Recursive State Estimation 2 Lecture 8 Recap Today Kalman Filter - - PowerPoint PPT Presentation

▶
recursive state estimation 2
SMART_READER_LITE
LIVE PREVIEW

Recursive State Estimation 2 Lecture 8 Recap Today Kalman Filter - - PowerPoint PPT Presentation

Apr 24, 2023 320 likes •675 views

Recursive State Estimation 2 Lecture 8 Recap Today Kalman Filter Extended Kalman Filter Particle Filter Kalman Filter Kalman Filter Note: Conditioning Kalman Filter Multi-Modal Kalman Filter Vision Force State Proprioception

slide-1
SLIDE 1

Recursive State Estimation 2

Lecture 8

slide-2
SLIDE 2

Recap

slide-3
SLIDE 3

Today

  • Kalman Filter
  • Extended Kalman Filter
  • Particle Filter
slide-4
SLIDE 4

Kalman Filter

slide-5
SLIDE 5

Kalman Filter

slide-6
SLIDE 6

Note: Conditioning

slide-7
SLIDE 7

Kalman Filter

slide-8
SLIDE 8
slide-9
SLIDE 9
slide-10
SLIDE 10
slide-11
SLIDE 11
slide-12
SLIDE 12

Multi-Modal Kalman Filter

Vision Force Proprioception State

slide-13
SLIDE 13

Multi-Modal Kalman Filter

slide-14
SLIDE 14
slide-15
SLIDE 15
slide-16
SLIDE 16

Propagating a Gaussian through a Linear Model

slide-17
SLIDE 17

Propagating a Gaussian through a Non-Linear Model

slide-18
SLIDE 18

Linearizing the Non-Linear Model

slide-19
SLIDE 19

Extended Kalman Filter

slide-20
SLIDE 20

Extended Kalman Filter

slide-21
SLIDE 21

Extended Kalman Filter

slide-22
SLIDE 22

Particle Filter

slide-23
SLIDE 23

Particle Filter

slide-24
SLIDE 24

Particle Filter

slide-25
SLIDE 25
slide-26
SLIDE 26

Particle Filter Example

0.1 0.1 0.3 0.4 u v 0.25

xt+1=xt + (0.1, 0) z1=HIT

p(z=HIT|x)

x0

slide-27
SLIDE 27
slide-28
SLIDE 28

When to Use Each?

Bayes Filter General Framework No implementation! Kalman Filter Linear Models Gaussian Distributions Extended Kalman Filter Non-Linear Models (linearizable) Gaussian Distributions Particle Filter Any Model Any Distribution Low Dimensional State Space

slide-29
SLIDE 29

Problems

A lot of hardcoded knowledge!

1.

State Representation

2.

Models

  • Forward Model
  • State to next state
  • Action to next state
  • Measurement Model

3.

Probabilistic Properties

  • Process Noise
  • Measurement Noise
slide-30
SLIDE 30

Ernst and Banks, “Humans integrate visual and haptic information in a statistically optimal fashion”, Nature’02

slide-31
SLIDE 31
slide-32
SLIDE 32
slide-33
SLIDE 33
slide-34
SLIDE 34

Ernst and Banks, “Humans integrate visual and haptic information in a statistically optimal fashion”, Nature’02

  • Merging Visual and Haptic
  • First, they estimate uncertainty about each modality

separately

  • Then, they measure the result of fusing them and the

uncertainty

  • Both mean and std dev can be predicted by a MLE!
  • Similar process as Kalman Filter over time