INDOOR LOCALIZATION BASED ON MULTIPATH FINGERPRINTING

M.Sc. work by Evgeny KupershteinSupervisors: Prof. Israel Cohen and Dr. Mati Wax14 April 2013

Talk Outline

1. Introduction

2. Location Fingerprinting Techniques

3. Single-site Localization via Multipath Fingerprinting

4. Conclusion

2

Introduction1

Motivation

People spend most of their active time indoors. GPS signal is unavailable

There is a growing interest in indoor position location. Location Based Services (LBS).

No good indoor position location technology is available yet. High-accuracy, easily deployable, low-

cost.

Time spent

People spend 80-90% of their time indoors.(Source Strategy Analytics)

4

Location Based Services (LBS)

Pedestrian navigation Location based advertising / marketing Asset tracking Location based analytics Public safety / emergency response (E911) Location based social networking / check-inns Location based actuation / notification Location based search / content Friends /people finding Geofencing/Geotaging (photos, etc)

5

Current Status

Current alternative GPS technologies do not meet the requirements of the industry, i.e., being low-cost, high-accuracy, easily deployable,

and without additional hardware in user equipment.

Location Fingerprinting techniques have been recentlydeveloped to overcome these problems.

6

The classical position location technique, like DOA, TOA, DTOA, are not valid in indoor, where LOS conditions do not exist.

IEEE SIGNAL PROCESSING MAGAZINE (July 2005)

Location Fingerprinting Techniques

2

Location Fingerprinting (LF)

LF is based on the premise that there is a one-to-onerelation between the characteristics of the receivedsignals and the emitter location.

Signal characteristics, known as “fingerprints”, used by LFtechniques are:

Received Signal Strength (RSS), Channel Impulse Response (Power Delay Profile) Direction of Arrival (DOA), Time Difference of Arrival (TDOA) etc.

8

Location Fingerprinting Diagram9

Off-Line Phase:

Training

On-Line Phase:

Locating

LF Classification Techniques

LF can be considered as a pattern recognition problemand numerous machine learning techniques can beapplied to this problem:

Probabilistic Methods: Bayesian, MMSE, MDM classifiers.

Nearest Neighbor Classifier.

Support Vector Machine.

Artificial Neural Networks.

10

Limitations of existing LF techniques11

Fingerprint instability caused by multipath and irrelevant environmental parameters.

Fingerprint ambiguity caused by ambiguity inherent in the physical environment.

For an acceptable accuracy, multiple overlapping base stations (BS) are required at each database point.

The achieved accuracy, usually 5-10m, is still insufficient for LBS.

3 Single-Site Emitter Localization via Multipath Fingerprinting

Current Multipath Fingerprinting Techniques

Spatial fingerprint*

The directions-of-arrival (DOAs) of the multipath rays. Requires a wide antenna array for good resolution. Captured by the array covariance matrix.

Temporal fingerprint*

The delays and relative powers of the multipath rays. Requires wide bandwidth for good resolution. Captured by the impulse response/power delay

profile.

* Developed by Wax et al. , US Patents issued in 2000-2001

13

Our Contributions14

A novel and powerful fingerprint based on the spatial-temporal covariance matrix was proposed Exploits both the DOA and the differential-delays of the multipath signals. Exploits only dominant reflections. Computationally efficient. Powerful similarity-profile matching criterion.

Necessary and sufficient conditions that guarantee unique localization were presented.

Frequency domain approach to the multipath fingerprinting using signal subspace was developed.

Applicability of this method to localization using the array channel impulse response (CIR) or frequency response (CFR) was shown.

The technique was tested with simulated and real data in indoor environments.

The manuscript based on this thesis was published in the IEEE Transactions on Signal Processing, January 2013.

Problem Formulation: propagation model

An arbitrary array composed of p sensors receives a widebandsignal s(t) impinging on the array through q reflections withdelays τ1,…,τq and corresponding directions θ1,…,θq.

