The document discusses location-based services and applications that utilize positioning systems. It describes several types of location-based services that are emerging, such as navigation assistance, geo-social networking, personalized advertising, and industrial monitoring. It also outlines key components of positioning systems, including network architecture, node interaction methods for measuring location like power profiling and angle of arrival, and sources of errors in indoor positioning.

1. Positioning in Wireless Networks
- Non-cooperative and Cooperative Algorithms -
Giuseppe Destino
Centre for Wireless Communications
University of Oulu
October 12, 2012
1

2. Location-Based Service Market
- Toward context-awareness -
Reveneu
PyramidResearch Forecasts 2008-2015
2

3. Location-Based Service Market
- Toward a pervasive platform -
Navigation devices
PyramidResearch Forecasts 2008-2015
3

4. Geo-Social Network
- Location and information sharing -
• Find your friend
• Get direction
• Information sharing
4

5. Shopping
- Personalized Advertising -
• Real-time sale
• Indoor navigation
• Find objects
• Information sharing
5

6. Smart and Safe Navigation
- In-car augmented reality -
• Navigation
• Localization of accidents
• Alert
• Information sharing
6

7. Industrial Monitoring
- Safety and Security -
• Monitoring of the environment
• Tracking of personnel
• Tracking of assets
7

8. ... and Many Others
• Health-care: remote monitoring, find personnel, track assets, etc.
• Indoor-sport: person tracking
• Indoor navigation: get directions, estimate travel time, etc.
• Sensor networks: measurement maps
• Surveillance: detect intruder, anomaly localization, etc.
• Warehouse: asset tracking and monitoring
8

9. Location-aware Network Optimization
9

10. Network Planning and Expansion
• Location-based RSS map
• Use mobile nodes for monitoring
• Adaptive network expansion
10

11. Cognitive Radio in the TV-White Space
• Location-based primary user database
• Allocate free TV-white space based on location information (FCC’ 10)
• 50 m, minimum distance between primary and secondary users
11

12. Positioning System
12

13. System Architecture
System Centric Node Centric
• Measurements convey to the • Measurements convey to the
radio access network mobile nodes
• Centralized calculations • Local calculations
13

14. Network
Nodes
• NA anchors, known fixed location A4 A3
• NT targets, unknown location
Topology
X
• Star-like, non-cooperative scheme
• Mesh, cooperative scheme
Syncronization
A1 A2
• Global, synchronous
• Local, asynchronous
14

15. Internode Interaction
- Measurement system -
Power Profile
• Channel Impulse Response (CIR), wideband signal
• Power Delay Profile (PDP), wideband signal
Angle
• Angle-of-Arrival (AoA), multiple-antenna
Distance (Ranging)
• Received Signal Strength Index (RSSI), always available
• Time-of-Arrival (ToA), technology dependent, asynchronous network
• Time-Difference-of-Arrival (TDoA), technology dependent, synchronous
network
15

16. Source of Errors
- Example of an indoor propagation channel -
S-V Indoor Propagation Model
III-A we will see, from another point
5: 300 ns.
Room 1 Room 3
Rate, X
individual rays in about 200 power
ts similar to those in Figs.3 and 4, we
in the range of 5-10 ns. The range
rom the• Noise our ray-resolving al-
fact that
with our • Multipaths sensitivity, is
measurements Room 2 Room 4
ny weak rays, in particular, those fall-
• Blockage
. The higher the sensitivity, the more
ld find, andMobilitythe larger the value
• hence,
ime, theprobability distribution of the Fig. 8. Four spatially averaged power profiles within various rooms.
ould be increased for small values of dashed lines correspond to exponential power decay profile of the
and the clusters.
opriate choiceof X is strongly coupled
istribution of the P ’ s . We find that.a
1/ X = 5 ns‘coupled with Rayleigh- rooms, we find that, on the average, rays within a clu
16

