CS-7638 PRACTICE SCRIPT 2026
QUESTIONS WITH SOLUTIONS GRADED A+
◉What does the term 'Gaussian' refer to in the context of the
Kalman filter? Answer: 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?
Answer: 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? Answer: 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? Answer: The resulting distribution is more
peaked than either of the original distributions.
◉What is the purpose of the Kalman filter? Answer: 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?
Answer: 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? Answer: Motion uncertainty quantifies the
confidence in the motion command used for prediction.
◉What does the term 'measurement probability' refer to in the
Kalman filter? Answer: 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? Answer: 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? Answer: 5, with an initial uncertainty that is large.
◉What happens to the uncertainty after the first measurement
update in a Kalman filter? Answer: 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? Answer:
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? Answer: 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? Answer: '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? Answer: 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? Answer: The final prediction is influenced by
the incorrect estimate, resulting in a less accurate prediction.
◉How does the Kalman filter handle multiple dimensions? Answer:
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? Answer: The velocity of the object, which is not
directly measured.
◉What is the role of covariance in a high-dimensional Kalman filter?
Answer: 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? Answer: 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? Answer: 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? Answer: 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? Answer: It produces a refined estimate
of the object's position and associated uncertainty.
QUESTIONS WITH SOLUTIONS GRADED A+
◉What does the term 'Gaussian' refer to in the context of the
Kalman filter? Answer: 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?
Answer: 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? Answer: 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? Answer: The resulting distribution is more
peaked than either of the original distributions.
◉What is the purpose of the Kalman filter? Answer: 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?
Answer: 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? Answer: Motion uncertainty quantifies the
confidence in the motion command used for prediction.
◉What does the term 'measurement probability' refer to in the
Kalman filter? Answer: 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? Answer: 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? Answer: 5, with an initial uncertainty that is large.
◉What happens to the uncertainty after the first measurement
update in a Kalman filter? Answer: 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? Answer:
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? Answer: 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? Answer: '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? Answer: 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? Answer: The final prediction is influenced by
the incorrect estimate, resulting in a less accurate prediction.
◉How does the Kalman filter handle multiple dimensions? Answer:
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? Answer: The velocity of the object, which is not
directly measured.
◉What is the role of covariance in a high-dimensional Kalman filter?
Answer: 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? Answer: 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? Answer: 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? Answer: 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? Answer: It produces a refined estimate
of the object's position and associated uncertainty.
