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For the multisensor systems with unknown noise variances, by the correlation method, the information fusion noise variance estimators are presented by taking the average of the local noise variance estimators under the least squares fusion rule. They have the average accuracy and have consistency. A self-tuning Riccati equation with the fused noise variance estimators is presented, and then a self-tuning decoupled fusion Kalman predictor is presented based on the optimal fusion rule weighted by scalars for state component predictors. In order to prove their convergence, the dynamic variance error system analysis (DVESA) method is presented, which transforms the convergence problem of the self-tuning Riccati equation into a stability problem of a dynamic variance error system described by the Lyapunov equation. A stability decision criterion of the Lyapunov equation is presented. By the DVESA method, the convergence of the self-tuning Riccati equation is proved, and then it is proved that the self-tuning decoupled fusion Kalman predictor converges to the optimal decoupled fusion Kalman predictor in a realization, so it has asymptotic optimality. A simulation example for a tracking system with 3-sensor shows the effectiveness, and verifies the convergence.