Iterative and Non-Iterative Theoretical Closed Forms Discrete Cosine Transform-Based Incremental LMS

Novel closed-form expressions of the discrete cosine transform (DCT)-based iterative and non-iterative incremental least mean square (DCTILMS) algorithms are derived here for wireless sensor networks (WSNs) and agent localization. As a direct application to this field of study, smart cities, smart homes, intelligent transportation systems, healthcare, robotics, low-cost and energy efficient smart sensor devices, internet of things (IoT), target tracking, and agent localization are very relevant applications. Moreover, there are many achieved objectives in this study, among them the great performance obtained by this algorithm, and the well performance in low-SNR environments. The practical implication of the present model is to reduce computational complexity. In this respect, incorporating only the initial design parameters, the theoretical transient and steady-state expressions of the DCT 1<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup>- and 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup>-moment formulas are derived in both iterative and non-iterative closed forms. The length of the main DCTILMS experiment can now be identified in advance by monitoring the theoretical DCT 1<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup>-moment closed-form formula. Extensive simulations are carried out to present that the theoretical DCT closed-form formulas are wellmatched with their empirical counterparts, thus confirming the soundness of our theoretical derivations.