17. The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Ra
Ranging with Bluethooth
- Measurement result with AP Class 1 and MT Class 2 -
(a) (b)
• Fig. 3
Connection-based RSSI (dB)
10 260 This i
Link Quality (8-bit quantity)
Distance vs. RSSI Distance vs. LQ
5
250
which
240
0 230
power
220 maine
-5
210 for the
-10 200
2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18
Distance (meter) Distance (meter)
• From
much
Inquiry-based RX power level (dBm)
(c) (d)
Transmit Power Level (dBm)
20
15 Distance vs. TPL
-40
-45 Distance vs. RX power level ings o
10 -50 tion.
5 -55
0 -60 rather
-5
-10
-65
-70
at our
-15 -75 which
-20 -80
2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 Class
Distance (meter) Distance (meter)
the A
[Hossain] A. Hossain and W.-S. Soh, A comprehensive study of bluetooth signal parameters for our m
Figure 3: Relationship between various Bluetooth signal pa-
localization’, in Proc. IEEE 18th International Symposium on Personal, Indoor and Mobile
Radio Communications, pp. 1-5, September 2007
rameters & distance. • Our B
17

18. RSSI Ranging with Wi-Fi
826 IEEE JOURNAL OF SELECTED TO
- Cardbus Wi-Fi, corridor environment -
and therefore
where the valu
and describes
ence of averag
In the same
distance const
[Mazuelas] S. Mazuelas, A.4. RelationLorenzo, P. Fernandez, RSSI in aE. Garcia, J. Blas, and E. Abril,
Fig. Bahillo, R. between distance and F. Lago, corridor.
Robust indoor positioning provided by real-time RSSI values in unmodified WLAN networks,
Therefore,
IEEE Journal of Selected Topics in Signal Processing, vol. 3, pp. 821 - 831, October 2009. a fe
Thus, we can impose certain constraints to the distance esti- 18

19. Frequency Diversity of RSSI
- TelosB Platform, IEEE 802.15.4 Compliant, d = 2m -
−55
−60
−65
RSS (dBm)
−70
−75
−80
8 9 0 2 4 6 8 10 12 14 16 18
Channel
Fig.
[Zhang] D. Zhang, Y. Liu, X. Guo, M. Gao, and L. Ni, On distinguishing the multiple radio paths in
RSS-based ranging, in Proc. IEEE INFOCOM 2012, pp. 2201 - 2209, March 2012. path
ent environ- Fig. 2. RSS measurement in different channels: λ1 ,
node distance=2m ceiv
19

20. Ranging based on Time Measurements
- Time-of-Arrival and Time-Difference-of-Arrival -
ToA TDoA
2 1 2 1
(TT x − TT x ) − (TRx − TRx )
d=c δ = c(TRx1 − TRx2 )
2
• Asynchronous method • Asynchronous Tx-Rx
• Two-way-communication • Synchronous Rx-Rx
• One-way-communication
20

21. Ranging Error
6 - IR UWBEURASIP Journal - Wireless Communications and Networking
Technology on
Line-of-Sight (LOS)
100 80
B = 0.5 B=1 B=2 B=4 B=6
90
Average range error (cm)
80
70
70
Path loss (dB)
60
50 60
40
30
20 50
10
0 40
0 20 40 0 20 40 0 20 40 0 20 40 0 20 40
8 EURASIP Journal on Wireless Communications and Networking
Ground-truth range (m)
Non-Line-of-Sight (NLOS)
(a) NIST North, LOS, fc = 5 GHz
400 130
B = 0.5 B=1 B=2 B=4 B=6
350
Average range error (cm)
300 110
100
Path loss Path loss (dB)
80
250
90 B = 0.5 B=1 B=2 B=4 B=6
Average range error (cm)
200
80 90
70
70
(dB)
150
60
100 70
50 60
50
40
30
0 50
200 20 40 0 20 40 0 20 40 0 20 40 0 20 40 50
10 Ground-truth range (m)
[Gentile] C. Gentile, and A. Kik, “A Comprehensive Evaluation of Indoor Ranging Using
0 40
Ultra-Wideband Technology”, NIST North, NLOS, fc =20 GHz 0
0 20 40 0 (a) 40 0 5 40
20 EURASIP Journal on Wireless Communications and
20 40 0 20 40
Networking, vol. 2007, pages 10.
Ground-truth range (m)
(b) Child Care, LOS, fc = 5 GHz
21

