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Outline

Paper Discussion: “Simultaneous Localization and Environmental Mapping with a Sensor Network”, Marinakis et. al. ICRA 2011. Outline. Problem: Simultaneous mapping and localisation in static, continuous and smooth field Solution Expectation Maximisation (EM) Implementation

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Outline

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  1. Paper Discussion: “Simultaneous Localization and Environmental Mapping with a Sensor Network”, Marinakis et. al. ICRA 2011

  2. Outline • Problem: • Simultaneous mapping and localisation in static,continuous and smooth field • Solution • Expectation Maximisation (EM) • Implementation • Grid-based representation of all PDFs • In simulation and practical

  3. Contributions • Claim: Use of smoothly varying parameters in the environment to aid localization • Simultaneous mapping of continuous field (with uncertainty) and localisation of sensors. • Interesting idea, but implementation does not fully take advantage of continuous field

  4. Background: Expectation Maximisation • Maximum likelihood estimator • Two steps in each iteration • Expectation – compute likelihood of observations with current model • Maximisation – using likelihood of observations, maximise likelihood of model parameters • Also used as Maximum a Posteriori estimator • How this paper uses EM • Maximisation step uses MAP rather than ML

  5. Background: Expectation Maximisation • Example: fitting Gaussian mixture models • Problem • Inputs: set of data points, number of Gaussians in mixture • Outputs: weights, means and covariances of each Gaussian • Weights must sum to 1.0 • Expectation • Compute likelihood of each point being in each Gaussian • Maximisation • Update weights, means and covariances based on likelihoods using “frequentist” definition

  6. Notation • = sensor pose(s) • Grid representation of domain • Probability of occupancy represented as grid • = prior • = model parameters • Grid representation of domain • Environmental parameter(s) represented by (multivariate) Gaussian at each cell • = estimate of model parameters • = observations of environmental parameters • Vector of measurements of environmental parameter(s)

  7. Approach • Expectation: • Maximisation

  8. Algorithm

  9. Results – WiFi RSSI

  10. Results - Simulation

  11. Discussion • Considers static sensors • A motion model can be incorporated in Expectation step • Grid representation of world • Continuous representation of world • Continuous representation of sensor network cost • Communications cost

  12. Conclusions • EM framework for simultaneous localisation and environmental mapping (i.e. continuous field) • Interesting idea, but implementation does not fully take advantage of continuous field

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