Differentiable Bayes Filters

Lecture 9

Announcement

- Feedback for Project proposal latest on Wednesday night

- Kevin Zakka started course notes (see Piazza) - bonus points for contributing

What will you take home today?

Recap Bayesian Filters

Kalman Filter

Extended Kalman Filter

Particle Filter

Differentiable Filters

Backpropagation through a Kalman Filter

Backpropagation through a Particle Filter

Recap Bayes Filters

xt�1 xt xt+1

zt+1zt�1 zt

utut�1 ut+1

Kalman Filter

Kalman Filter

Extended Kalman Filter

Prediction Step: Update Step:

x̂t = Axt�1 +But (1)

P̂t = APt�1AT +Qt (2)

it = zt �Hx̂t (3)

Kt =P̂tH

T

HP̂tHT +Rt

(4)

xt = x̂t +Ktit (5)

Pt = (In �KtH)P̂t (6)

Particle Filter

Particle Filter

When to use what? How to choose hyperparameters?

Priors and Hyperparameters

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

Differentiable filters

A note on variables

In Robotics and Control:

In Machine Learning:

In Artificial Intelligence:

BackpropKF : Learning Discriminative Deterministic State Estimators. Haarnoja et al. NeurIPS 2016

- Differentiable version of the Kalman Filter

- Uses Images as observations; learns a sensors that outputs state directly

Differentiable Kalman Filter - Structure

Differentiable Kalman Filter - Structure

Differentiable Kalman Filter – Loss Function

Differentiable Kalman Filter – Experiments and Baselines

Differentiable Kalman Filter – Experiments and Baselines

• Kitti – Visual Odometry Datatset• 22 stereo sequences with LIDAR

• 11 sequences with ground truth(GPS/IMU data)

• 11 sequences without ground truth (forevaluation)

Differentiable Kalman Filter – Experiments and Baselines

Results reproduced by Claire Chen

Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.

Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.

Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.

Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors. Jonschkowski et al. RSS 2018.

Particle Filter Networks with Application to Visual Localization. Karkus et al. CORL 2018.

Differentiable Particle Filter – Loss Function

Differentiable Particle Filter – Experiments and Baselines

Differentiable Particle Filter – Experiments and Baselines

Differentiable Particle Filter – Experiments and Baselines