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In this paper, the Gauss-Hermite quadrature filter (GHQF) is introduced to estimate battery state of charge (SOC) based on a common electrical analogue battery model useful for realtime applications. A high fidelity circuit-based electrical analogue battery model was used with a new parameter estimation algorithm. When the model runs off-line, the terminal voltage estimation error is at the 30mV level for a battery module with 14.4V nominal voltage, which is more accurate than previously reported comparable behavioral models. However, the battery SOC is calculated based on coulomb-counting, which is considered inaccurate and has many drawbacks, such as the problem of estimating the initial SOC and the "current loss" problem. In this paper a filter is used to improve the SOC estimation accuracy for the battery model to be used for realtime applications. The extended Kalman filter (EKF), the unscented Kalman filter (UKF) and the Gauss-Hermite quadrature filter are all studied and compared in this work. The Gauss-Hermite quadrature filter excels among the commonly used filters when used with the high fidelity electrical analogue battery model. This conclusion is experimentally verified on a 6.8 Ah Lithium-ion battery module.