Compressive Sensing with Chaotic Sequences: An Application to Localization in Wireless Sensor Networks

Short Word-Length Entering Compressive Sensing Domain: Improved Energy-Efficiency in Wireless Sensor Networks

“…We consider GD localization in three dimensions as in [11,12]. The error function to be minimized in this optimization problem is given by:…”

“…The localization error criterion used to assess performance is chosen as the normalized error measure (NEM) given in dBs. This is a relative error measure involving ) (12) where k is the iteration number, Ҡ is the total number of target path points and N is the number of anchors.…”

“…All anchors are assumed to be in the radio range of the target path. In [11,12], a helical path with r = 40 and ҡ = 20 was considered. It was shown that the TOA values as a function of time had low frequency content.…”

“…To resolve this ambiguity, reconstruction is constrained to be on the unit sphere to reduce the search space [8]. However, it has been shown in [11,12] that for target localization or tracking in WSNs, the computationally expensive recovery by convex optimization can be replaced by simple linear interpolation due to the usually low frequency content of TOA measurements from moving targets. In addition to its computational efficiency, linear interpolation can be made to operate in real time or with small delay whereas other optimization techniques such as 1 -minimization are batch processing techniques requiring the whole or a considerably large part of the signal to be available to be processed for optimized reconstruction [4,13].…”

“…However, this is more than compensated for by the achieved communication energy efficiency. Localization at the fusion center is performed by the method of gradient descent (GD) [14,11,12].…”