localization of low complexity communication devices via mutual inductive coupling

Localization of Small-Scale Communications Devices viaMutual Inductive Coupling

Simone Baffelli

ETH Zurich

[email protected]

March 18, 2013

Simone Baffelli (ETHZ) Final Presentation March 18, 2013 1 / 34

Outline

1 Introduction and Motivation

2 Short Theory of Inductive Coupling

3 Problem Setting

4 Algorithm

5 Simulation Results

6 Measurements

7 Conclusions


Magnetic Positioning

Networks communicatingby mutual inductivecoupling

Advantages of MagneticLocalization

Low complexity, easyto miniaturizeBased on existingsystems (RFID)Narrowband

Potential Applications

LogisticsMedical Instruments(in vivo tracking)


State of The Art

Measurable quantities containing location information:

3D Field Vector

Requires orthogonal fieldsensors. Complex tomanufacture, esp. at smallscales

More information per singlemeasurement can beobtained

Single Axis Measurement

Simpler sensors, easier torealize

Relatively new approach,not much researchexists [1, 2]


Theory: Field of an Ideal Coil

Assumption: Coil has aideal circular shape,d ≈ 0.

In this case, we have aclosed-form expression:

d r

H

x

Br =Ca2 cos (θ)

2α2βρ2

[E(k2)]

Bθ =C

2α2β sin (θ)

[(r 2 + a2 cos (2θ)

)E(k2)

− α2K(k2)] (1)

Source [3], Image Source [4]


Theory: Inductive Coupling

Coupling measurement contains position and orientation information

Mji =Φji

Ii

Mji =∮

δCi

∮δCj

dCi ·dCj

dij

Mji ≈Bi ·Aj

Iijif dij � r

kji =Mji√LiLj

k11 k12 k13 k14 k15

k21 k22 k23 k24 k25

k31 k32 k33 k34 k35

k41 k42 k43 k44 k45

k51 k52 k53 k54 k55

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

distance on the z axis [m]

estim

ate

d k

[dim

ensio

nle

ss]

pointwise model

quasistatic model


System Model

Goal: estimate agentparameters

Anchors and Agents

Identical lowcomplexity nodesAnchor position isknown perfectly

System geometry is 5D, every node is described by a 5D vector pwhich is the concatenation [r, o]T of

3D position : r = (x , y , z)

Orientation : o = (α, β) (only two angles because of rot. symmetry)


Theory: Localization Problem Formulation

Coupling coefficient depends on position and orientation of anchorsand agents

kij = f (pi , pj)

Goal: with Na anchors, given k1j to kNaj , find a solution for pj

Problem: imprecise measurements kij = kij + e

To determine pj, minimize:

pj = argminp′j

Na∑i=1

∣∣∣kij − kij

(p′j

)∣∣∣2


Theory: Optimization Problem

pj = argminp′j

Na∑i=1

∣∣∣kij − kij

(p′j

)∣∣∣2The localization process requires to solve a nonlinear least squaresproblem, in a 5D param. space:

Many local minima existCommon nonlinear convex optimization algorithms may lead to badresults


Theory: Optimization Problem

−2 0 2−2

−1

0

1

2

x [m]

y [

m]

−25

−20

−15

−10

Unweighted

−2 0 2−2

−1

0

1

2

x [m]

y [

m]

−25

−20

−15

−10

Weighted

For certain configuration, cost function is very flat:Flat gradient, possible convergence problems

Weight the cost function

pj = argminp′j

Na∑i=1

∣∣∣wi

(kij − kij

(pj

′

))∣∣∣2Equalize contributions of all anchors using wi = d

′ij

n(Distance from

trial pos.)0ptimal n between 2 and 3


Theory: Optimization Algorithms

−2 0 2−2

−1

0

1

2

x [m]

y [

m]

−25

−20

−15

−10

non convex

−2 0 2−2

−1

0

1

2

x [m]

y [

m]

−25

−20

−15

−10

convex

Possible approaches to solve non-convex optimization:Global Approaches:

Direct Monte Carlo sampling of the parameter space (inefficient)Simulated Annealing

Approaches based on assumption of local convexity:Restrict to assumedly convex region around the optimum and use aconvex optimization method

Our choice: Exhaustive/MC initialization, refine using convexoptimization method.


