\[ \hat{x}(k+1) = A \hat{x}(k) + B u(k) + K (y(k) - C \hat{x}(k)) \] \[ u(k) = \arg\min_u \sum_{i=k}^{k+N} \left( x_i^T Q x_i + u_i^T R u_i \right) \] \[ K = P C^T (C P C^T + R_v)^{-1} \] \[ P = A P A^T + R_w - A P C^T (C P C^T + R_v)^{-1} C P A^T \]