Steady-state optimal measurement fusion white noise deconvolution estimators

White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration, communication, signal processing, and state estimation. For the multisensor linear discrete time-invariant stochastic systems with correlated measurement noises, a steady-state measurement fusion system is obtained by the weighted least square (WLS) method. A steady-state optimal weighted measurement fusion white noise deconvolution estimator is presented using the Kalman filtering method. By a new derivation method, it is rigorously proved that the steady-state white noise deconvolution fuser is numerically identical to the centralized steady-state white noise deconvolution fuser, i.e. it has the asymptotically global optimality. It can reduce the computational burden because of the lower dimension of the measurement vector. A simulation example for the Bernoulli-Gaussian input white noise shows the effectiveness of the proposed results.