CS-7638 EXAMINATION STUDY SHEET 2026
QUESTIONS WITH ANSWERS GRADED A+
◉What is the role of the equations in the Kalman filter regarding
location and velocity? Answer: The equations propagate constraints
from observations of location to estimate the hidden variable of
velocity.
◉How do observable and hidden variables function in a Kalman
filter? Answer: Observable variables (like location) provide
information that helps estimate hidden variables (like velocity)
through correlation.
◉What is a key advantage of using Kalman filters in motion
estimation? Answer: Kalman filters are efficient for calculating
estimates of both observable and hidden variables in dynamic
systems.
◉What is the formula for predicting the next location in a Kalman
filter? Answer: The formula is x' = x + Δt * x, where x' is the
predicted location, x is the current location, and x is the velocity.
,◉What does a tilted Gaussian indicate in the context of Kalman
filters? Answer: A tilted Gaussian indicates a correlation between
location and velocity, reflecting uncertainty in both variables.
◉What does the covariance in a Kalman filter represent? Answer:
Covariance represents the uncertainty and correlation between the
estimated states (location and velocity).
◉What is the effect of multiple observations on the estimation of
hidden variables in Kalman filters? Answer: Multiple observations
improve the estimates of hidden variables by providing more data to
infer their values.
◉What is the significance of the major axis of the covariance
ellipsoid in Kalman filters? Answer: The major axis indicates the
direction of motion and the correlation between the estimated
states.
◉What is the implication of having a diagonal covariance in a
Kalman filter? Answer: A diagonal covariance indicates no
correlation between the states, leading to maximum uncertainty in
predictions.
◉How does the Kalman filter update its estimates after a new
measurement? Answer: It combines the prior estimates with the
, new measurement to refine the estimates of both location and
velocity.
◉What is the role of the prediction step in the Kalman filter?
Answer: The prediction step estimates future states based on
current estimates and assumed dynamics of the system.
◉What is the relationship between the Kalman filter and self-
driving cars? Answer: Kalman filters are used in self-driving cars to
estimate the locations and velocities of other vehicles based on
limited observations.
◉What does it mean if the covariance does not align strictly with the
principal axes? Answer: It indicates that there is correlation
between the states, affecting the predictions made by the filter.
◉What is a common error in understanding the Kalman filter's
predictions? Answer: A common error is assuming that predicted
Gaussians lie on a diagonal line instead of the correct horizontal line
for constant velocity.
◉What does the term 'states' refer to in the context of Kalman
filters? Answer: 'States' refer to the variables that reflect the
physical conditions of the system, such as location and velocity.
QUESTIONS WITH ANSWERS GRADED A+
◉What is the role of the equations in the Kalman filter regarding
location and velocity? Answer: The equations propagate constraints
from observations of location to estimate the hidden variable of
velocity.
◉How do observable and hidden variables function in a Kalman
filter? Answer: Observable variables (like location) provide
information that helps estimate hidden variables (like velocity)
through correlation.
◉What is a key advantage of using Kalman filters in motion
estimation? Answer: Kalman filters are efficient for calculating
estimates of both observable and hidden variables in dynamic
systems.
◉What is the formula for predicting the next location in a Kalman
filter? Answer: The formula is x' = x + Δt * x, where x' is the
predicted location, x is the current location, and x is the velocity.
,◉What does a tilted Gaussian indicate in the context of Kalman
filters? Answer: A tilted Gaussian indicates a correlation between
location and velocity, reflecting uncertainty in both variables.
◉What does the covariance in a Kalman filter represent? Answer:
Covariance represents the uncertainty and correlation between the
estimated states (location and velocity).
◉What is the effect of multiple observations on the estimation of
hidden variables in Kalman filters? Answer: Multiple observations
improve the estimates of hidden variables by providing more data to
infer their values.
◉What is the significance of the major axis of the covariance
ellipsoid in Kalman filters? Answer: The major axis indicates the
direction of motion and the correlation between the estimated
states.
◉What is the implication of having a diagonal covariance in a
Kalman filter? Answer: A diagonal covariance indicates no
correlation between the states, leading to maximum uncertainty in
predictions.
◉How does the Kalman filter update its estimates after a new
measurement? Answer: It combines the prior estimates with the
, new measurement to refine the estimates of both location and
velocity.
◉What is the role of the prediction step in the Kalman filter?
Answer: The prediction step estimates future states based on
current estimates and assumed dynamics of the system.
◉What is the relationship between the Kalman filter and self-
driving cars? Answer: Kalman filters are used in self-driving cars to
estimate the locations and velocities of other vehicles based on
limited observations.
◉What does it mean if the covariance does not align strictly with the
principal axes? Answer: It indicates that there is correlation
between the states, affecting the predictions made by the filter.
◉What is a common error in understanding the Kalman filter's
predictions? Answer: A common error is assuming that predicted
Gaussians lie on a diagonal line instead of the correct horizontal line
for constant velocity.
◉What does the term 'states' refer to in the context of Kalman
filters? Answer: 'States' refer to the variables that reflect the
physical conditions of the system, such as location and velocity.