22. Fundamentals of Positioning Algorithms
22

23. Positioning via Connectivity
- Proximity Positioning -
System model
• Single target A4 A3
• Connectivity/proximity
information
Position estimation
X
• Logic intersection (1,4) (1,2,3,4)
• Centroid:
NA
wi a i (1,2,4)
i=1
ˆ
z= NA
wi A1 A2
i=1
wi ∝ 1/di .
23

24. Finger-Printing
- Signal Space based Positioning -
System model
• Single target
• Measurement phase
• Real-time localization A A
1 4 3
Position estimation 0.8
• Fingerprint: fpq = (ˆp , φq , f (rx ))
i
z i
0.6
X
• Database: Ω {fpq }, |Ω| = P QNA
i
0.4
• Real-time measurement: 0.2
i AN
˜
s {f (rx )}i=1
• Search method, e.g. Nearest neighbor 0
A1 A2
0.2
NA 0.2 0 0.2 0.4 0.6 0.8 1 1.2
ˆ
z = arg min (˜pq − fpq )2
fi i
i
fpq ∈Ω
i=1
s.t. ˜pq = (ˆp , φq , f (rx ))
fi z i
24

25. Triangulation
- Angle-based and Positioning -
X
System model
• Single target
• AoA measurements
A1 H A2
Position estimation
−1
˜
pML (θ) = pR + GT Σ−1 Gθ
ˆ ˜
Gθ Σ−1 θ − θ R )
θ θ θ
− sin(θR1 )/dR1 cos(θR1 )/dR1
 
. .
Gθ . .
 
 . . 
− sin(θR1 )/dRNA cos(θRNA )/dRNA
25

26. Multilateration
- TDoA-based Positioning -
System model A4 A3
Anchor node
• NA ≥ η + 1 anchors Target node
• Single target
• Differential distance estimation
• Syncrhonous system
Z1
Position estimation
z − ai F − z − aR F = ∆diR ,
∀i ∈ IA R A1 A2
26

27. Trilateration
- ToA-based Positioning -
System model
• NA ≥ η + 1 anchors A4 A3
• Single/Multi-targets NT ≥ 1 Anchor node
Target node
• Distance estimation
Position estimation
• Single target Z1
z − aj F = dij , ∀j ∈ IA
• Multi-target
zi − aj = dij , ∀i ∈ IT , j ∈ IA

 F A1 A2
.

.
 .
zi − zj = dij , ∀i ∈ IT , j ∈ IT

F
27

28. Trilateration Using AoA
- Hybrid Angle-Distance Positioning -
System model
• NA ≥ η + 1 anchors
• Multi-targets NT ≥ 1 X
• Differential-AoA {βi }k
i=1
N (N +1)/2+2N
• k> 2
Position estimation
!
• Differential angle β c
O !
A1 A2
• Angle-to-distance
dXA1 = 2
2ro − (1 − cos(2β))
• Position estimation
zi − aj = dij , ∀i ∈ IT , j ∈ IA

 F
.

.
 .
zi − zj = dij , ∀i ∈ IT , j ∈ IT

F
28

29. Positioning Accuracy
29

30. Range-based Position Estimation Problem
- System model -
Network
• NA anchor nodes
• NT target nodes
• Connectivity range RMAX
Measurement
1, dij ≤ RMAX
• connectivity, cij
0, dij > RMAX
˜ ˜
• ranging, dij ∼ fij (dij |dij ), if cij = 1
˜ dij , LOS
• channel, E{dij } =
dij + bij , NLOS, bij > 0
30

31. Rigid-Bar Model
c d
Graph f
• Connectivity
• Distance values
a b
e
Is the graph unique?
31

32. Mirroring Ambiguity
- Symmetric ambiguity -
The white node is subject to a flip-ambiguity.
32

33. Swing Ambiguity
- Folding in the η-dimensions -
c d c d
f f
a b a b
e e
d
f
c
c
e
e
f
a b a b
d
Equivalent graphs with incongruent nodes
Notice the distances between (c,e) and (c,f)
33

