To enhance the estimation accuracy of battery's state of charge, it is imperative to estimate the battery model parameter. To reduce the calculation efforts, the number of the battery model parameter to be estimated should be less while ensuring the state of charge estimation accuracy. Especially in engineering applications, the calculating ability is usually limited. So, it needs to choose the critical battery model parameter to be estimated. This paper's contributions are as follows: The global sensitivity analysis of the battery model parameter is achieved by the Monte Carlo simulation method. The results show that the open circuit voltage and the ohmic resistance are the high sensitivity parameters. Guided by the results of parameter sensitivity analysis, a dual extended Kalman filters method is utilized to achieve online battery model parameter estimation. The experiments prove that the state of charge estimation accuracy is improved by the online parameter estimation. Estimating high sensitivity parameters can reduce running time. And the SOC estimation accuracy can be guaranteed.