<p>Dynamic tasks or resources localization in distributed edge computing systems with inaccuracies in node positioning represent a critical research direction. Existing closed-form methods often introduce auxiliary variables to pseudo-linearize the performance models, followed by parameter estimation via weighted least squares (WLS). Although such a procedure is frequently refined in a subsequent step, the inclusion of extra variables tends to amplify estimation errors, causing the results to deviate from the Cramér–Rao lower bound (CRLB) under high-noise scenarios. To address this limitation, we propose a two-phase closed-form algorithm. In the first phase, extra variables are eliminated using an orthogonal projection matrix, and an initial solution is derived via least squares (LS). Since the omitted terms contain relevant information about task location and dynamics, this preliminary estimate remains suboptimal. A second phase is therefore designed to enhance its accuracy. The proposed estimator has potential for real-time implementation, because it avoids iterative convergence and provides deterministic computational steps. Both theoretical analysis and numerical simulations demonstrate that the proposed estimator achieves the CRLB under moderate Gaussian noise conditions. Simulation results further confirm the computational efficiency of the method and its superiority over existing closed-form alternatives.</p>