Robust Linearly Constrained Kalman Filter for General Mismatched Linear State-Space Models

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.