Summary: For the multisensor linear discrete time-invariant stochastic system with unknown colored observation noises, the consistent fused estimators of unknown model parameters and noise variances are obtained by using the recursive extended-least-squares method and solving the correlation function equations. Substituting them into the optimal decoupled fused Kalman filter, we obtain a self-tuning decoupled fused Kalman filter. By means of the dynamic variance error system analysis method and the dynamic error system analysis method, this filter is proved to be convergent to the optimal decoupled fusion Kalman filter with asymptotic optimality. A simulation example for a target-tracking system with 3 sensors shows its effectiveness.