indoor localization accuracy estimation from fingerprint...
TRANSCRIPT
![Page 1: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/1.jpg)
Indoor Localization Accuracy Estimationfrom Fingerprint Data
Artyom Nikitin 1
Christos Laoudias2 Georgios Chatzimilioudis2
Panagiotis Karras3 Demetrios Zeinalipour-Yazti2,4
1Skoltech, 143026 Moscow, Russia
2University of Cyprus, 1678 Nicosia, Cyprus
3Aalborg University, 9220 Aalborg, Denmark
4Max-Planck-Institut fur Informatik, 66123 Saarbrucken, Germany
![Page 2: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/2.jpg)
Outline
1 Motivation
2 Background
3 Our Solution
4 Experiments
5 Conclusions
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 2/31
![Page 3: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/3.jpg)
Motivation: Indoor Localization
Indoor Navigation Services spread widely.
Applications: localization, marketing, warehouse optimization,guides, games, etc.
Different sources of data: cellular, Wi-Fi, BT, magnetic fieldof the Earth, light, sound, etc.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 3/31
![Page 4: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/4.jpg)
Motivation: Indoor Localization
Indoor Navigation Services spread widely.
Applications: localization, marketing, warehouse optimization,guides, games, etc.
Different sources of data: cellular, Wi-Fi, BT, magnetic fieldof the Earth, light, sound, etc.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 3/31
![Page 5: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/5.jpg)
Motivation: Accuracy Estimation
Important to estimate the accuracy of localization.
Online: important for the end-user (Google Maps, CONE).
Offline: important for the service provider.
Provide quality guarantees.Perform decision making.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 4/31
![Page 6: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/6.jpg)
Motivation: Accuracy Estimation
Important to estimate the accuracy of localization.
Online: important for the end-user (Google Maps, CONE).
Offline: important for the service provider.
Provide quality guarantees.Perform decision making.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 4/31
![Page 7: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/7.jpg)
Motivation: Accuracy Estimation
Important to estimate the accuracy of localization.
Online: important for the end-user (Google Maps, CONE).
Offline: important for the service provider.Provide quality guarantees.Perform decision making.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 4/31
![Page 8: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/8.jpg)
Outline
1 Motivation
2 Background
3 Our Solution
4 Experiments
5 Conclusions
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 5/31
![Page 9: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/9.jpg)
Background: Localization Approaches
Modeling
Known APs positions
Known data model, e.g., Path Loss: L = 10n log10(d) + C
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 6/31
![Page 10: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/10.jpg)
Background: Localization Approaches
Modeling + Fingerprinting
Known APs positions
Known data model, e.g., Path Loss: L = 10n log10(d) + C
Known pre-collected fingerprints (position + readings)
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 6/31
![Page 11: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/11.jpg)
Background: Localization Approaches
Fingerprinting
Known APs positions
Known data model, e.g., Path Loss: L = 10n log10(d) + C
Known pre-collected fingerprints (position + readings)
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 6/31
![Page 12: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/12.jpg)
Background: Accuracy Estimation
Existing solutions
Heuristics: e.g., fingerprint density, cluster & merge, etc.
+ Do not require models− No theoretical guarantees
Theoretical: e.g., use Cramer-Rao Lower Bound (CRLB)
+ Provide theoretical guarantees− Model is required
Our goal:
+ No model required
+ Provide guarantees via CRLB
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 7/31
![Page 13: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/13.jpg)
Background: Accuracy Estimation
Common theoretical approach for offline accuracy estimation:
1 Measurements are random, e.g., Gaussian.
2 From the known information estimate the likelihood, i.e., theprobability p(m|r) of measuring m at r.
3 From the likelihood calculate Cramer-Rao Lower Bound(CRLB) on the variance of any unbiased estimator of r.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 8/31
![Page 14: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/14.jpg)
Background: Accuracy Estimation
Common theoretical approach for offline accuracy estimation:
1 Measurements are random, e.g., Gaussian.2 From the known information estimate the likelihood, i.e., the
probability p(m|r) of measuring m at r.
