Recursive and Non-Recursive Theoretical Closed-Form Hybrid Incremental LMS Algorithm

A novel hybrid incremental least mean square algorithm (HILMS) based on discrete cosine transform (DCT) and variable step-size (VSS) algorithms is developed and analyzed in wireless sensor networks (WSNs) and agent localization. The comparative theoretical first- and second-moment closed-form relations are derived indicating the best selection region and the related gain between the DCT and VSS algorithms. In the low and high signal-to-noise ratio (SNR) scenarios, the DCTILMS and VSSILMS algorithms indicate far better performance compared to the VSSILMS and DCTILMS algorithms, respectively. The recursive and non-recursive theoretical closed-form expressions of the HILMS first- and second-moment relations are derived under the transient and steady-state conditions. In the simulations, we show that the empirical performance is in excellent agreement with the theoretical transient and steady-state results. As expected, the proposed HILMS algorithm outperformed both the DCT and VSS algorithms in low- and high-SNR environments.