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

Compressed sensing by random under-sampling has been recently used in the context of energy-efficient moving-target gradient descent localization in wireless sensor networks. The present work investigates the possibility of using deterministic chaos in sensing or acquiring time-of-arrival measurement data instead of randomness. The rationale behind this approach is that the output of a chaos system has been empirically proven to behave as random in just a few steps; the advantage gained is ease of implementation on system hardware. In addition, unlike random-sampling which entails difficulty in signal reconstruction, chaos can be re-generated easily to get back the original signal. On the other hand, chaos can add a security dimension to the system in the sense that it is impossible to re-generate a chaotic sequence unless its parameters are known. The simulations conducted reveal the promising potential of the proposed method in terms of localization error function. The proposed method yielded comparable results to those of the previous work with the additional advantage of being less expensive in hardware design.