radloco: a rapid and low cost indoor location-sensing system - recoeng
TRANSCRIPT
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
RadLoco: A Rapid and Low Cost IndoorLocation-Sensing System
Eugene Hyun, Michael McGuire, Mihai Sima
Department of Electrical and Computer EngineeringUniversity of Victoria
Chinacom 2008 Conference
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
Outline
1 Location Aware ComputingMotivationCurrent TechnologiesProblem Definition
2 Location Sensing SystemOverviewData CollectionLocation EstimationSimple Graphical Example
3 Experiment and ResultsECS Room 116ECS 5th and 6th floors
4 Conclusions
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
MotivationCurrent TechnologiesProblem Definition
Location Aware Computing
MotivationLocation aware computing consists of the use of locationinformation to improve the value of a wireless network for theusers
Examplesproviding navigation through unfamiliar environmentsdynamic pre-allocation of resources
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
MotivationCurrent TechnologiesProblem Definition
Location Aware Computing
MotivationLocation aware computing consists of the use of locationinformation to improve the value of a wireless network for theusers
Examplesproviding navigation through unfamiliar environmentsdynamic pre-allocation of resources
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
MotivationCurrent TechnologiesProblem Definition
Location Aware Computing
MotivationLocation aware computing consists of the use of locationinformation to improve the value of a wireless network for theusers
Examplesproviding navigation through unfamiliar environmentsdynamic pre-allocation of resources
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
MotivationCurrent TechnologiesProblem Definition
Current Technologies for Location-Sensing
Global Position System (GPS) and CellularNetworks
poor location performance indoors
Wireless Local Area NetworksMany environments have ubiquitous wirelessnetworksWireless network access is beingincorporated into smaller mobile devices
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
MotivationCurrent TechnologiesProblem Definition
Current Technologies for Location-Sensing
Global Position System (GPS) and CellularNetworks
poor location performance indoors
Wireless Local Area NetworksMany environments have ubiquitous wirelessnetworksWireless network access is beingincorporated into smaller mobile devices
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
MotivationCurrent TechnologiesProblem Definition
Current Technologies for Location-Sensing
Global Position System (GPS) and CellularNetworks
poor location performance indoors
Wireless Local Area NetworksMany environments have ubiquitous wirelessnetworksWireless network access is beingincorporated into smaller mobile devices
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
MotivationCurrent TechnologiesProblem Definition
Problem Definition
ProblemThe relationship between location and radio signal strengthis highly non-linear and not known a priori.Survey data collection is time consuming.
SolutionUse non-parametric estimation technique to reducenoise and required number of survey points.Sensory network of Ultrasonic/Radio devices to aid inrapid survey data collection.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
MotivationCurrent TechnologiesProblem Definition
Problem Definition
ProblemThe relationship between location and radio signal strengthis highly non-linear and not known a priori.Survey data collection is time consuming.
SolutionUse non-parametric estimation technique to reducenoise and required number of survey points.Sensory network of Ultrasonic/Radio devices to aid inrapid survey data collection.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Location Sensing System Overview
x y
Details2 stages: Data Collection and Data Processing
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Location Sensing System Overview
x y
DetailsData Collection: Cricket Sensory Network
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Cricket Sensory Network for Ground Truth Location
Sensory Networkprovide ground truth location for survey point.
use modified steepest descent and Newton’smethod optimization
Cricket Detailsaccuracy = mean accuracy of 14 cmsensors = ultrasonic (40 kHz), radio (433 MHz)developers = Networks and Mobile SystemsGroup at MIT.
cost = $3000 for 12 crickets covering 500 m2
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Cricket Sensory Network for Ground Truth Location
Sensory Networkprovide ground truth location for survey point.
use modified steepest descent and Newton’smethod optimization
Cricket Detailsaccuracy = mean accuracy of 14 cmsensors = ultrasonic (40 kHz), radio (433 MHz)developers = Networks and Mobile SystemsGroup at MIT.
cost = $3000 for 12 crickets covering 500 m2
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Location Sensing System Overview
x y
DetailsData Collection: WLAN
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
WLAN information
WLAN dataRSS from base stationMAC of base stationTimeSSID (network ID)
Survey DataWLAN data and ground truth location compose of asurvey point.Collect several survey points within a floor or room tocreate a survey data set.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
WLAN information
WLAN dataRSS from base stationMAC of base stationTimeSSID (network ID)
Survey DataWLAN data and ground truth location compose of asurvey point.Collect several survey points within a floor or room tocreate a survey data set.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Location Sensing System Overview
x y
DetailsData Processing: Location Estimation
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Location Estimation
Estimation AlgorithmNon-Parametric Kernel/Parzen EstimationTechnique using a sum of multivariate GaussianDistributions.
Variablesb = vector of base stations (WLAN)z = vector of receive signal strengthmeasurements (WLAN)θ = x & y coordinates (survey points)θ̂ = x & y coordinate (estimated location)
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Location Estimation
Estimation AlgorithmNon-Parametric Kernel/Parzen EstimationTechnique using a sum of multivariate GaussianDistributions.