3 From the likelihood calculate Cramer-Rao Lower Bound(CRLB) on the variance of any unbiased estimator of r.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 8/31
![Page 15: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/15.jpg)
Background: Accuracy Estimation
Common theoretical approach for offline accuracy estimation:
1 Measurements are random, e.g., Gaussian.2 From the known information estimate the likelihood, i.e., the
probability p(m|r) of measuring m at r.3 From the likelihood calculate Cramer-Rao Lower Bound
(CRLB) on the variance of any unbiased estimator of r.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 8/31
![Page 16: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/16.jpg)
Background: Accuracy Estimation
Common theoretical approach for offline accuracy estimation:
1 Measurements are random, e.g., Gaussian.2 From the known information estimate the likelihood, i.e., the
probability p(m|r) of measuring m at r.3 From the likelihood calculate Cramer-Rao Lower Bound
(CRLB) on the variance of any unbiased estimator of r.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 8/31
![Page 17: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/17.jpg)
Background: Accuracy Estimation
Common theoretical approach for offline accuracy estimation:
1 Measurements are random, e.g., Gaussian.2 From the known information estimate the likelihood, i.e., the
probability p(m|r) of measuring m at r.3 From the likelihood calculate Cramer-Rao Lower Bound
(CRLB) on the variance of any unbiased estimator of r.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 8/31
![Page 18: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/18.jpg)
Background: Accuracy Estimation
How to find the likelihood?
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 9/31
![Page 19: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/19.jpg)
Background: Accuracy Estimation
Modeling. We know:
Model, e.g., Path Loss: L = 10n log10(|x − xAP |) + CModel parameters, e.g., n = 2,C = 20 log10
4πλ (FSPL)
Position xAP of the APNoise
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 10/31
![Page 20: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/20.jpg)
Background: Accuracy Estimation
Modeling. We know:
Model, e.g., Path Loss: L = 10n log10(|x − xAP |) + C
Model parameters, e.g., n = 2,C = 20 log104πλ (FSPL)
Position xAP of the AP
Noise
1 Predict using model
2 Estimate noise
3 Compare to measurements
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 10/31
![Page 21: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/21.jpg)
Background: Accuracy Estimation
Modeling. We know:
Model, e.g., Path Loss: L = 10n log10(|x − xAP |) + C
Model parameters, e.g., n = 2,C = 20 log104πλ (FSPL)
Position xAP of the AP
Noise
1 Predict using model
2 Estimate noise
3 Compare to measurements
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 10/31
![Page 22: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/22.jpg)
Background: Accuracy Estimation
Modeling. We know:
Model, e.g., Path Loss: L = 10n log10(|x − xAP |) + C
Model parameters, e.g., n = 2,C = 20 log104πλ (FSPL)
Position xAP of the AP
Noise
1 Predict using model
2 Estimate noise
3 Compare to measurements
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 10/31
![Page 23: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/23.jpg)
Background: Accuracy Estimation
Modeling + Fingerprinting. We know:
Model, e.g., Path Loss: L = 10n log10(|x − xAP |) + CModel parameters, e.g., n = 2,C = 20 log10
4πλ
Position xAP of the APNoise
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 11/31
![Page 24: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/24.jpg)
Background: Accuracy Estimation
Modeling + Fingerprinting. We know:
Model, e.g., Path Loss: L = 10n log10(|x − xAP |) + C
Model parameters, e.g., n = 2,C = 20 log104πλ
Position xAP of the AP
Noise
1 Assume parametric model
2 Get fingerprints
3 Estimate parameters
4 Estimate noise
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 11/31
![Page 25: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/25.jpg)
Background: Accuracy Estimation
Modeling + Fingerprinting. We know:
Model, e.g., Path Loss: L = 10n log10(|x − xAP |) + CModel parameters, e.g., n = 2,C = 20 log10
4πλ
Position xAP of the APNoise
1 Assume parametric model
2 Get fingerprints
3 Estimate parameters
4 Estimate noise
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 11/31
![Page 26: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/26.jpg)
Background: Accuracy Estimation
Modeling + Fingerprinting. We know:
Model, e.g., Path Loss: L = 10n log10(|x − xAP |) + C
Model parameters, e.g., n = 2,C = 20 log104πλ
Position xAP of the AP
Noise
1 Assume parametric model
2 Get fingerprints
3 Estimate parameters
4 Estimate noise
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 11/31
![Page 27: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/27.jpg)
Background: Accuracy Estimation
Modeling + Fingerprinting. We know:
Model, e.g., Path Loss: L = 10n log10(|x − xAP |) + C
Model parameters, e.g., n = 2,C = 20 log104πλ
Position xAP of the AP
Noise
1 Assume parametric model
2 Get fingerprints
3 Estimate parameters
4 Estimate noise
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 11/31
![Page 28: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/28.jpg)
Background: Accuracy Estimation
Pure Fingerprinting
No model provided.
