<p>The ARX-Laguerre technique provides a compact and efficient approach to system identification for engineering applications. It builds on the classical Auto-Regressive with eXogenous input (ARX) model by projecting its parameters onto two orthogonal Laguerre function bases, each defined by a single Laguerre pole and a truncation order. Optimizing these poles leads to a nonlinear problem that significantly reduces the number of model parameters compared to the standard ARX model. Given the nonlinear nature of this optimization problem, earlier studies successfully employed a Genetic Algorithm (GA)-based approach to optimize only the Laguerre pole in noise-free scenarios. This work extends that approach by using GA to jointly optimize both the Laguerre poles and the truncation order in the presence of noise. Within this framework, five algorithms are introduced to enhance ARX-Laguerre modeling for Single Input Single Output (SISO) systems. The first algorithm explains the Recursive Least Squares (RLS) optimization method. The second details the construction steps of the ARX-Laguerre model. The third proposes a novel model reduction technique aimed at computing a low-complexity system transfer function. The fourth presents an innovative GA-based Laguerre pole optimization method tailored for noisy environments. The fifth introduces an integrated approach to simultaneously determine the optimal truncation order and Laguerre pole values under noise. The effectiveness of the proposed algorithms is validated through application to a real-world single degree-of-freedom (DoF) drone system. It is observed that the obtained model’s output closely matches the real drone’s behavior, with a mean error of just 0.01%.</p>