How do you design a Kalman filter for state estimation?

Kalman filter is optimal recursive estimator for linear systems with Gaussian noise. Model: State equation x[k] = A*x[k-1] + B*u[k-1] + w[k-1], Observation z[k] = H*x[k] + v[k]. Predict: x_pred = A*x_est + B*u, P_pred = A*P*A' + Q. Update: K = P_pred*H'*(H*P_pred*H' + R)^-1, x_est = x_pred + K*(z - H*x_pred), P = (I - K*H)*P_pred. Design requires: System model (A, B, H), Process noise covariance Q, Measurement noise covariance R. Tuning Q/R ratio affects responsiveness vs smoothing. Extensions: EKF (nonlinear), UKF (unscented), particle filters.