Indoor Localization Without the Pain Krishna Kant Chintalapudi, - - PowerPoint PPT Presentation

Foreword Algorithm Details Measuring Quality and Performance

Indoor Localization Without the Pain

Krishna 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

Foreword Algorithm Details Measuring Quality and Performance

1 Foreword

Indoor Positioning Systems EZ Localization Algorithm Related Solutions

2 Algorithm Details

Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

3 Measuring Quality and Performance

Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Indoor Positioning Systems EZ Localization Algorithm Related Solutions

What’s an IPS An Indoor Positioning System (IPS) or Indor Location System is a term used for distributed system of portable devices used to wirelessly 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. Instead

• f 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

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Indoor Positioning Systems EZ Localization Algorithm Related Solutions

Key concept of EZ approach WiFi-based indoor localization with no pre-deployment calibrations. We assume WiFi coverage but we do not assume knowledge

• f the network physical layout (e.g. APs position).

We construct RF signal model based on Received Signal Strength (RSS) measurements recorded by the mobile devices and corresponding to APs in their view. This measurements are taken at various unknown locations and reported to a localization server. Ocassionally, we obtain a location fix e.g. GPS lock at the entrance or near a window. There’s no need even for the floorplans.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Indoor Positioning Systems EZ Localization Algorithm Related Solutions

Indor localization schemes Localization in indoor robotics SLAM (Simultaneous Localization and Mapping) method building a map of the enviroment using sensors e.g.

• dometers or LADAR.

Systems relied on specialized infrastructure LANDMARC system (based on RFID). Schemes building RF signal maps

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

Model-Based Techniques TIX, ARIADNE. Ad-Hoc localization DV-Hop, DV-Dist, SPA, N-Hop.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

Figure: System overview

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

Figure: Relative position

Localizablity

”Given enough distance constraints between APs and mobile devices, it is possible to estabilish all their locations in a relative sense. Knowing the absolute locations of any three non-colinear mobile devices then allows determination of the absolute locations of the rest.” Z. Yang, Y. Liu, and

X.-Y. Li. Beyond Trilateration: On the Localizability of Wireless Ad-Hoc Networks.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

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 ith AP and jth mobile user. pi,j [dBm] - ith AP’s signal strength measured at jth mobile user.

• ci,

xj ∈ R2 - locations of the ith AP and jth mobile user. Pi - ith AP transmit power (RSS measured at a distance of 1m). γi - path loss exponent. R - a random variable that hopes to capture models imperfections.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

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 locations

• f APs and mobile users. Let m and n are numbers of APs and

mobile users respectively. Each RSS observation adds single equation to LDPL model, thus we have set of mn simultaneous

• equations. The number of unknowns is equal to 4m + 2n. If we

have enough locations, then mn > 4m + 2n and it makes the LDPL system uniquely solvable.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

Choosing the right set of RSS measuremts

Three (or more) collinear locations cannot be used in trilateration to determine an unknown location. RSS observations cannot be co-circular with respect to the AP. Even avoiding co-circular

• bservations and having

enough equations, the LDPL model don’t have to be uniquely solvable. ր

Figure: Non-localizability

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

How to ensure that LDPL system has an unique solution?

Open problem: What are the necessary and sufficient conditions under which LDPL has an unique solution? In practice we ensure following three conditions to make sure that the 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 a

full rank.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

How to tackle this set of over-determined equations?

We’re searching for a solution that minimizes the least mean absolute error (N is the number of equations): JEZ = 1 N

• i,j

|Pij − P0

i + 10γi log dij|

Optimization iterative schemes such as the Newton-Raphson

• r Gradient Descent have failed due to immense number of

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

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

Hybrid algorithm: Genetic Algorithm + Gradient Descent

1 Pick initial generation of solution randomly and refine then

using Gradient Descent.

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

fitness is estimated by computing

1 JEZ . The successive

generations 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 , Sold 2

from prevoius generation and mixing them Snew = a • Sold

1

+ ( 1 − a) • Sold

2

where a ∈ Uniform( (0, 1)U )

3 The algorithm terminates when solutions do not improve for

ten consecutive generations.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

How can we speed up solving LDPL system

If we know the floorplan we can narrow the search of the location to within the floor perimeter. We can limit AP transmission powers to (-50, 0) dBm and loss exponent γi to (1.5, 6.0). We can cut down the total number of variables from 4m + 2n to 4m. The GA has to pick only 4m unknowns related to AP parameters and the remaining 2n can be computed using trilateration. We can use already determined locations.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

How significant are receiver gain differences

There are differences in RSS measured by different mobile devices at the same location, even among devices of the same make and model. 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

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

The very first solution to gain differences problem

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

ij = Pi − G k + 10γi log dk ij + R

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

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

Relative Gain Estimation Algorithm (1)

We’re trying to estimate the difference in gain between ith and jth mobile device ∆G ij = G i − G j and the uncertainty σ(∆G ij). The difference in RSS obtained using two different mobile devices is equal to their gain difference, but only when this mesuremts were taken in the same location. But how we knew that this receivers are close to each other? Let k1 and k2 are 2 mobile devices at 2 unknown locations j1 and 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

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

Relative Gain Estimation Algorithm (2)

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

j1 = 0, pk1 2 j1 − pk1 1 j1, . . . , pk1 m j1 − pk1 1 j1

V k2

j2 = 0, pk2 2 j2 − pk2 1 j2, . . . , pk2 m j2 − pk2 1 j2 For both vectors this

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

j1 and V k2 j2 are 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

k1 j1 , px k2 j2 ) 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

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

Relative Gain Estimation Algorithm (3)

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

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

How to finally localize a new device with unknown gain

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

i2j − pk i1j = Pi2 − Pi1 + γi1 log(di1j) − γi2 log(di2j)

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

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

Picking the right subsets of APs and of unknown locations

We cannot select all APs that could be seen on a given floor because they might belong to neightbour building. Selecting all APs from our own network is still problematic because of the computational hardship. Some of the APs are seen as multiple SSIDs. During training phase we must choose the RSS mesurements taken at difreent locations.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

APSelect algorithm

APSelect The main concept of APSelect is to choose the set of RSS measurements that minimize the information overlap in the sence

• f a some similarity metric.

1 We normalize all RSS measurements pij to lie within the range

ˆ pij ∈ (0, 1).

2 Then we introduce the similarity metric

λij = 1 − 1

n

• k | ˆ

pik − ˆ pjk| and cluster the most similar clusters.

3 We iterate the clustering process till all pairs of clusters have

similarity lower than 90%. Finally we choose the clusters representatives.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Main Concept Solving the System of LDPL Equations Reducing the Search Space Differences in Receiver Gain Real World Challenges

LocSelect algorithm

LocSelect We can reuse APSelect algorithm and flip the problem by treating AP as locations and vice versa.

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions

Algorithms taken into consideration

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

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions

Small building floorplan

Figure: Small building floorplan

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions

Small building performance

Figure: Localization error CDF in small building

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions

Large building floorplan

Figure: Large building floorplan

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions

Large building performance

Figure: Localization error CDF in large building

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions

How accuracy depend on amount of training data

Figure: Dependence on amount of training data

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions

How long it takes EZ to estimate its model

# APs # mobile devs. known Lenovo T61 HP PRoline 5 50 3 65 53 5 25 3 38 22 5 12 3 16 12

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

Indoor Localization Without the Pain

Foreword Algorithm Details Measuring Quality and Performance Experiment Methodology Implementation in Small and Large Scale Dependence of Training Data Time Performance Conclusions

Thank you

Indoor Localization Without the Pain