In EKF navigation, which matrix relates the predicted state to the measurement via the measurement function h(x)?

• A. F, the state transition Jacobian
• B. K, the Kalman gain
• C. H, the measurement Jacobian
• D. Q, the process noise

Answer: (C)

In EKF navigation, the matrix that links the predicted state to the measurement through the nonlinear function h(x) is the measurement Jacobian, H. Since h is nonlinear, we linearize it around the predicted state x̂⁻ by computing H = ∂h/∂x evaluated at x̂⁻. This gives the linear relationship z ≈ h(x̂⁻) + H (x − x̂⁻), meaning small state perturbations translate into measurement perturbations via H. That’s why H is the bridge between the predicted state and what the sensors measure. The other matrices have different roles: F governs how the state evolves, K is the Kalman gain used to fuse information, and Q represents process noise.