indoor localization without the pain - krishna kant chintalapudi

ForewordAlgorithm Details

Measuring Quality and Performance

Indoor Localization Without the PainKrishna Kant Chintalapudi, Anand Padmanabha Iyer,

Venkata N. Padmanabhan

Presentation by Adam Przedniczek

2011-10-19

This presentation was based on the publication Indoor Localization Without the Pain by

Krishna Kant Chintalapudi, Anand Padmanabha Iyer and Venkat Padmanabhan, MobiCon ’10 .

Indoor Localization Without the Pain



1 ForewordIndoor Positioning SystemsEZ Localization AlgorithmRelated Solutions

2 Algorithm DetailsMain ConceptSolving the System of LDPL EquationsReducing the Search SpaceDifferences in Receiver GainReal World Challenges

3 Measuring Quality and PerformanceExperiment MethodologyImplementation in Small and Large ScaleDependence of Training DataTime PerformanceConclusions




Indoor Positioning SystemsEZ Localization AlgorithmRelated Solutions

What’s an IPS

An Indoor Positioning System (IPS) or Indor Location System is aterm used for distributed system of portable devices used towirelessly localize people and objects inside an indoor space.Due to the signal attenuation caused by construction materials,inside the buldings we cannot rely on the sattelite signal. Insteadof using GPS, one can make use of such indoor features as e.g.ambient sound, light/color or WiFi signal.

IPS applications

Augmented reality

Targeted advertising

Store navigation and airport maps

Guided tours of museums





Key concept of EZ approach

WiFi-based indoor localization with no pre-deploymentcalibrations.

We assume WiFi coverage but we do not assume knowledgeof the network physical layout (e.g. APs position).

We construct RF signal model based on Received SignalStrength (RSS) measurements recorded by the mobile devicesand corresponding to APs in their view. This measurementsare taken at various unknown locations and reported to alocalization server.

Ocassionally, we obtain a location fix e.g. GPS lock at theentrance or near a window.

There’s no need even for the floorplans.





Indor localization schemes

Localization in indoor roboticsSLAM (Simultaneous Localization and Mapping) methodbuilding a map of the enviroment using sensors e.g.odometers or LADAR.

Systems relied on specialized infrastructureLANDMARC system (based on RFID).

Schemes building RF signal maps

Calibration-intensive: RADAR, Horus, SurroundSense.Assuming a very dense WiFi deployment: DAIR.

Model-Based TechniquesTIX, ARIADNE.

Ad-Hoc localizationDV-Hop, DV-Dist, SPA, N-Hop.




Main ConceptSolving the System of LDPL EquationsReducing the Search SpaceDifferences in Receiver GainReal World Challenges

Figure: System overview





Figure: Relative position

Localizablity

”Given enough distance constraints between APs and mobile devices, it ispossible to estabilish all their locations in a relative sense. Knowing theabsolute locations of any three non-colinear mobile devices then allowsdetermination of the absolute locations of the rest.” Z. Yang, Y. Liu, andX.-Y. Li. Beyond Trilateration: On the Localizability of Wireless Ad-Hoc Networks.





Measuring distance from Received Signal Strength (RSS)

pi ,j = Pi − 10γi log di ,j + R

di ,j =√

(~xj − ~ci )T (~xj − ~ci )

di ,j [m] - distance between i th AP and j th mobile user.pi ,j [dBm] - i th AP’s signal strength measured at j th mobile user.~ci , ~xj ∈ R2 - locations of the i th AP and j th mobile user.Pi - i th AP transmit power (RSS measured at a distance of 1m).γi - path loss exponent.R - a random variable that hopes to capture models imperfections.





How di ,j can be computed in Log-Distance Path Loss model?

