CS-7638 MIDTERM EXAM 2026/2027 WITH
ACTUAL CORRECT QUESTIONS AND
VERIFIED DETAILED ANSWERS
|CURRENTLY TESTING QUESTIONS AND
SOLUTIONS|NEWEST |BRAND NEW
VERSION|JUST RELEASED!!
What is the primary function of the Kalman filter's measurement update step?
It combines the prior estimate with new measurements to improve accuracy.
What happens to the variance when two identical means are averaged?
The new variance becomes half of the original variance.
What is the motion update in the context of the Kalman filter?
The motion update predicts the new position based on the current estimate and motion
uncertainty.
What is the formula for the new mean after a motion update?
The new mean is the old mean plus the motion (u).
What is the formula for the new variance after a motion update?
The new variance is the old variance plus the variance of the motion Gaussian.
What is the initial estimate (μ) set to in the Kalman filter example?
The initial estimate (μ) is set to 0.
What is the significance of a large initial uncertainty in the Kalman filter?
A large initial uncertainty means the estimate is heavily influenced by the first measurement.
What are the measurements and motions used in the Kalman filter example?
1|Page
,Measurements: 5, 6, 7, 9, 10; Motions: 1, 1, 2, 1, 1.
What is the expected first estimate for position in the Kalman filter example?
The expected first estimate for position should be approximately 5.
What does the term 'Gaussian' refer to in the context of the Kalman filter?
It refers to the probability distribution used to model uncertainties in the estimates.
What is the role of the predict function in the Kalman filter?
The predict function computes the new prediction based on the current estimate and motion.
What is the relationship between measurement uncertainty and the Kalman filter's
performance?
Measurement uncertainty affects how much influence new measurements have on the
estimate.
What is the result of combining two Gaussian distributions with the same variance?
The resulting distribution is more peaked than either of the original distributions.
What is the purpose of the Kalman filter?
The Kalman filter is used to estimate the state of a dynamic system from noisy measurements.
What does the term 'separated Gaussians' refer to in this context?
It refers to two Gaussian distributions that are far apart in mean but have the same covariance.
What is the significance of the term 'motion uncertainty' in the Kalman filter?
Motion uncertainty quantifies the confidence in the motion command used for prediction.
What does the term 'measurement probability' refer to in the Kalman filter?
It refers to the likelihood of observing a measurement given the current state estimate.
What does the term 'update step' refer to in the context of the Kalman filter?
2|Page
,The update step refers to the process of refining the estimate based on new measurements.
What is the initial estimate for position when running a Kalman filter?
5, with an initial uncertainty that is large.
What happens to the uncertainty after the first measurement update in a Kalman filter?
The uncertainty shrinks to 3.99, which is slightly better than the measurement uncertainty.
What is the effect of adding motion in a Kalman filter?
The uncertainty increases to 5.99, which reflects the motion uncertainty.
What is the final prediction for position after several updates in a Kalman filter?
10.99, which is the result of the last position moved by 1.
What is the significance of the variables 'measurements_sig' and 'motion_sig' in Kalman filter
code?
'measurements_sig' should be renamed to 'measurement_variance' and 'motion_sig' to
'motion_variance' for clarity.
What does the Kalman filter do in terms of uncertainty after each measurement?
It updates the estimate and reduces uncertainty based on the measurement's reliability.
What happens when the initial position estimate is incorrect but has low uncertainty?
The final prediction is influenced by the incorrect estimate, resulting in a less accurate
prediction.
How does the Kalman filter handle multiple dimensions?
It uses a multivariate Gaussian to estimate position and velocity, allowing for better predictions.
What is inferred from multiple position measurements in a Kalman filter?
The velocity of the object, which is not directly measured.
3|Page
, What is the role of covariance in a high-dimensional Kalman filter?
Covariance is represented as a matrix that defines the spread of the Gaussian across
dimensions.
What does a 2-dimensional Gaussian represent in the context of Kalman filters?
It defines the uncertainty in both dimensions, with the mean indicating the estimated position.
What is the effect of high uncertainty in one dimension versus another in a Gaussian?
It can have a small uncertainty in one dimension while having a large uncertainty in another.
What is the recursive formula used in Kalman filters for updating estimates?
It updates the mean (mu) and variance (sigma) based on new measurements and motions.
What is the outcome of applying a Kalman filter to a sequence of measurements and motions?
It produces a refined estimate of the object's position and associated uncertainty.
Why are Kalman filters popular in artificial intelligence and control theory?
They effectively estimate states and predict future positions based on noisy measurements.
What is the relationship between position measurements and velocity in Kalman filters?
Position measurements allow the filter to infer velocity, which aids in future predictions.
What does the term 'variance' refer to in the context of Kalman filters?
It refers to the uncertainty in the estimates, which is updated with each measurement.
How does the Kalman filter improve predictions over time?
By continuously updating estimates with new measurements and adjusting for uncertainties.
What happens to the Kalman filter's prediction if the initial position is set incorrectly?
The final prediction may be less accurate, reflecting the influence of the incorrect initial
estimate.