Theory: Distance Bound

The coupling coefficient gives a implicit lower bound for the distance:

kij ≈Bi · Aj

Ii√

LiLj6

C−S

‖Bi‖‖Aj‖Ii√

LiLj=‖Bi‖Aj

Ii√

LiLj

Because of rotationalsymmetry, consider asingle angle:

kij (dij , θ) 6‖Bi (dij , θ)‖Aj

Ii√

LiLj


Theory: Distance Bound

Desired: upper bound for dij , eliminate θ by maximization

kij (dij , θ) 6 maxθ

‖Bi (dij , θ)‖Aj

Ii√

LiLj

Using a LUT, look for the maximum dij given kij

The intersection of balls contains the agent

0 2 4 6 8 10 12 14 1610

−10

10−8

10−6

10−4

10−2

100

102

dij[m]

k [dim

ensio

nle

ss]

Upper bound, θ max

α = π/6, β = π/4, θ = π/4

Coupling

−2 0 2−2

−1

0

1

2

x [m]

y [

m]

−25

−20

−15

−10

Search Region


Simulation Parameters

Simulation parameters:

Coil radius r = 0.05mBox of 4 meters per side.N = 10 turnsAnchors and agents distributed uniformly within box, random o

Figure of merit: norm of the distance, epos :

epos = ‖r − r‖

FoM does not consider orientation:

depending on application, may consider o too


Simulations: Performance Comparison

Compare performance of localization algorithm

Ideal, noiseless case

Na = 7

1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

position error [m]

Pro

babili

ty

Performance Comparison

Exhaustive Search

ReducedEx+Convex

Red+Convex

Linear Scale

10−5

10−4

10−3

10−2

10−1

100

0

0.2

0.4

0.6

0.8

1

position error [m]P

roba

bili

ty


Log Scale

Best case, 20 % outliers

Ball intersection slighlty better, Higher density


Simulations: Influence of Anchors

Compare performance with different number of anchors

1 2 3 4 5 60.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

position error [m]

Pro

babili

ty

CDF of localization error

Reduced + Convex

Exhaustive + Convex

Linear Scale

10−5

10−4

10−3

10−2

10−1

100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

position error [m]

Pro

babili

ty


Num

ber

of A

nchors

5

10

15

20

Log Scale

Dramatic improvement increasing the number of anchors

Smoother cost function?

From now on, we will use Na = 14


Simulations: Performance Under Gaussian Noise

SNR = 10 log10

(Var[kij ]

σ2

)k = k + e, e ∼ N

(0, σ2

)Two saturation zones

Noise limited and ”convexity limited” cases

0 20 40 60 80 1000

0.5

1

1.5

2

2.5

3

3.5

4

SNR [dB]

RM

SE

positio

nin

g e

rror

[m]

RMSE vs SNR

RMSE

10−5

10−4

10−3

10−2

10−1

100

101

0

0.2

0.4

0.6

0.8

1

position error[m]

pro

babili

ty


SN

R

−50

0

50

100

Log Scale


Simulations: Truncation Model

Model systematic measurement errors

Assume the measured quantity to be known within specific tolerancebounds:

kij γ = emax

e ∼ U(−

emax

2,

emax

2

)kij = kij + e

This model represents a measurement with a given tolerance γ :

k

γ = 0.00499

k

γ = 0.05

k

γ = 0.25


Simulations: Performance Under Reduced Precision

Acceptable performance even at higher tolerance values

Estimating the order of magnitude of k sufficent for reasonable results

0 0.1 0.2 0.3 0.4 0.50

0.1

0.2

0.3

0.4

0.5

tolerance γ

RM

SE

positio

nin

g e

rror

[m]

RMSE vs Noise

RMSE

10−5

10−4

10−3

10−2

10−1

100

101

0

0.2

0.4

0.6

0.8

1

position error [m]

pro

babili

ty

Empirical CDF

γ

0

0.1

0.2

0.3

0.4

0.5

Log Scale


Simulations: Tracking

Follow a 5D trajectory, γ = 0.05

Search ball around previous estimate,use previous information

Similar performance with 164 of the

points

−2

2 −2

2

−1

y [m]x [m]

z [m

]

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

time index

Dis

tance [m

]

RMSE Evolution For Tracking

Tracking, n= 125

resetExhaustive n = 8000

Exhaustive n = 125

RMSE


Measurements

Measurement: Fingerprinting methodMeasure impedance Zin (f , k)

Calibration measurement: frequency response Zcal (f ) as a function ofheight zSimulate ksim for zGiven: Zmeas (f ), find argmin

zmin

|Zmeas (f ) − Zcal (f )|

k = ksim (zmin)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

horizontal displacement [m]

k [dim

ensio

nle

ss]

Exact QS

Measured QS

Exact Pointwise

Measured Pointwise


Measurements

Tag moved with converted CNC router

Measure Zin using HP VNA

Tag and Reader Measurement Hardware


Measurements

Most estimates converge to the closest anchor

Overestimation of k leads to shorter distances than expected

300 350 400200

220

240

260

280

300

300 350 400200

220

240

260

280

300

300 350 400200

220

240

260

280

300

300 350 400200

220

240

260

280

300

−6 −5 −4 −3 −2 −1 0

log10

(k)

