Recursive and Explicit Theoretical Enclosed Forms Variable Step-Size Incremental LMS

recursive and explicit theoretical enclosed-form relations of variable step-size (VSS) incremental least mean square (VSSILMS) are derived in agent localization and wireless sensor networks (WSNs). Possible relevant applications of this work include WSNs, environmental, flora and fauna, agent localization, urban, health, and military applications. Under transient and steady-state conditions, the theoretical VSS 1^st- and 2^nd-moment relations are derived in recursive and explicit enclosed-form relations incorporating only the initial parameter settings. In advance of the real simulations, the problematic simulation length can be determined by monitoring the convergence of the VSS 1^st-moment enclosed-form relation. During real simulations, the enclosed-form expressions derived from the theoretical VSS 1^st- and 2^nd-moment models agree well with the empirical results.