State of charge (SOC) estimators with online identified battery model have proven to have high accuracy and better robustness due to the timely adaption of time varying model parameters. In this paper, we show that the common methods for model identification are intrinsically biased if both the current and voltage sensors are corrupted with noises. The uncertainties in battery model further degrade the accuracy and robustness of SOC estimate. To address this problem, this paper proposes a novel technique which integrates the Frisch scheme based bias compensating recursive least squares (FBCRLS) with a SOC observer for enhanced model identification and SOC estimate. The proposed method online estimates the noise statistics and compensates the noise effect so that the model parameters can be extracted without bias. The SOC is further estimated in real time with the online updated and unbiased battery model. Simulation and experimental studies show that the proposed FBCRLS based observer effectively attenuates the bias on model identification caused by noise contamination and as a consequence provides more reliable estimate on SOC. The proposed method is also compared with other existing methods to highlight its superiority in terms of accuracy and convergence speed.