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

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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

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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

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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

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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

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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)

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Approach• Expectation:

• Maximisation

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Algorithm

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Results – WiFi RSSI

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Results - Simulation

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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

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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