Networked Sensing Information and Control by Venkatesh Saligrama

By Venkatesh Saligrama

This booklet provides learn on informational and mathematical facets of networked sensing structures. It brings jointly across the world reputed researchers from varied groups, concerned about the typical topic of disbursed sensing, inferencing, and keep watch over over networks. The timeliness of the e-book is evidenced through the explosion of a number of self reliant specified classes dedicated to particular points of sensor networks in reputed overseas meetings.

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14] G. Tolle, J. Polastre, R. Szewczyk, D. Culler, N. Turner, K. Tu, S. Burgess, T. Dawson, P. Buonadonna, D. Gay, and W. Hong. A macroscope in the redwoods. In Proceedings of Sensys, 2005. [15] K. Whitehouse and D. Culler. Calibration as parameter estimation in sensor networks. In Proceedings of the 1st ACM International Workshop on Wireless Sensor Networks and Applications, pages 59–67, 2002. [16] W. M. Wonham. Linear Multivariable Control. Springer-Verlag, New York, 1979. 34 Laura Balzano and Robert Nowak Appendix Theorem 1: Proof.

Now suppose that the signal subspace is a lowpass frequency subspace spanned by low-frequency DFT vectors. In this case, blind gain calibration is exactly equivalent to multi-FIR-channel blind deconvolution (the two problems are related by the DFT). In general, however, the signal subspace may not be a low-frequency subspace, and the two problems are quite different. In this sense, blind calibration is much more general than multi-channel blind deconvolution, but the relation between the two problems suggests that more sophisticated solution methods, such as IQML [8], might be applicable to blind calibration.

Recall that by definition X j = diag(xj ). Also note that diag(xj )d = diag(d)xj . So we can equivalently state the requirement as diag(d)xj ∈ S, j = 1, . . , k . 20) The proof proceeds in two steps. First, A2 implies that k ≥ r signal observations will span the signal subspace with probability 1. This allows us to re-cast the question in terms of a basis for the signal subspace, rather than particular realizations of signals. Second, it is shown that A3 (in terms of the basis) suffices to guarantee that the system of equations has rank n − 1.

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