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 2

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 3

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 4

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 5

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) 6

7. Approach Expectation: Maximisation 7

8. Algorithm 8

9. Results – WiFi RSSI 9

10. Results - Simulation 10

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 11

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 12