If the Pi and γi are given, di ,j can be computed as follows:

di ,j = 10(Pi−pi,j

10γi)

A novel approach of EZ algorithm

We DO NOT assume the a priori knowledge of Pi and γi !!!We threat them as unknowns in addition to the unknown locationsof APs and mobile users. Let m and n are numbers of APs andmobile users respectively. Each RSS observation adds singleequation to LDPL model, thus we have set of mn simultaneousequations. The number of unknowns is equal to 4m + 2n. If wehave enough locations, then mn > 4m + 2n and it makes theLDPL system uniquely solvable.





Choosing the right set of RSS measuremts

Three (or more) collinearlocations cannot be used intrilateration to determine anunknown location.

RSS observations cannot beco-circular with respect tothe AP.

Even avoiding co-circularobservations and havingenough equations, the LDPLmodel don’t have to beuniquely solvable. ↗ Figure: Non-localizability





How to ensure that LDPL system has an unique solution?

Open problem: What are the necessary and sufficient conditionsunder which LDPL has an unique solution?In practice we ensure following three conditions to make sure thatthe LDPL can be uniquely solved:

1 Each unknown location must see at least 3 APs.

2 Each AP must be seen from at least 5 locations.

3 The Jacobian of the system of LDPL equations must have afull rank.





How to tackle this set of over-determined equations?

We’re searching for a solution that minimizes the least meanabsolute error (N is the number of equations):

JEZ =1

N

∑i ,j

|Pij − P0i + 10γi log dij |

Optimization iterative schemes such as the Newton-Raphsonor Gradient Descent have failed due to immense number ofJEZ local minima.

Simulated annealing and genetic algorithms (GA) also failed,because they can miss some local minima.





Hybrid algorithm: Genetic Algorithm + Gradient Descent

1 Pick initial generation of solution randomly and refine thenusing Gradient Descent.

2 Let U be the number of all unknowns. Solutions S ∈ RU

fitness is estimated by computing 1JEZ

. The successivegenerations evolves as follows:

We retain 10% of solutions with the highest fitness.We add 10% randomly generated solutions (refined using GD).20% of solutions are perturbated based mutations.60% are derived by picking 2 solutions Sold

1 ,Sold2 from prevoius

generation and mixing them Snew = ~a • Sold1 + (~1−~a) • Sold

2

where ~a ∈ Uniform( (0, 1)U )

3 The algorithm terminates when solutions do not improve forten consecutive generations.





How can we speed up solving LDPL system

If we know the floorplan we can narrow the search of thelocation to within the floor perimeter.

We can limit AP transmission powers to (-50, 0) dBm andloss exponent γi to (1.5, 6.0).

We can cut down the total number of variables from 4m + 2nto 4m. The GA has to pick only 4m unknowns related to APparameters and the remaining 2n can be computed usingtrilateration.

We can use already determined locations.





How significant are receiver gain differences

There are differences in RSS measured by different mobile devicesat the same location, even among devices of the same make andmodel.

Mobile device RSS [dBm]Laptop Xenovo X61 -41

HP IPAQ #1 -43

HP IPAQ #2 -31

Samsung SGHi780 #1 -51

Samsung SGHi780 #2 -49

HTC ADV7510 -49

HTC ADV7501 -37

Table: Gain differences across tested devices





The very first solution to gain differences problem

For each user we can simply introduce an unknown parameter Gthat corresponds to the receiver gain.

pkij = Pi − G k + 10γi log dk

ij + R

The G k value is estimated using genetic algorithm with narrowingthe search space to a generous span (-20, 20) dB.But there’s a better way ...





Relative Gain Estimation Algorithm (1)

We’re trying to estimate the difference in gain between i th

and j th mobile device ∆G ij = G i − G j and the uncertaintyσ(∆G ij).

The difference in RSS obtained using two different mobiledevices is equal to their gain difference, but only when thismesuremts were taken in the same location. But how weknew that this receivers are close to each other?

