A significantly low cost and tractable progressive learning approach is proposed and discussed for efficient spatiotemporal monitoring of a completely unknown, two dimensional correlated signal distribution in localized wireless sensor field. The spatial distribution is compressed into a number of its contour lines and only those sensors that their sensor observations are in a @math margin of the contour levels are reporting to the information fusion center (IFC). The proposed algorithm progressively finds the model parameters in iterations, by using extrapolation in curve fitting, and stochastic gradient method for spatial monitoring. The IFC tracks the signal variations using these parameters, over time. The monitoring performance and the cost of the proposed algorithm are discussed, in this letter.
Spatial modeling of signal distributions using contour lines has been addressed in @cite_13 @cite_31 @cite_21 . Modeling the spatial distribution with uniformly spaced contour levels and tracking their variation using time-series analysis in sensors was studied in @cite_21 . Using non-uniformly spaced contour lines was reported first in @cite_31 . They assumed the probability density function () of the signal strength and used method to calculate the optimal sub-optimal contour levels. An iterative algorithm was proposed in @cite_13 to extract the of the signal strength with low cost in spatial monitoring of the signal distribution.
@cite_31 @cite_21 @cite_13
2085176360 2571527823 2953338282 2136684675
This paper presents algorithms for efficiently detecting the variation of a distributed signal over space and time using large scale wireless sensor networks. The proposed algorithms use contours for estimating the spatial distribution of a signal. A contour tracking algorithm is proposed to efficiently monitor the variations of the contours with time. Use of contours reduces the communication cost by reducing the participation of sensor nodes for the monitoring tasks. The proposed schemes use multi-sensor collaboration techniques and non-uniform contour levels to reduce the error in reconstructing the signal distribution. Results from computer simulations are presented to demonstrate the performance of the proposed schemes. We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and numerically by Krzakala [30], message passing algorithms can effectively solve the reconstruction problem for spatially coupled measurements with undersampling rates close to the fraction of nonzero coordinates. We use an approximate message passing (AMP) algorithm and analyze it through the state evolution method. We give a rigorous proof that this approach is successful as soon as the undersampling rate δ exceeds the (upper) Renyi information dimension of the signal, d(pX). More precisely, for a sequence of signals of diverging dimension n whose empirical distribution converges to pX, reconstruction is with high probability successful from d(pX) n+o(n) measurements taken according to a band diagonal matrix. For sparse signals, i.e., sequences of dimension n and k(n) nonzero entries, this implies reconstruction from k(n)+o(n) measurements. For “discrete” signals, i.e., signals whose coordinates take a fixed finite set of values, this implies reconstruction from o(n) measurements. The result is robust with respect to noise, does not apply uniquely to random signals, but requires the knowledge of the empirical distribution of the signal pX. We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and numerically by KrzakalaEtAl , message passing algorithms can effectively solve the reconstruction problem for spatially coupled measurements with undersampling rates close to the fraction of non-zero coordinates. We use an approximate message passing (AMP) algorithm and analyze it through the state evolution method. We give a rigorous proof that this approach is successful as soon as the undersampling rate @math exceeds the (upper) R 'enyi information dimension of the signal, @math . More precisely, for a sequence of signals of diverging dimension @math whose empirical distribution converges to @math , reconstruction is with high probability successful from @math measurements taken according to a band diagonal matrix. For sparse signals, i.e., sequences of dimension @math and @math non-zero entries, this implies reconstruction from @math measurements. For discrete' signals, i.e., signals whose coordinates take a fixed finite set of values, this implies reconstruction from @math measurements. The result is robust with respect to noise, does not apply uniquely to random signals, but requires the knowledge of the empirical distribution of the signal @math . An algorithm to extract contour lines using wireless sensor networks is proposed in this work. In con- trast with previous work on edge detection that is primarily concerned with the region of a certain phenomenon, contour lines offer more detailed information about the underlying phenomenon such as signal's amplitude, density and source location. A distributed algorithm to extract the contour lines information from local measurements is developed so that the phenomenon can be monitored in the basestation without demanding excessive raw data transmission. Sim- ulation results are provided to demonstrate the efficiency of the proposed algorithm. Furthermore, a thorough per- formance analysis is conducted to understand the effects of the sensor density and the background noise power on the performance of the system.