CSE-473 Project 2

Monte Carlo Localization

Localization as state estimation

Markov Localization as State Estimation (2)

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Kalman filters, Hidden Markov Models, DBN

Markov!

Markov!

[Schiele et al. 94], [Weiß et al. 94], [Borenstein 96],

[Gutmann et al. 96, 98], [Arras 98]

Kalman Filters

[Burgard et al. 96,98], [Fox et al. 99], [Konolige et al. 99]

Piecewise constant

Represent density by random samples Estimation of non-Gaussian, nonlinear processes

Monte Carlo filter, Survival of the fittest, Condensation, Bootstrap filter, Particle filter

Filtering: [Handschin, 70], [Gordon et al., 93], [Kitagawa 96]

Computer vision: [Isard et al. 96, 98] DBN: [Kanazawa et al., 95]

Particle Filters

Converges to true density

Sample-based Density Representation

Importance Sampling

Weight samples: g

fw

Sample-based Density Representation

Sensor Information: Importance Sampling

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Robot Motion

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Set of samples St = {<l1, p1>, … <lN, pN>} described by position l and weight p

Initialize sample set S0 according to prior knowledge

For each motion do: Sampling: Generate from each sample in St-1 a new sample according to

motion model

For each observation s do: Importance sampling: Re-weight each sample with the likelihood

Resampling: Draw N samples from sample set St according to their

likelihood

Monte Carlo Localization (SIR)

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Motion Model P(l | a, l’)

Model odometry error as Gaussian noise on and

Motion Model P(l | a, l’)

Start

Global Localization (sonar)

Using Ceiling Maps for Localization

[Dellaert et al. 99]

Vision-based Localization

P(z|x)

h(x)z

Vision-based Localization

[CVPR-99]

Comparison to Grid-based Markov Localization (2)

Office environment: 20,000 samples versus 150

million states

NMAH: Global localization in 15 seconds instead

of 4 minutes

Vision-based: Can track the position in situations

in which grid-based approach fails

Condensation Tracking

Mixed-State Tracking

Tracking Multiple People