Variablesb = vector of base stations (WLAN)z = vector of receive signal strengthmeasurements (WLAN)θ = x & y coordinates (survey points)θ̂ = x & y coordinate (estimated location)
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Simple Graphical Example
Explanation3 base stations and 4 cricket sensors
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Simple Graphical Example
Explanationcrickets provide ground truth location (blue dots)
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Simple Graphical Example
Explanationbase stations provide RSS vector (z)
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Simple Graphical Example
Explanationtake RSS measurement at current unknown location
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Simple Graphical Example
Explanationand use the survey points collected prior
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Simple Graphical Example
Explanationto calculate the weight from z feature and Kernel estimator
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
OverviewData CollectionLocation EstimationSimple Graphical Example
Simple Graphical Example
Explanationestimated location is calculated using weights and θ feature
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
ECS Room 116ECS 5th and 6th floors
ECS 116 - Experimental Setup
EnvironmentEngineering and Computer Science building lecture hall116117 seats divided into 8 rows10 x 13 meters with 2 seats/m
Equipmenthardware: Dell Inspiron laptop + Intel 802.11g WLAN cardsoftware: Netstumber, Radloco, MySQL
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
ECS Room 116ECS 5th and 6th floors
ECS 116 - Experimental Setup
EnvironmentEngineering and Computer Science building lecture hall116117 seats divided into 8 rows10 x 13 meters with 2 seats/m
Equipmenthardware: Dell Inspiron laptop + Intel 802.11g WLAN cardsoftware: Netstumber, Radloco, MySQL
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
ECS Room 116ECS 5th and 6th floors
ECS 116 - Experimental Results
DescriptionWe were able to obtain over 80% accuracy within 4 metersor 6 seats.Motivation for ECS 5th and 6th floor
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
ECS Room 116ECS 5th and 6th floors
ECS 5th and 6th floors - Experimental Setup
EnvironmentBuilding has an atrium like structureExperiments were restricted to hallways and publicconference rooms.
Base Station (WAP) InformationWAPs from networks UVicOpen or engrnet.more than 35 unique WAPs and minimum of 12 WAPsvisible at any location on a floor.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
ECS Room 116ECS 5th and 6th floors
ECS 5th and 6th floors - Experimental Setup
EnvironmentBuilding has an atrium like structureExperiments were restricted to hallways and publicconference rooms.
Base Station (WAP) InformationWAPs from networks UVicOpen or engrnet.more than 35 unique WAPs and minimum of 12 WAPsvisible at any location on a floor.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
ECS Room 116ECS 5th and 6th floors
Experimental Results - Decimation of Survey Set
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Error Distance (cm)
Pro
ba
bil
ity
No decimation, h = 2.8, survey set size = 662, mean error = 227
Decimation by 2, h = 3, survey set size = 331, mean error = 253
Decimation by 4, h = 3, survey set size= 166, mean error = 284
DescriptionDecimating survey set yields near identical performance.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
ECS Room 116ECS 5th and 6th floors
Experimental Results - 6th vs. 5th floor
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Error Distance (cm)
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ba
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5th floor, h = 3.5, # of points = 188, mean error = 216
6th floor, h = 2.8, # of points = 662, mean error = 227
DescriptionBoth floor have similar accuracy of 3.5 m more than 80% of thetime.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
ECS Room 116ECS 5th and 6th floors
Experimental Results - Number of Base Stations
0 100 200 300 400 500 600 700 8000
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Error Distance (cm)
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bab
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3 WAPs or base stations
4 WAPs or base stations
5 WAPs or base stations
6 WAPs or base stations
7 WAPs or base stations
12 WAPs or base stations
16 WAPs or base stations
DescriptionIncreasing base stations yields better accuracy
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
ECS Room 116ECS 5th and 6th floors
Experimental Results - Combined Datasets
0 100 200 300 400 500 600 700 8000
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Error Distance (cm)
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Both Floors, mean error = 283 cm
5th Floor, mean error = 219 cm
6th Floor, mean error = 296 cm
DescriptionCombined floors data sets provides 3D location accuracy withover 98% floor accuracy
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
Conclusions
Major Contributionslocation-sensing system that locates mobile computingdevices indoors based on WLAN technology.sensory network composed of radio/ultrasonic devicesallow rapid data collection98% accuracy floor accuracy and location estimationswithin 3.5m of true location
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
Conclusions
Further ResearchIEEE 802.16, WiMAX, can be extended for indoor location.sensory network calibration on wallsreal-time location estimation for the RadLoco software
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
Conclusions
List of Publications1 Eugene Hyun, Michael McGuire, Mihai Sima, "RadLoco: A Rapid and Low Cost
Indoor Location-Sensing System" IEEE 3rd International Conference onCommunications and Networking in China, Hangzhou, Aug 2008.
2 Michael McGuire, Eugene Hyun, Mihai Sima, "Location Aware Computing forAcademic Environments" The 3rd International Conference on Quality of Servicein Heterogeneous Wired/Wireless Networks (MobConQoE ’07), Vancouver,Canada, Aug 2007.
