In EKF navigation, which factor most directly governs how strongly a measurement influences the state update?

• A. Initial state
• B. Process noise covariance Q
• C. Measurement function h(x)
• D. Measurement noise covariance R

Answer: (D)

In EKF navigation, the strength of a measurement’s update is governed by the Kalman gain, which balances how confident you are in the prior prediction with how confident you are in the measurement. The math shows this clearly: K = P H^T (H P H^T + R)^{-1}. The measurement noise covariance R sits directly in the denominator of this expression. When R is small, the measurement is trusted more, the denominator shrinks, and the Kalman gain grows, so the state update is strong toward the measurement. When R is large, the measurement is trusted less, the denominator grows, and the update is weaker. The initial state sets the prior, the process noise Q affects prediction between measurements, and the measurement function h(x) defines how states map to measurements but does not directly set how strongly a measurement will influence the update.