Data is too complex, e.g., ambient magnetic field:vector field = direction + magnitude;predictable outdoors;perturbed indoors by metal constructions and electricalequipment.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 12/31
![Page 29: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/29.jpg)
Background: Accuracy Estimation
Pure Fingerprinting
No model provided.Data is too complex, e.g., ambient magnetic field:
vector field = direction + magnitude;predictable outdoors;perturbed indoors by metal constructions and electricalequipment.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 12/31
![Page 30: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/30.jpg)
Background: Accuracy Estimation
Pure Fingerprinting
No model provided.Data is too complex, e.g., ambient magnetic field:
vector field = direction + magnitude;predictable outdoors;perturbed indoors by metal constructions and electricalequipment.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 12/31
![Page 31: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/31.jpg)
Outline
1 Motivation
2 Background
3 Our Solution
4 Experiments
5 Conclusions
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 13/31
![Page 32: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/32.jpg)
Our solution: Goal
Pure fingerprinting approach
Arbitrary data sources
FM = {(ri ,mi ) : i = 1,N, ri ∈ Rdr , mi ∈ Rdm}mi - dm-dimensional vector of measurements at location ri .
Given the FM, assign to any location a navigability score.
Visualize navigability scores to assist INS deployer.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 14/31
![Page 33: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/33.jpg)
Our solution: ACCES Framework
ACCES framework
1 Interpolation:FM + Gaussian Process Regression (GPR) ⇒ likelihood
2 CRLB:Likelihood + CRLB ⇒ lower bound on localization error
3 Lower bound on localization error ⇒ navigability score
Theoretical bound on localization errorAssume that behaves similar to real error
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 15/31
![Page 34: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/34.jpg)
Our Solution: Interpolation
Gaussian Process Regression:
Input: fingerprint map of measurements
Output: Gaussian likelihood p(m|r) of measuring m at r(prediction + uncertainty)
Intuition:measurements are Gaussian random variablesspatial correlation: close are correlated, far are not
Properties:models arbitrary noisy datacaptures FM’s spatial sparsity
Nuances:parameters tuning is required (kernel, length scale, etc.)assume normality condition (does not directly work for NLOS)directly applicable only to scalar data ⇒ assume independencecomputationally expensive ⇒ clustering
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 16/31
![Page 35: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/35.jpg)
Our Solution: Interpolation
Gaussian Process Regression:
Input: fingerprint map of measurements
Output: Gaussian likelihood p(m|r) of measuring m at r(prediction + uncertainty)
Intuition:measurements are Gaussian random variablesspatial correlation: close are correlated, far are not
Properties:models arbitrary noisy datacaptures FM’s spatial sparsity
Nuances:parameters tuning is required (kernel, length scale, etc.)assume normality condition (does not directly work for NLOS)directly applicable only to scalar data ⇒ assume independencecomputationally expensive ⇒ clustering
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 16/31
![Page 36: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/36.jpg)
Our Solution: Interpolation
Gaussian Process Regression:
Input: fingerprint map of measurements
Output: Gaussian likelihood p(m|r) of measuring m at r(prediction + uncertainty)
Intuition:measurements are Gaussian random variablesspatial correlation: close are correlated, far are not
Properties:models arbitrary noisy datacaptures FM’s spatial sparsity
Nuances:parameters tuning is required (kernel, length scale, etc.)assume normality condition (does not directly work for NLOS)directly applicable only to scalar data ⇒ assume independencecomputationally expensive ⇒ clustering
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 16/31
![Page 37: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/37.jpg)
Our Solution: Interpolation
Gaussian Process Regression (1-D example)
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 16/31