3 Eugene Hyun, Diego Felix, Michael McGuire, Mihai Sima, "AThree-Dimensional Indoor Location-Sensing using Radio and Ultrasonic SensingTechnologies", ETRI Journal (in Preparation)
4 Eugene Hyun, Mihai Sima, Michael McGuire, "Reconfigurable Implementationof Wavelet Transform on an FPGA-Augmented NIOS Processor", IEEECanadian Conference on Electrical and Computer Engineering (CCECE ’06),Ottawa, Canada. May 2006, pp. 1052-1055.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Location Aware ComputingLocation Sensing System
Experiment and ResultsConclusions
Thank you!
Thank you!
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Block Diagram of Estimated Location
w x-X1X
w x-X2
w x-XN
1
2
N
weighted average function
wi =K(x − X i)∑Ni=1 K(x − X i)
(1)
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Software Setup
RSS
BSSID
radlocoradloco
FLOORMAP
Update MapCollect Data
x & y coordinates
stepsstart Netstumbler and load Radloco perlscript
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Software Setup
RSS
BSSID
radlocoradloco
FLOORMAP
Update MapCollect Data
x & y coordinates
stepsload map into Radloco and click on map to record data
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Software Setup
RSS
BSSID
radlocoradloco
FLOORMAP
Update MapCollect Data
x & y coordinates
stepscrickets provide ground truth coordinates
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Software Setup
RSS
BSSID
radlocoradloco
FLOORMAP
Update MapCollect Data
x & y coordinates
stepsRSS, BSSID and coordinates are saved to MySQL database
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Software Setup
stepsdata processing is performed in Matlab
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Bayesian Estimation Algorithm - 1
Minimum Mean Square Estimate (MMSE)The MMSE of the terminal location is
θ̂MMSE = E [θ|x ] =
∫S
θfΘ(θ|x)dθ (2)
The above equation can be expanded to
θ̂MMSE =
∫S
θfX ,Θ(x ,θ)
fX (x)dθ =
∫S θfX ,Θ(x ,θ)dθ
fX (x)=
∫S θfX ,Θ(x ,θ)dθ∫S fX ,Θ(x ,θ)dθ
(3)
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Bayesian Estimation Algorithm - 2
Minimum Mean Square Estimate (MMSE)
The joint approximate PDF is given by
f̂Θ,X (θ, x) =1N
(hx)−L(hθ)−2
N∑i=1
KX
(x − X i
hx
)KΘ
(θ − θi
hθ
)(4)
with K(·) being the Kernel functions for location and RSS measurements.The value L represents length of vector x .
Kernel Function
For the kernel functions K(·) we use the standard multivariate Gaussiandistribution:
KX (x) =
(1√2π
)L
exp(−1
2(xT x)
)(5)
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Bayesian Estimation Algorithm - 3
Joint approximate PDF
If we substitute the estimated PDF from Equation (4) into (3) and performintegration by substitution using u = θ − θi , we can reduce:∫
θ KΘ (θ − θi) dθ =
∫(u + θi) KU(u)du = θi (6)
since the mean of the random variable U is:∫uKU(u)du = 0
and ∫KUdu = 1
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Bayesian Estimation Algorithm - 4
Minimum Mean Square Estimate (MMSE)
The resulting estimated location θ̂ is then a weighted averagewhere the sum is taken across the weighted locations in thesubset:
θ̂ =N∑
i=1
wiθi (7)
with the weights wi for each survey point i being defined as:
wi =K(x − X i)∑Ni=1 K(x − X i)
(8)
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Kernel Width
Kernel widthSmall values of hx indicate that the RSS vectors can change radically withshort spatial displacements of the mobile device while larger values indicatethat the RSS changes significantly only with large spatial displacements.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Kernel Width
Optimal Kernel Width
two datasets are needed for training:
1 survey set - dataset A2 validation set - dataset B.
Each location in dataset B estimated using Kernel Estimator with surveydataset A, while varying the parameter hx .
The hx that produces the minimum MSE is the optimal kernel width forthe training dataset B.
In theory, we need a training set of infinite size to determine optimalkernel. Therefore optimal means best kernel given our finite datasets.
A third dataset C can be used for verification and is considered the testdataset. The set C is not used for training because it would extend thesurvey set.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Kernel Width
Cross-Validationcollecting multiple datasets may be costly and time consuming:determine the optimal kernel width hx for one dataset using across-validation approach.
MSE(h) =N∑
i=1
θi −N∑
k=1, 6=i
wkθk
T
×
θi −N∑
k=1,6=i
wkθk
(9)
remove a survey point from the survey set, then estimating the locationof the survey point using the rest of the survey points, while varying hx
values.
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Error Calculation
Explanationgreen dot = true locationred dot = estimated location
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System
Block Diagram of WeightsSoftware Setup
Estimation EquationsError Calculation
Error Calculation
Explanation
error distance =√
(px − p̂x)2 + (py − p̂y )2)
Eugene Hyun, Michael McGuire, Mihai Sima RadLoco: A Rapid and Low Cost Indoor Location-Sensing System