Chapter 6: Multivariate Filters

Question 1

Kalman Filter Algorithm - 3 Steps

Answer 1

1) Initialization (one-time)
2) Predict (repeatedly)
3) Update (repeatedly)

Question 2

Initialization

Answer 2

1. Initialize the state of the filter

2. Initialize our belief in the state

Question 3

Prediction

Answer 3

1. Use the process model/dynamical model to estimate the state at the next time step
2. Adjust your belief to adjust for uncertainty in position

Question 4

Update

Answer 4

1. Obtain a measurement and associated belief about it’s accuracy
2. Compute residual between estimated state and measurement
3. Compute scaling factor based on whether the measurement or prediction is more accurate
4. Set state between the prediction and measurement based on scaling factor
5. Update belief in state based on how certain we are in measurement

Question 5

Multivariate Gaussians use ___ for the mean and — ——— for the covariances

Answer 5

Multivariate Gaussians use vectors for the mean and a matrix for the covariances

Question 6

The multivariate Kalman filter needs to use ______ _______ to perform ___ ___________

Answer 6

The multivariate Kalman filter needs to use linear algebra to perform the estimations

Question 7

x

Answer 7

state mean vector

Question 8

P

Answer 8

state covariance matrix

Question 9

F

Answer 9

state transition function. When multiplied by x in the predict step, it computes the prior.

Question 10

Q

Answer 10

process covariance matrix

Question 11

B

Answer 11

control-input model

Question 12

u

Answer 12

control vector

Question 13

H

Answer 13

= observation model = measurement function

Question 14

z

Answer 14

measurement mean vector

Question 15

R

Answer 15

measurement covariance matrix

Question 16

y

Answer 16

residual

Question 17

K

Answer 17

Kalman gain

Question 18

hidden variables

Answer 18

variables that aren’t measured directly but can dramatically improve the state estimate since they can be inferred from and have a strong correlation to observed variables.

Question 19

observed variables

Answer 19

variables that are measured directly

Question 20

Despite all the fancy math, Kalman filters, in essence, are really only ___________.

Answer 20

multiplying and adding gaussians

Question 21

The way that we represent the number 1 in multiple dimensions

Answer 21

I, the identity matrix

Question 22

Ratio of how much prediction vs measurement we use

Answer 22

K, Kalman gain

Question 23

A function to convert from the state space into the measurement space

Answer 23

measurement function

Question 24

S

Answer 24

system uncertainty/innovation covariance