Nov. 1985.
56. M. Nevel'son and R. Has'minskii, Stochastic Approximation and Recursive Estimation. Providence, Rhode Island: American Mathematical Society, 1973.
57. Y. Chow, "Some convergence theorems for independent random variables," Ann. Math. Statist., vol. 37, pp. 1482-1493, 1966.
58. Y. Chowand T. Lai, "Limiting behavior of weighted sums of independent random variables," Ann. Prob., vol. 1, pp. 810-824, 1973.
59. W. Stout, "Some results on the complete and almost sure convergence of linear combinations of independent random variables and martingale differences," Ann. Math. Statist., vol. 39, pp. 1549-1562, 1968.