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Background: Soft errors in semiconductor devices caused by cosmic rays have been recognized as a significant threat to the reliability of electronic devices on the ground. Recently, concerns about soft errors induced by cosmic-ray muons have increased. Some previous studies have indicated that low-energy negative muons have a more significant contribution to the occurrence of soft errors than positive muons. Thus, charge-identified low-energy muon flux data on the ground are required for accurate evaluation of the soft error rate. However, there are no such experimental data in the low-energy region. Materials and Methods: We designed a new muon detector system to measure low-energy muon flux data with charge identification. The major components consist of two drift chambers and a permanent magnet. The charge and momentum of detected muon can be identified from the deflection of the muon trajectory in the magnetic field. An algorithm to estimate the muon momentum is developed using numerical optimization by combining the classical Runge-Kutta and quasi-Newton methods. The momentum search algorithm is applied to event-by-event data of positive and negative muons obtained by Monte Carlo simulations with Particle and Heavy Ion Transport code System, and its performance is examined. Results and Discussion: The momentum search algorithm is fully applicable even in the case of an inhomogeneous magnetic field. The precision of the momentum determination is evaluated by considering the stochastic fluctuation caused by multiple scattering and the position resolution of the drift chambers. It was found that multiple scattering has a significant contribution to the precision in the momentum region below 50 MeV/c, while the detector position resolution considerably affects the precision above that. Conclusion: It was confirmed that the momentum search algorithm works well with a sufficient precision of 15% in the low-momentum region below 100 MeV/c, where no muon flux data exist.