![Page 38: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/38.jpg)
Our Solution: CRLB
Cramer-Rao Lower Bound:
Input: likelihood p(m|r) of measuring m at r
Output: smallest RMSE achievable by any unbiasedestimator of r
Intuition:likelihood carries information about the distributiondistribution does not vary locally ⇒ degradation
Properties:theoreticaleasily found for unbiased estimators
Nuances:an underestimation of the real error ⇒ we care aboutqualitative behavioranalytical representation depends on GPR parameters ⇒ weinvolve numerical methods
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 17/31
![Page 39: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/39.jpg)
Our Solution: CRLB
Cramer-Rao Lower Bound:
Input: likelihood p(m|r) of measuring m at r
Output: smallest RMSE achievable by any unbiasedestimator of r
Intuition:likelihood carries information about the distributiondistribution does not vary locally ⇒ degradation
Properties:theoreticaleasily found for unbiased estimators
Nuances:an underestimation of the real error ⇒ we care aboutqualitative behavioranalytical representation depends on GPR parameters ⇒ weinvolve numerical methods
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 17/31
![Page 40: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/40.jpg)
Our Solution: CRLB
Cramer-Rao Lower Bound:
Input: likelihood p(m|r) of measuring m at r
Output: smallest RMSE achievable by any unbiasedestimator of r
Intuition:likelihood carries information about the distributiondistribution does not vary locally ⇒ degradation
Properties:theoreticaleasily found for unbiased estimators
Nuances:an underestimation of the real error ⇒ we care aboutqualitative behavioranalytical representation depends on GPR parameters ⇒ weinvolve numerical methods
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 17/31
![Page 41: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/41.jpg)
Our Solution: CRLB
CRLB: error of any unbiased location estimator is bounded as
RMSE ≥√tr(I−1(r)),
where I(r) is a Fisher Information Matrix :
I(r) = −E(∂2 log p(m|r)
∂ri∂rj
)
From GPR:m|r ∼ N (µ(r),Σ(r))
Thus,
I(r) =1
2
dm∑k=1
[(σ2k+µ2k)H(σ−2k )+H(µ2kσ
−2k )−2µkH(µkσ
−2k )+2H(log σk)
]
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 18/31
![Page 42: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/42.jpg)
Our Solution: CRLB
CRLB: error of any unbiased location estimator is bounded as
RMSE ≥√tr(I−1(r)),
where I(r) is a Fisher Information Matrix :
I(r) = −E(∂2 log p(m|r)
∂ri∂rj
)From GPR:
m|r ∼ N (µ(r),Σ(r))
Thus,
I(r) =1
2
dm∑k=1
[(σ2k+µ2k)H(σ−2k )+H(µ2kσ
−2k )−2µkH(µkσ
−2k )+2H(log σk)
]
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 18/31
![Page 43: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/43.jpg)
Outline
1 Motivation
2 Background
3 Our Solution
4 Experiments
5 Conclusions
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 19/31
![Page 44: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/44.jpg)
Experiments: Data
UJIIndoorLoc-Mag database
8 corridors over 260 m2 lab
40,159 discrete captures
Magnetometer readings
Measurements along thecorridors ⇒ 1-D data
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 20/31
![Page 45: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/45.jpg)
Experiments: Algorithms
Real accuracy: RMSE via WkNN
Naıve approach: Fingerprint Spatial Sparsity Indicator:
FSSI (r) = mini∈1,N
‖r − ri‖
considers only distance between measurements
ACCES: our solution
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 21/31
![Page 46: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/46.jpg)
Experiments: Algorithms
Real accuracy: RMSE via WkNN
Naıve approach: Fingerprint Spatial Sparsity Indicator:
FSSI (r) = mini∈1,N
‖r − ri‖
considers only distance between measurements
ACCES: our solution
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 21/31
![Page 47: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/47.jpg)
Experiments: Algorithms
Real accuracy: RMSE via WkNN
Naıve approach: Fingerprint Spatial Sparsity Indicator:
FSSI (r) = mini∈1,N
‖r − ri‖
considers only distance between measurements
ACCES: our solution
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 21/31
![Page 48: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/48.jpg)
Experiments: Metrics
DQRelSim(X ,Y ) - behavior similarity of sequences X = Xi ,Y = Yi for 1-D case.
