<p>In ensemble filters, limitations such as finite ensemble size and imperfect physical parameterizations exist, introducing sampling and model errors can cause background spread and covariances to be underestimated, leading to filter divergence. When applied to parameter estimation, such filtering can cause parameters to converge to inappropriate values, resulting in a poor performance of parameter estimation. To alleviate the problem, an inflation method is commonly employed in ensemble filters data assimilation to increase prior variances and mitigate filter divergence. In previous study, the adaptive covariance inflation algorithm called t-X has been successfully applied to state estimation of an intermediate coupled model (ICM). This study uses the t-X to conduct an in-depth investigation within an observation system simulation experiment (OSSE) framework using the ICM and the Ensemble Adjustment Kalman Filter (EAKF) for El Niño and Southern Oscillation (ENSO) simulation and prediction. The goal is to develop a joint approach for optimizing both model parameters and states simultaneously. Results show optimizing parameters concurrently with model initial states further enhances the simulation and prediction capabilities of the model. The t-X shows a great advantage in optimizing the parameter with an error of only 0.07%. And it significantly reduces the prediction errors for the "Niño 3.4" and "Niño 1 + 2" zones by 89.31% and 93.31%, respectively. It can be seen that the advantages of the t-X are mainly in the equatorial eastern Pacific and south boundaries of the ICM.</p>