This paper addresses an infinite horizon distributed H2/H∞ filtering for discrete-time systems under conditions of bounded power and white stochastic signals.The filter algorithm is designed by computing a pair of gains namely the estimator and the coupling.Herein,we implement a filter to estimate unknown parameters such that the closed-loop multi-sensor accomplishes the desired performances of the proposed H2 and H∞ schemes over a finite horizon.A switched strategy is implemented to switch between the states once the operation conditions have changed due to disturbances.It is shown that the stability of the overall filtering-error system with H2/H∞ performance can be established if a piecewise-quadratic Lyapunov function is properly constructed.A simulation example is given to show the effectiveness of the proposed approach.