Based on model matching approach

this paper presents an algorithm for designing optimal filter that minimizes the magnitude of the filter error

in the case of linear discrete-time system in which the process noise and measurement noise are unknown but magnitude bounded.The presented algorithm can be used to optimal infinite-horizon filter design.When the initial condition of the system is a priori known

the optimal filter is converted into a standard tow-block 

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optimization.When the system contains unknown but bounded initial condition

the optimal filter can be obtained by solving finite standard 

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optimization problems that can be solved by existed techniques.A simulation example shows the effectiveness and feasibility of the proposed results.