34. Higher-dimensional Ambiguity
- Folding in higher dimension -
2D Network Representation 3D Network Representation
1.4 0.35
0.3
1.2 0.25
0.2
1
0.15
0.1
0.8
0.05
0.6 0
1.5
0.4
1
0.2 0.5
0 0.4 0.6 0.8 1
0 −0.6 −0.4 −0.2 0 0.2
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 −0.8
34

35. Position Information
Theorem: Generalized Information Matrix Decomposition (Destino, ’12)
In a network with NA = η + 1 anchors, NT targets and connectivity C, the
position error bound to the location of the k-th node is given by the inverse of
NA k−1
Sk ζnk Υnk + ζnk Υnk − QT G−1 Qk ,
k k−1
n=1 n=NA +1
equivocation
anchor-to-target information
target-to-target information
where Gk−1 and Qk are obtained by partitioning Fd as
Gk−1 Qk
Fd = ˘d .
QT
k Fk ,
• ζnk , Ranging Information Intensity (RII)
• Υnk , Ranging Direction Matrix (RDM)
35

36. Equivocation Matrix
Theorem: Decomposition of the Equivocation Matrix (Destino, ’12)
Consider a network with NA anchors and NT targets, the equivocation matrix
of the k-th target node, denoted by Ek , with k = N can be decomposed as
k−1 k−1 k−1
e
Ek = ζik Υik + κkj Υkj ,
ik ik
i=ma i=ma j=ma
j=i
link uncertainty coupling uncertainty
where ma = NA + 1 and sa = max (i, j) + 1.
36

37. Impact of the Information Coupling
- Benefits of node cooperation -
Investigation of the Information Coupling
- cooperative network -
10
Anchor node A1
Target node
8 Error with coupling
Error w/o coupling
6
4
y-coordinate, [m]
2
Z1
A2
0
−2 Z3
Z4
−4 Z2
−6
−8 A3
−10
−10 −8 −6 −4 −2 0 2 4 6 8 10
x-coordinate, [m]
Decoupling by disconnection
(c46 = 0, c56 = 0) → (ζ46 = 0, ζ56 = 0) → κ75 = 0.
67
37

38. Impact of the Information Coupling
De-coupling via Anchor Nodes
- Anchor placement -
- cooperative network -
12 12
Anchor node Anchor node
10 Target node 10 Target node
Error Ellipse for m1 Error Ellipse for m1
Error Ellipse for m2 < m1 Error Ellipse for m2 < m1
8 8
6 6
y-coordinate, [m]
y-coordinate, [m]
4 4
2 2
0 0
−2 −2
Z19 Z19
Z20 Z20
−4 −4
−6 Z22 Z21 −6 Z22 A6
−8 −8
−10 −10
−15 −10 −5 0 5 10 15 −15 −10 −5 0 5 10 15
x-coordinate, [m] x-coordinate, [m]
Decoupling by anchor replacement
• κkj = ζik ζjk χij , i = 20, j = 21, k = 22.
ik
j−1
• χij = ζtj vik [G−1 ]η vtj
T ¯
vtj S−1 vkj
T
j it j
t=NA +1
¯
• Z21 → A6 → S−1 = 0 → χij = 0 → κkj = 0
j ik
38

39. Impact of RII in the Position Information
2
Ranging Information Intensity
10
Ranging Information Intensity, ζij 1
10
σij = 0.1 [m]
σij = 0.25 [m]
0
10 σij = 0.5 [m]
σij = 1 [m]
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Maximum bias, bMAX [m]
NA k−1
Sk ζnk Υnk + ζnk Υnk − Ek
n=1 n=NA +1
equivocation
anchor-to-target information
target-to-target
39

