A multitask incremental least mean square algorithm using orthonormal codes

A new multitask incremental least mean-square (MILMS) algorithm using orthonormal codes is developed. In the multitask topology, nodes belong to different clusters, with each cluster performing its own ILMS estimation. The closed-form expressions of both the theoretical transient and steady-state mean squared deviation (MSD) are derived. The proposed MILMS algorithm is further reinforced by two combination strategies, referred to here as the combine-then-adapt (CTA), and adapt-then-combine (ATC), giving rise to two new improved algorithms, the CTA-MILMS and ATC-MILMS that substantially improve the MSD. Two further variants of these two improved algorithms are also developed based on the combination of the variable step size (VSS) and discrete cosine transform (DCT) techniques, leading to the two combined algorithms, termed here as CTA-VSSMILMS and ATC-VSSMILMS, respectively. Analysis of the first and second moments of the step size, under the transient and steady-state conditions, is also included. The problem of agent localization is solved using the MILMS algorithm by deploying a fixed number of anchors with known positions that surround agents with unknown positions. Extensive experiments were carried out to show the excellent match between the theoretical transient and steady-state expressions and their corresponding empirical results in terms of MSD performance. Moreover, we show that both the ATC-VSSMILMS and CTA-VSSMILMS algorithms improve the accuracy and computational speed of the MSD results of the proposed MILMS algorithm, thanks to the VSS-induced reduction of the number of needed steps and the DCT-induced data compression effect.