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

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