State Estimation with Kalman Filters
A quick look at the discrete state-space update step. The linear measurement update equation is given by: $$x_k = A x_{k-1} + B u_k + w_k$$ Where the Kalman Gain $K_k$ scales the innovation: $$K_k = P_k^- H^T (H P_k^- H^T + R)^{-1}$$ Inline math check: the error covariance shrinks when $R \to 0$.