Lecture 6 And 7 Slides

Question 1

Alternative derivation of Kalman filter

Answer 1

Question 2

For invertible A, C

Answer 2

Question 3

Alternative update step

Answer 3

Question 4

Kalman smoother

Answer 4

Question 5

Law of total expectation

Answer 5

Question 6

Prove law of total variation

Answer 6

Question 7

Kalman smoother: algorithm

Answer 7

Question 8

Kalman filter and smoother are same when

Answer 8

t = n

Question 9

Key difference between Kalman Filter and Kalman Smoother

Answer 9

Filter is interested in all data before each point

Smoother is interested in every data point (updated and based on future results as they come through)

Question 10

How to Kalman smoother

Answer 10

Do kalman filter

Then at last density it coincides with Kalman smoother, which we then work out backwards

In the below quantity, we begin with n = t, then decrement n