On the asymptotic behavior of linearly constrained filters for robust multi-channel signal processing

The Kalman filter (KF) is known to loose its optimality properties when the model used does not perfectly match true system. Extending use of linear constraints this recently proved be efficient mitigate a large class parametric mismatch, through linearly constrained and minimum variance (LCKF LCMVF). However, asymptotic performances these new filters are still an open question. In work, we bring first answer latter problem in case measurement mismatch. We show that both LCKF LCMVF equivalent unconstrained which directions cancelled by projection, allowing better understanding their properties. particular, steady-state mean square error, it exists, derived. consistency with respect nonlinear mismatches also improved via constraints. An array processing example provided assess derived formulas, performance filters.