15

TOA (ns)AO

A (

)

0 100 200 300 400 500 6000

50

100

150

200

250

300

350Power (dBm)

-100

-95

-90

-85

-80

-75

Problem Formulation: sampled signal16

The outputs of the antenna array are sampledsimultaneously at N times (“taps"), with an interval ofD=1/BW seconds:

The received signal at the i-th sensor, can be expressed as

1

c i k

qj

i k i k k ik

x t D t a s t D e n t D

1x t 1x t D 1 1x t N D

px t px t D 1px t N D

Problem Formulation: the data structure17

1 0x 1 1x N 1 2x N 1 1x

2 0x 2 1x N 2 2x N 2 1x

0px 1px N 2px N 1px

The “snapshot” vector , combined fromvectors , can be expressed as

where

p tx

1

2

tt

xx

tx

t t t x Aγ n

1 1 , , q qt t A = a s a s

1pN tx i tx 1, ,i p

Span{A}=Spatial-temporal Signal Subspace = Fingerprint

1 0x

1 1x

1 1x N

2 0x

2 1x N

0px

1px N

pN q 1q

1p 1N

Problem Formulation18

The snapshot sampled at time t is given by

where

Span{A}=Spatial-temporal Signal Subspace = Fingerprintand

t t t x Aγ n

1 1 , , q qt t A = a s a s

11

1

, ,

, , 1

, ,

c p kc kTjj

k k p k

T

i i i

T

q

a e a e

t s t s t N D

t t t

a

s

γ

How to Extract the Spatial-Temporal Fingerprint?

19

The Problem: DOA estimation of the multipath signals is

computationally intensive since the multipath signals are coherent. Requires multi-dimensional non-linear maximization (Ziskind-

Wax (1988)). The simpler one-dimensional maximization MUSIC algorithm is

applicable only to uniform linear and circular arrays (Shan-Wax-Kailath (1985), Wax-Sheinvald (1994)).

In typical scenarios the number of multipath rays may be larger than the array dimension, making all the parametric methods void.

The solution: Use a computationally simpler entity – the signal

subspace - as the basis for the fingerprint.

1x t

2x t

3x t

1a

2a 3tx 2tx

1tx

Note that snapshots stay in the 2-dimensional subspace spanned by

The Signal Subspace Example20

For a 3-antenna array, 2-ray multipath:and a single tap (space only), we have

where are the “steering vectors” of the array.

1 1 1 2 2 2t s t t s t t t x a a n

1 1 1 2 2 2, , , , ,

1 2 . a a and

1 2 a a and

itx

Assumptions21

The antenna array is sampled M-times at {tm}, m=1,…,M,forming M snapshots.

The signal is identical for all snapshots.

The directions-of-arrival and the differential-delays of the multipath reflections are identical for all the M snapshots.

Propagation coefficients of reflections γk are fixed during the snapshot, but may vary from snapshot to snapshot.

All noise samples are assumed to be i.i.d. Gaussian random variables with μ=0 and unknown variance 2.

The Similarity Metric22

Maximum Likelihood Estimator of the emitter location i

Maximization with respect to , yields

where

and

2

2

22, 1, ; , 1

1 1ˆ arg max expdeti

M

m i mpNi K m

i t t

ΓAx A γ

I

21 , , Mt t Γ γ γ and

2

, 1, , 1,1

ˆˆ arg max arg maxi i

i i

M

mi K i Km

i t Tr

A AA A

P x P R

1H HAP A A A A

1

1ˆM

Hm m

mt t

M

R x x

Projection Matrix Sample-covariance Matrix

Estimating the Signal Subspace23

The expected value of is given by

where

Assuming that the matrix has full rank it can be easily verified that

where are eigenvectors of , corresponding to the first dominant eigenvalues.

R̂

2H HE t t ΣR x x A A I

HE t t Σ γ γ

q q Σ

qSpan SpanA V

1, ,q q V v v Rq

1ˆ H Hq q q q

AP V V V V

Estimating the Signal Subspace24

Estimation of the projection matrix of the i-th location is carried out as follows1. Calculate the sample-covariance matrix of location i by

2. Perform an eigenvalue decomposition of

3. Estimate the signal subspace dimension .

4. Select the first eigenvectors of corresponding to the signal subspace:

5. Estimate the projection matrix by

ˆiR

1

1ˆL

Hl l

lt t

L

R x x

iP

ˆ .iRq̂

q̂ ˆiR

ˆ ˆ1, , .q q V v v

1

ˆ ˆ ˆ ˆˆ .H Hi q q q q

P V V V V

Signal Subspace Dimension Estimation25

The dimension of the signal subspace is equal to the number of impinging multipath signals q.

We want to capture only dominant reflections.

