Midterm Exam

Question 1

A histogram filter is an example of a __________ filter.

Answer 1

Discrete

Question 2

A Kalman Filter is an example of a ____________ filter.

Answer 2

Continuous

Question 3

Histogram Filter beliefs are unimodal? (True/False)

Answer 3

False. They are multimodal (i.e. it can represent multiple Gaussian “bumps”.)

Question 4

Kalman Filter beliefs are unimodal? (True/False)

Answer 4

True

Question 5

Histogram filters are represented as grids? (True/False)

Answer 5

True

Question 6

Kalman filters are represented by Gaussians? (True/False)

Answer 6

True

Question 7

Is the efficiency of a histogram filter quadratic or exponential?

Answer 7

Exponential. Any k-dimensional space when subdivided into grids the number of cells scales exponentially. This means it works best for low dimensional problems.

Question 8

Is the efficiency of a Kalman filter quadratic or exponential?

Answer 8

Quadratic. This is because the problem is defined using a vector that contains the means, and then a covariance matrix that is quadratic. The reason for this is that if your measurement space is fixed size, it always scales quadratically. (Video says to just take this on faith.)

Question 9

In a robotics context, is a histogram filter an EXACT or APPROXIMATE estimate of the a posteriori distribution?

Answer 9

Approximate. This is because of the discretization. Since we’re binning things we lose information on the precise location.

Question 10

In a robotics context, is a Kalman filter an EXACT or APPROXIMATE estimate of the a posteriori distribution?

Answer 10

Approximate. The lecture video just says the math is too involved, but that the KF is exact only for linear systems. Since practically every real-world application is non-linear, this means that KF can be considered approximates.

Question 11

A Particle Filter is an example of a ____________ filter.

Answer 11

Continuous

Question 12

Particle Filter beliefs are multi-modal? (True/False)

Answer 12

True

Question 13

In a robotics context, is a Particle Filter an EXACT or APPROXIMATE estimate of the a posteriori distribution?

Answer 13

Approximate

Question 14

Is the efficiency of a Particle Filter quadratic or exponential?

Answer 14

Neither (or unknown). Trick question. This is something the jury is still out on. Research is ongoing.

Question 15

What is the key advantage of particle filters?

Answer 15

They’re very easy to program.