4|Page
ACTUAL CORRECT QUESTIONS AND
VERIFIED DETAILED ANSWERS
|CURRENTLY TESTING QUESTIONS AND
SOLUTIONS|NEWEST |BRAND NEW
VERSION|JUST RELEASED!!
What is the primary function of the Kalman filter's measurement update step?
It combines the prior estimate with new measurements to improve accuracy.
What happens to the variance when two identical means are averaged?
The new variance becomes half of the original variance.
What is the motion update in the context of the Kalman filter?
The motion update predicts the new position based on the current estimate and motion
uncertainty.
What is the formula for the new mean after a motion update?
The new mean is the old mean plus the motion (u).
What is the formula for the new variance after a motion update?
The new variance is the old variance plus the variance of the motion Gaussian.
What is the initial estimate (μ) set to in the Kalman filter example?
The initial estimate (μ) is set to 0.
What is the significance of a large initial uncertainty in the Kalman filter?
A large initial uncertainty means the estimate is heavily influenced by the first measurement.
What are the measurements and motions used in the Kalman filter example?
1|Page
,Measurements: 5, 6, 7, 9, 10; Motions: 1, 1, 2, 1, 1.
What is the expected first estimate for position in the Kalman filter example?
The expected first estimate for position should be approximately 5.
What does the term 'Gaussian' refer to in the context of the Kalman filter?
It refers to the probability distribution used to model uncertainties in the estimates.
What is the role of the predict function in the Kalman filter?
The predict function computes the new prediction based on the current estimate and motion.
What is the relationship between measurement uncertainty and the Kalman filter's
performance?
Measurement uncertainty affects how much influence new measurements have on the
estimate.
What is the result of combining two Gaussian distributions with the same variance?
The resulting distribution is more peaked than either of the original distributions.
What is the purpose of the Kalman filter?
The Kalman filter is used to estimate the state of a dynamic system from noisy measurements.
What does the term 'separated Gaussians' refer to in this context?
It refers to two Gaussian distributions that are far apart in mean but have the same covariance.
What is the significance of the term 'motion uncertainty' in the Kalman filter?
Motion uncertainty quantifies the confidence in the motion command used for prediction.
What does the term 'measurement probability' refer to in the Kalman filter?
It refers to the likelihood of observing a measurement given the current state estimate.
What does the term 'update step' refer to in the context of the Kalman filter?
2|Page
,The update step refers to the process of refining the estimate based on new measurements.
What is the initial estimate for position when running a Kalman filter?
5, with an initial uncertainty that is large.
What happens to the uncertainty after the first measurement update in a Kalman filter?
The uncertainty shrinks to 3.99, which is slightly better than the measurement uncertainty.
What is the effect of adding motion in a Kalman filter?
The uncertainty increases to 5.99, which reflects the motion uncertainty.
What is the final prediction for position after several updates in a Kalman filter?
10.99, which is the result of the last position moved by 1.
What is the significance of the variables 'measurements_sig' and 'motion_sig' in Kalman filter
code?
'measurements_sig' should be renamed to 'measurement_variance' and 'motion_sig' to
'motion_variance' for clarity.
What does the Kalman filter do in terms of uncertainty after each measurement?
It updates the estimate and reduces uncertainty based on the measurement's reliability.
What happens when the initial position estimate is incorrect but has low uncertainty?
The final prediction is influenced by the incorrect estimate, resulting in a less accurate
prediction.
How does the Kalman filter handle multiple dimensions?
It uses a multivariate Gaussian to estimate position and velocity, allowing for better predictions.
What is inferred from multiple position measurements in a Kalman filter?
The velocity of the object, which is not directly measured.
3|Page
, What is the role of covariance in a high-dimensional Kalman filter?
Covariance is represented as a matrix that defines the spread of the Gaussian across
dimensions.
What does a 2-dimensional Gaussian represent in the context of Kalman filters?
It defines the uncertainty in both dimensions, with the mean indicating the estimated position.
What is the effect of high uncertainty in one dimension versus another in a Gaussian?
It can have a small uncertainty in one dimension while having a large uncertainty in another.
What is the recursive formula used in Kalman filters for updating estimates?
It updates the mean (mu) and variance (sigma) based on new measurements and motions.
What is the outcome of applying a Kalman filter to a sequence of measurements and motions?
It produces a refined estimate of the object's position and associated uncertainty.
Why are Kalman filters popular in artificial intelligence and control theory?
They effectively estimate states and predict future positions based on noisy measurements.
What is the relationship between position measurements and velocity in Kalman filters?
Position measurements allow the filter to infer velocity, which aids in future predictions.
What does the term 'variance' refer to in the context of Kalman filters?
It refers to the uncertainty in the estimates, which is updated with each measurement.
How does the Kalman filter improve predictions over time?
By continuously updating estimates with new measurements and adjusting for uncertainties.
What happens to the Kalman filter's prediction if the initial position is set incorrectly?
The final prediction may be less accurate, reflecting the influence of the incorrect initial
estimate.
4|Page
