Kalman Filter Quiz

Answers and explanations appear as you take the quiz.

1. Which sequence describes one standard Kalman filtering cycle?
   • Predict the state, then update it with a measurement
   • Update with a measurement first, then predict the next state
   • Replace the state estimate with each raw measurement
   • Predict the sensor reading but omit the measurement correction
2. With predicted variance 4 and measurement variance 4 in the scalar case, what is the Kalman gain?
   • 1
   • 0.5
   • 4
   • 8
3. Using gain 0.5, predicted state 10 and measurement 14, what updated state results?
   • 10
   • 14
   • 12
   • 7
4. If measurement noise variance increases while prediction uncertainty stays fixed, what happens to the gain?
   • It becomes the measurement variance
   • It increases above one
   • It remains exactly unchanged
   • It decreases, so the measurement receives less weight
5. Which conditions support the classical Kalman filter's optimality result?
   • A nonlinear process with arbitrary noise distributions
   • Linear dynamics and Gaussian noise with a correctly specified model
   • A stationary mean with no state or measurement covariance model
   • A discrete-state process with arbitrary transition rules
6. Which residual is called the innovation during measurement update?
   • The accumulated process-noise estimate
   • The covariance of the previous state
   • Observed measurement minus predicted measurement
   • Predicted measurement minus observed measurement
7. Persistent innovation bias may point to what?
   • A proof that the system is stationary
   • A guarantee that all states are correct
   • A need to set measurement noise to zero
   • A biased sensor or misspecified process model
8. What does the covariance P represent in the filter?
   • Uncertainty in the estimated hidden state
   • The measured state itself
   • The sensor identity label
   • The number of filter updates