For the multisensor linear discrete time-invariant stochastic systems with correlated noises and unknown noise statistics, an on-line noise statistics estimator is presented by using the correlation method. Substituting it into the steady-state Riccati equation, the self-tuning Riccati equation is obtained. Using the Kalman filtering method, based on the self-tuning Riccati equation, a self-tuning weighted measurement fusion white noise deconvolution estimator is presented. By the dynamic error system analysis (DESA) method, it is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steadystate white noise deconvolution estimator in a realization, so that it has the asymptotic global optimality. A simulation example for Bernoulli-Gaussian input white noise shows its effectiveness.