Abstract
It is well known that Wiener filter and Kalman filter (KF) like techniques are sensitive to misspecified covariances, uncertainties in the system matrices, filter initialization, or unwanted system behaviors. A possible solution to robustify these estimation techniques is to impose linear constraints (LCs). In this article: 1) we introduce a general class of linearly constrained KF (LCKF), where a set of nonstationary LCs can be set at every time step; 2) explore the use of such LCs to mitigate modeling errors in general mismatched linear discrete state-space models; and 3) provide the theoretical formulation to show that the gain-constrained KF is a particular instance of the proposed LCKF. Because such LCs can be taken into account in any KF generalization, this sets the basis for a new robust filtering framework. An illustrative example is provided to support the discussion.
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