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

Apr 24, 2023 •320 likes •671 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

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
Multi-Modal Kalman Filter
Propagating a Gaussian through a Linear Model
Propagating a Gaussian through a Non-Linear Model
Linearizing the Non-Linear Model
Extended Kalman Filter
Extended Kalman Filter
Extended Kalman Filter
Particle Filter
Particle Filter
Particle Filter
Particle Filter Example v x 0 x t+1 =x t + (0.1, 0) p(z=HIT|x) 0.1 u 0.1 0.25 0.3 0.4 z 1 =HIT
When to Use Each? Kalman Filter Bayes Filter General Framework Linear Models No implementation! Gaussian Distributions Extended Kalman Filter Particle Filter Any Model Non-Linear Models (linearizable) Any Distribution Gaussian Distributions Low Dimensional State Space
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
Ernst and Banks, “Humans integrate visual and haptic information in a statistically optimal fashion”, Nature’02
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

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