The solution: select q as the number of large eigenvalues that contain, say, α = 90% of the signal’s energy

A typical eigenvalue profile of the signal covariance matrix

1

1

ˆ min , . . 1, 2, ,

Q

iipN

ii

q Q s t Q pN

Conditions for Unique Localization26

The M snapshots of the vector taken atcan be expressed as

whereand

An array can uniquely localize sources havingreflections if

2pN rank

q

Γ

, ,

, ,

Γ Γ

Γ

X = A A

for everyi.e.

and any set of

tx 1, , Mt t

, ΓX = A

1 1, , , ,M Mt t t t Γ X = x x γ γ and 1 1, , , , , .q q = =

q pN

Simulation environment27

Similarity-Profile (SP) 28

0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

80

X (m)

Y (m

)

y

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Real Location

Potentially Ambiguous

Location

ˆjTrace P R

R̂

Similarity-Profile Matching Criterion 29

The SP of the i-th location in the database is defined by

The query SP obtained from the received signals

The localization is carried out by

1ˆ ˆ, ,i i K iTr Tr f P R P R

1ˆ ˆ, , KTr Tr f P R P R

2

21,

ˆ arg min ii K

i

f f

Algorithm Optimization30

where

Now, using the Cholesky Decomposition:

we get

For the last formulation provides significant computational and storage savings!

22

2 2

H Hi i i i f f P r r r r P P r r

ˆ ˆi ivec vec r r R R 1 , ,

TT TKvec vec P P P

H HP P GG

2

20,

ˆ arg min Hi

i Ki

G r r 2K pN

2K pN

2 2pN pN

Simulation Results: SP vs ML31

802.11g (Wi-Fi)

8 taps (N=8)

BW=20MHz

SNR:0-60dB

Grid Step:1m

ML Maximum Likelihood

0 1 2 3 4 5 6 7 80

102030405060708090

100

Error (m)

Perc

ent o

f loc

atio

ns (%

)

CDF of position location error

SP, 6 antSP, 3 antSP, 1 antML, 6 antML, 3 antML, 1 ant

Simulation Results: subspace dimension32

6 antennas

BW=20MHz

0 1 2 3 4 5 6 7 8 9 10 11 120

10

20

30

40

50

Subspace dimension

Perc

ent o

f loc

atio

ns (%

)

Signal subspace dimension distribution

8 taps4 taps2 taps1 tap

Simulation Results: tap influence33

6 antennas

BW=80MHz

0 1 2 3 4 5 6 7 80

102030405060708090

100

Error (m)

Perc

ent o

f loc

atio

ns (%

)

CDF of position location error

8 taps4 taps2 taps1 tap

Real Data Experiment34

Office floor 33×33×5m.

802.11g Wi-Fi access point with 6-antenna uniform circular array.

BW=20MHz.

Database grid step:0.5m

Emitter: laptop.

X (m)

Y (m

)

0 5 10 15 20 25 300

5

10

15

20

25

30

Database grid.

Antenna array:

Simulation Results: Real Data35

6 antennas

8 taps

BW=20MHz

0 1 2 3 4 5 6 7 80

102030405060708090

100

Error (m)

Perc

ent o

f loc

atio

ns (%

)

CDF of position location error

ExperimentSimulation

Conclusion4

Summary

We have presented a new localization method that Enables single-site localization of wireless emitters in a

rich multipath environments. Achieves good localization accuracy of about 1m in typical

indoor environments. Applicable to modern communication technologies, like

WLAN and 3G/4G, supported by most modernsmartphones, tablets, laptops and etc.

Does not require new hardware in user equipment.

The presented technique is a promising candidate for providing high quality, cost-effective and ubiquitous localization in indoor environments.

37

gskuper@gmail.com

Thank You!38

Appendix39

It can be shown that baseband noise is Decoupled Circular Gaussian Process. Hence, because of independence of noise in different antennas of the array, for each time instance is complex jointly-Gaussian circularly symmetric random vector.

The probability density of circularly-symmetric Gaussian vectors is defined as

whereis a circularly-symmetric jointly-Gaussian complex

random vector completely determined by its covariance matrix

For more details, see “R. G. Gallager. Circularly-symmetric Gaussian random vectors. January 1, 2008”.

, ,c LPF s LPFn t n t jn t

1 ,...,i i p it n t n tn

11 expdet

HZ Zn

Z

f z z K zK

1 2, ,..., TnZ Z ZZ

*, H H TZK E where ZZ Z Z