0.1944

0.4609 0.1116

0.3913

−0.5

0.5

y [m]

RMSE:0.10354

x [m]

z [m

]

Localization Results


Conclusion and Outlook

Detailed investigation of localization using mutual inductive coupling

Secondary use of existing infrastructure for low complexity nodes

Results are promising but optimization problems cause outliers

Improvement of algorithms seems possible in future work

Measurements

Measure k without access to the agent (Mobility)Adaptable to different models for kIncrease mutual inductance to observe visible changes in Zin

Possible extension to multiple agents

Tested, not investigated in detail


H. Li, G. Yan, P. Jiang, and P. Zan, “A portable electromagnetic localizationmethod for micro devices in vivo,” in Automation Congress, 2008. WAC2008. World, 28 2008-oct. 2 2008, pp. 1 –4.

V. Schlageter, P.-A. Besse, R. Popovic, and P. Kucera, “Tracking systemwith five degrees of freedom using a 2d-array of hall sensors and a permanentmagnet,” Sensors and Actuators A: Physical, vol. 92, no. 1-3, pp. 37 – 42,2001. [Online]. Available:http://www.sciencedirect.com/science/article/pii/S0924424701005374

J. Simpson, J. Lane, C. Immer, R. Youngquist, and T. Steinrock, “Simpleanalytic expressions for the magnetic field of a circular current loop,” NASA,Tech. Rep., 2001.

K. Finkenzeller, RFID Handbook: Fundamentals and Applications inContactless Smart Cards and Identification, 2nd ed. New York, NY, USA:John Wiley & Sons, Inc., 2003.


http://www.sciencedirect.com/science/article/pii/S0924424701005374

CDF of the Localization Experiment

10−5

10−4

10−3

10−2

10−1

100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

position error [m]

pro

babili

ty


Quasistatic Model

10−5

10−4

10−3

10−2

10−1

100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

position error [m]pro

babili

ty


Pointwise Model


Cost Function For Different Numbers of Anchors

−2 0 2−2

−1

0

1

2

x [m]

y [

m]

−25

−20

−15

−10

20 Anchors

−2 0 2−2

−1

0

1

2

x [m]

y [

m]

−25

−20

−15

−10

7 Anchors


CDF For Tracking

1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

x

F(x

)

Empirical CDF

Tracking, n= 125

Exhaustive n = 8000

Exhaustive n = 125

Linear Scale

10−5

10−4

10−3

10−2

10−1

100

0

0.2

0.4

0.6

0.8

1

x

F(x

)

Empirical CDF

Log Scale


Simulations: Performance Comparison, Na = 14

1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

position error [m]

Pro

ba

bili

ty


Exhaustive SearchReduced

Ex+ConvexRed+Convex

Linear Scale

10−5

10−4

10−3

10−2

10−1

100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

position error [m]

Pro

babili

ty


Log Scale


Simulations: Performance Comparison, 2D Na = 4

1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

position error [m]

Pro

babili

ty


Exhaustive Search

ReducedEx+Convex

Red+Convex

Linear Scale

10−5

10−4

10−3

10−2

10−1

100

0

0.2

0.4

0.6

0.8

1

position error [m]

Pro

babili

ty


Log Scale


Tracking and Distance

0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

time index

dis

tan

ce

[m

]

∣

∣ri− r

i+1∣

∣

Tracking RMSE


Bound: Correlation Between Measured And Real Radius

0 1 2 3 40

1

2

3

4

5

6

exact radius [m]

estim

ate

d r

ad

ius [

m]

5D, Na = 7

0 1 2 3 40

1

2

3

4

5

6

exact radius [m]

estim

ate

d r

ad

ius [

m]

2D, Na = 4


Simulations: Optimal weighting exponent

Choose n = 2 because of better convergence at realistic scales

2 4 6 8 100.9

0.92

0.94

0.96

0.98

1

position error [m]

Pro

babili

ty


unweightedw

ij=r

wij=r

2

wijr3

wij=r

4

wij=r

5

wij=r

6

Linear Scale

10−5

10−4

10−3

10−2

10−1

100

101

0

0.2

0.4

0.6

0.8

1

position error [m]

Pro

babili

ty


unweightedw

ij=r

wij=r

2

wijr3

wij=r

4

wij=r

5

wij=r

6

Log Scale


Simulations: Number of Anchors

5 10 15 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

number of anchors

RM

SE

[m

]

RMSE

5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

number of anchors

P1

mm

Reduced + Convex

Exhaustive + Convex

Probability of |r − r| 6 1mm


localization of low complexity communication devices via mutual inductive coupling

Education

wi kij kij pj

kij eto

d rhxbr

d param

imprecise measurements

d vector pwhich

concatenation r

ot of3d position