Abstract
The paper presents an H∞ -type estimation problem for discrete-time systems subject to multiplicative noise. Such systems naturally arise in many applications in aerospace engineering, including navigation, communications, estimation of target states, imagery. In this paper the attention is focused on determining a design method of a fixed (reduced) order filter. It is shown that if the system output is not corrupted with multiplicative noise then the existence of such filter is equivalent with the feasibility of a specific system of linear matrix inequalities. In the case when the output includes multiplicative noise components the existence conditions depend on the solutions of a system of linear matrix inequalities subject to a rank minimization condition. For the considered problem the rank constraint can be solved as a semi-definite programming problem using a particular affine transformation.
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