Let k1 and k2 are 2 mobile devices at 2 unknown locations j1and j2. We have their RSS measurents from m APs:Qk1

j1= 〈pk1

1 j1, pk1

2 j1, . . . , pk1

m j1〉 Qk2

j2= 〈pk2

1 j2, pk2

2 j2, . . . , pk2

m j2〉






We transform both vectors by subtracting from all its elementstheir very first item: V k1

j1= 〈0, pk1

2 j1− pk1

1 j1, . . . , pk1

m j1− pk1

1 j1〉

V k2j2

= 〈0, pk22 j2− pk2

1 j2, . . . , pk2

m j2− pk2

1 j2〉 For both vectors this

differences are independent of its receiver gain. Thus, ifvectors V k1

j1and V k2

j2are close to each other, then we can

assume that j1 and j2 are proximate.Then we can create a set Mk1k2 of RSS measurements pairs(px

k1j1, px

k2j2

) at proximate locations. Now, we can state:

∆G k1k2 =1

|Mk1k2 |∑

(p1,p2)∈Mk1k2

(p1 − p2)

σ(∆G k1k2) =1

|Mk1k2|

√ ∑(p1,p2)∈Mk1k2

(p1 − p2 −∆G k1k2)2






We compute ∆G ij and σ(∆G ij) for every pair of mobiledevices whenever it’s possible.Some mobile devices might not have even a single pair ofmeasurements in proximate location. In such cases we can usethe transitivity property: ∆G ij = ∆G ik + ∆G kj .Finally, we build graph with mobile devices in nodes. The 2nodes are connected if and only if they have at least a singlemeasurement at proximate location. In each connectedcomponent we randomly choose root node and assign its gainby sampling uniformly randomly in the interval (-20, 20) dB.Gains for the rest of nodes from this component are computedby solving set of equations of the form G j − G i = ∆G ij in aweighted least mean square sence with weights set toσ(∆G ij).





How to finally localize a new device with unknown gain

Beacuse we don’t know the gain of the new mobile device, wemust rebuild our set of equation to the gain-independent form:

pki2j − pk

i1j = Pi2 − Pi1 + γi1 log(di1j)− γi2 log(di2j)

The location of the new device is derived by solving set of suchsimultaneous equations in a least mean square sense.





Picking the right subsets of APs and of unknown locations

We cannot select all APs that could be seen on a given floorbecause they might belong to neightbour building.

Selecting all APs from our own network is still problematicbecause of the computational hardship.

Some of the APs are seen as multiple SSIDs.

During training phase we must choose the RSS mesurementstaken at difreent locations.





APSelect algorithm

APSelect

The main concept of APSelect is to choose the set of RSSmeasurements that minimize the information overlap in the senceof a some similarity metric.

1 We normalize all RSS measurements pij to lie within the rangep̂ij ∈ (0, 1).

2 Then we introduce the similarity metricλij = 1− 1

n

∑k |p̂ik − p̂jk | and cluster the most similar clusters.

3 We iterate the clustering process till all pairs of clusters havesimilarity lower than 90%. Finally we choose the clustersrepresentatives.





LocSelect algorithm

LocSelect

We can reuse APSelect algorithm and flip the problem by treatingAP as locations and vice versa.




Experiment MethodologyImplementation in Small and Large ScaleDependence of Training DataTime PerformanceConclusions

Algorithms taken into consideration

EZ

EZ + Loc (EZ with known AP locations and measurements)

RADAR

Horus





Small building floorplan

Figure: Small building floorplan





Small building performance

Figure: Localization error CDF in small building





Large building floorplan

Figure: Large building floorplan





Large building performance

Figure: Localization error CDF in large building





How accuracy depend on amount of training data

Figure: Dependence on amount of training data





How long it takes EZ to estimate its model

# APs # mobile devs. known Lenovo T61 HP PRoline5 50 3 65 53

5 25 3 38 22

5 12 3 16 12

Table: Time of building the RF model (given in minutes)





Thank you


indoor localization without the pain - krishna kant chintalapudi

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