Magnetometers are widely equipped in smartphones. They measure the direction and the magnitude of the magnetic field of the environment. Since the measurements are not transition data, there is no drift when estimating position and orientation using a magnetometer. Furthermore, magnetic field localization using magnetometers requires no extra devices set in the environment, and this indicates the cost of localization using a magnetometer can be lower than other localization methods that need multiple devices set in the localizing area. Therefore, magnetic field localization is an interesting method for indoor localization. However, there exists a research gap in the algorithms that have been applied to magnetic field localization. In the current research, the Extended Kalman filter (EKF) and the Particle filter (PF) are applied to magnetic field localization. The EKF is more efficient than the PF, but has low accuracy when the distribution is multimodal. On the other hand, the PF is more computationally costly compared to the EKF but is more robust to the multimodality. As a result, a survey of the possible solutions to the current research gap was carried out. From this survey, Gaussian sum filter (GSF) was found to be a promising candidate as the solution to the research gap. To test the performance and assumptions of the GSF, the GSF was applied to a fully simulated magnetic field localization system and a localization system with the measurements obtained from a real-world magnetometer. The results from these simulations show that the GSF is more suitable for multimodality than the EKF. Besides, the computational cost of the GSF is found to be lower than the PF while the GSF has an equivalent or even better accuracy than the PF.