40. Ranging in NLOS Channels
Ranging Error Distribution
25
TF404 eLab LOS d : LOS
NLOS 7,12
NLOS2 d : NLOS
7 2,12
2
12
d4,12: NLOS
A2
20 Fitting
4
5
15
A1
pdf
8
10
11
6
10
5
y A3
9
x TF407 TF406 TF405
0
−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Ranging error (in meters)
40

41. Information of NLOS links
- Discard or do not discard? -
0.15
PEBLOS
PEBN LOS
PEBLOS with incompletion
0.125
Mean-square-error, MSE [m2 ]
0.1
Answer: Do not discard NLOS!
0.075
0.05
0.025
0 5 10 15 20 25 30 35 40 45 50
Probability of NLOS links, pN LOS [%]
Simulation: NA = 4 anchors, NT = 10 targets, σd = 0.3 meters, bMAX = 3 meters. Full connectivity.
ˆ
Metric: MSE = E{(Z − Z)2 }
41

42. Non-Cooperative Positioning
Scenario of Non-cooperative Positioning
8
Anchor node
Target node
6
4
y-coordinate, [m]
2
0
−2
−4
−6
−8
−8 −6 −4 −2 0 2 4 6 8
x-coordinate, [m]
42

43. Maximum-Likelihood - Weighted Least Squares
• Independent measurements
• Anchor-to-target ranging
• Gaussian model
Non-Cooperative Maximum Likelihood Formulation:
 
NA N ˜
(dij − ai − zj 2 )2
ˆ
ˆ
z = max K exp −
 
2
2σij
ˆ∈RηNT
z i=1 j=NA +1
anchor-to-target
Non-Cooperative Weighted Least-squares Formulation:
NA N
2
ˆ
z = min wij ˜ ˆ
dij − ai − zj F
ˆ∈RηNT i=1 j=N +1
z
A
anchor-to-target
43

44. Illustration of the Log-Likelihood Function
- 2-D, 4-Anchors and 1-Target -
Perfect Measurements Noisy Measurements
44

45. The Least-Square Formulation Revised
NA 2 NA
˜
di − ai − z
ˆ F = ( ai − z F + ρi − ai − z F )2
ˆ
i=1 i=1
When the variables ρi s are not harmful?
45

46. Linear Algebra Intuition
- The null space -
Property: Noise in the Null-space
Let n denote a perturbation vector and assume that n lies in the
null-space of A, i.e. n ∈ N (A). Then,
A(x + n) = Ax
46

47. Illustration of the Null-Space Analysis
- Distance contraction principle -
Exact ranging Positive ranging errors
8 8
Anchor node Anchor node
Target node Target node
6 Global optimum 6 Global optimum
4 4
y-coordinate, [m]
y-coordinate, [m]
2 2
0 0
−2 −2
−4 −4
−6 −6
−8 −8
−8 −6 −4 −2 0 2 4 6 8 −8 −6 −4 −2 0 2 4 6 8
x-coordinate, [m] x-coordinate, [m]
Negative ranging errors Error in the null-space of the angle-kernel
8 8
Anchor node Anchor node
Target node Target node
6 Global optimum 6 Global optimum
4 4
y-coordinate, [m]
y-coordinate, [m]
2 2
0 0
−2 −2
−4 −4
−6 −6
−8 −8
−8 −6 −4 −2 0 2 4 6 8 −8 −6 −4 −2 0 2 4 6 8
x-coordinate, [m] x-coordinate, [m]
47

48. Robust Non-Cooperative Positioning
- Distance contraction based algorithms -
Algorithm 1 WC-DC Algorithm 2 NLS-DC
1: ˜
Measurements, {di }, 1: ˜
Measurements, {di },
2: Anchor positions, PA 2: Anchor positions, PA
3: Estimate a feasible region, BD 3: Estimate a feasible region, BD
4: z0 ← BD ;
ˆ 4: z0 ← BD ;
ˆ
5: ˆ
Ω ← O([PA ; z0 ]);
ˆ 5: ˆ
Ω ← O([PA ; z0 ]);
ˆ
6: ρ ← arg min
ˆ ˆˆˆ
ρ Ω ρT ; 6: ρ ← arg min
ˆ ˆˆˆ
ρ Ω ρT ;
ρ∈RNA
ˆ ρ∈RNA
ˆ
s.t. ˜
di + ρi ≤ 0 ∀i s.t. ˜
di + ρi ≤ 0 ∀i
ˆ ˜
7: [ω dc ]i ← ρi /di ; NA
˜ ˆ ˆ
7: z ← arg min
ˆ (di − ρi − di )2 .
8: z ← ω dc PA .
ˆ ηˆ
z∈R i=1
48