Construction:Difference Quotient ⇒ DQ(X ) and DQ(Y )DTW ⇒ optimally warped DQ(X )′ and DQ(Y )′ fromNormalization
Values:Similar: 1, if X = Y + constDissimilar: 0, if either X or Y is constantOpposite: −1, if X = −Y + const
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 22/31
![Page 49: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/49.jpg)
Experiments: Settings
DQRelSim(ACCES ,RMSE ) vs DQRelSim(FSSI ,RMSE )
1 “Cut” scenario:Contiguous sequence of measurements is removed⇔ fingerprints were not collected
2 “Flat” scenario:Contiguous sequence of measurements is made constant⇔ low signal variability
3 “Sparse” scenario:Measurements are removed uniformly⇔ different frequency of fingerprint collection
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 23/31
![Page 50: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/50.jpg)
Experiments: Evaluation
“Cut” scenario: magnetic field magnitude
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 24/31
![Page 51: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/51.jpg)
Experiments: Evaluation
“Cut” scenario: similarity of RMSE, ACCES, FSSI
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 24/31
![Page 52: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/52.jpg)
Experiments: Evaluation
“Flat” scenario: magnetic field magnitude
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 25/31
![Page 53: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/53.jpg)
Experiments: Evaluation
“Flat” scenario: similarity of RMSE, ACCES, FSSI
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 25/31
![Page 54: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/54.jpg)
Experiments: Evaluation
“Sparse” scenario: behaviour of RMSE, ACCES
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 26/31
![Page 55: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/55.jpg)
Outline
1 Motivation
2 Background
3 Our Solution
4 Experiments
5 Conclusions
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 27/31
![Page 56: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/56.jpg)
Conclusions
Summary:
ACCES provides offline accuracy estimations and FMassessment.
Does not consider the origin of the data.
Applicable to pure fingerprinting.
Shows reasonable correspondence to the real localization errorbehaviour.
Future work:
Extensive experimental study with other data.
Comparison to online accuracy estimation algorithms.
Adding support for arbitrary models.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 28/31
![Page 57: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/57.jpg)
Conclusions
Summary:
ACCES provides offline accuracy estimations and FMassessment.
Does not consider the origin of the data.
Applicable to pure fingerprinting.
Shows reasonable correspondence to the real localization errorbehaviour.
Future work:
Extensive experimental study with other data.
Comparison to online accuracy estimation algorithms.
Adding support for arbitrary models.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 28/31
![Page 58: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/58.jpg)
Advertisement: Anyplace
Anyplace Indoor Information Service
Wi-Fi + IMU
Optimize data usage
3 awards
Crowdsource-based
Open-source
anyplace.cs.ucy.ac.cy
github.com/dmsl/anyplace
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 29/31
![Page 59: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/59.jpg)
Advertisement: Anyplace
Anyplace Indoor Information Service
Wi-Fi + IMU
Optimize data usage
3 awards
Crowdsource-based
Open-source
anyplace.cs.ucy.ac.cy
github.com/dmsl/anyplace
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 29/31
![Page 60: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/60.jpg)
Advertisement: Anyplace
Anyplace Indoor Information Service
Wi-Fi + IMU
Optimize data usage
3 awards
Crowdsource-based
Open-source
anyplace.cs.ucy.ac.cy
github.com/dmsl/anyplace
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 29/31
![Page 61: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/61.jpg)
Advertisement: Anyplace
Anyplace Indoor Information Service
Wi-Fi + IMU
Optimize data usage
3 awards
Crowdsource-based
Open-source
anyplace.cs.ucy.ac.cy
github.com/dmsl/anyplace
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 29/31
![Page 62: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/62.jpg)
Demo
Thank You!
Come to see our demoyesterday!
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 30/31
![Page 63: Indoor Localization Accuracy Estimation from Fingerprint Datadzeina/talks/mdm17-acces-presentation.pdf · Indoor Localization Accuracy Estimation from Fingerprint Data ... 1Skoltech,](https://reader034.vdocument.in/reader034/viewer/2022042314/5f0278527e708231d4046b71/html5/thumbnails/63.jpg)
Conclusions
Summary:
ACCES provides offline accuracy estimations and FMassessment.
Does not consider the origin of the data.
Applicable to pure fingerprinting.
Shows reasonable correspondence to the real localization errorbehaviour.
Future work:
Extensive experimental study with other data.
Comparison to online accuracy estimation algorithms.
Adding support for arbitrary models.
IEEE MDM 2017 | Nikitin, Laoudias, Chatzimilioudis, Karras, Zeinalipour 31/31