49. Non-Cooperative Positioning
- Algorithm comparisons -
Comparison of Different Localization Algorithms
- non-cooperative network -
3.75
TS-WLS
3.5 WC-DC
NLS-DC
3.25 PEBNLOS
3
Location accuracy, ε [m]
2.75
2.5
¯
2.25
2
1.75
1.5
1.25
1
0.75
0.5
0.25
0 1 2 3 4 5
Maximum Bias, bMAX [m]
Network: Area (14.14 × 14.14) [m2 ], 4 anchors (square location), 10 targets (inside the anchors).
Noise: σd = 0.3 [m], pNLOS = 1. Location accuracy: ε =
¯ ˆ
E{(Z − Z)2 } [m] .
49

50. Non-Cooperative Positioning
- Algorithm comparisons -
Comparison of Different Localization Algorithms
- non-cooperative network -
2
TS-WLS
WC-DC
NLS-DC
1.75 PEBN LOS
Location accuracy, ε [m]
1.5
¯
1.25
1
0.75
0.5
0.25
0 0.25 0.5 0.75 1
Probability of NLOS, pNLOS
Network: Area (14.14 × 14.14) [m2 ], 4 anchors (square location), 10 targets (inside the anchors).
Noise: σd = 0.3 [m], bmax = 3 [m]. Location accuracy: ε =
¯ ˆ
E{(Z − Z)2 } [m].
50

51. Cooperative Algorithm
Scenario of Cooperative Positioning
8
Anchor node
Target node
6
4
y-coordinate, [m]
2
0
−2
−4
−6
−8
−8 −6 −4 −2 0 2 4 6 8
x-coordinate, [m]
51

52. Maximum-Likelihood - Weighted Least Squares
• Independent measurements
• Target-to-target cooperation
• Gaussian model
Cooperative Maximum Likelihood Formulation:
   
NA N ˜ N N ˜
(dij − ai − zj 2 )2
ˆ (dij − zi − zj 2 )2
ˆ
ˆ
z = max K exp −
  exp −
 
2
2σij 2
2σij
ˆ∈RηNT
z i=1 j=NA +1 j=NA +1 j=NA +1
j=i
anchor-to-target target-to-target
Cooperative Weighted Least-squares Formulation:
NA N N N
2 2
ˆ
z = min wij ˜ ˆ
dij − ai − zj F + wij ˜ ˆ
dij − zi − zj F
ˆ∈RηNT i=1 j=N +1
z i=NA +1 j=NA +1
A
j=i
anchor-to-target target-to-target
52

53. Facts of the WLS Optimization Problem
Number of local minima grows with:
• number of nodes N ,
• the lack of connections,
• the noise.
Robustness to measurement errors can be achieved by:
• adding constraints (hard mitigation method),
• using weights (soft mitigation method).
Optimization complexity grows with:
• number of nodes N ,
• the lack of connections,
• the lack of a priori information,
• number of costraints.
53

54. Global Optimization
- Smoothing continuation method -
Optimization via GDC Technique
- sum of Gaussian functions -
0
smoothing parameter, λ → 0
−1
λ
Objecitve function, g −2
−3
−4
−5
−6
−7
Estimated minimum
Smoothed objective
Original objective
−8
−5 0 5 10
Optimization variable, x
• Smooth, g(x) → g λ (x)
• Minimize, xm = min g λ (x)
x
• Continue (minimum tracking), λ < λ and x0 = xm
54

55. Efficient Implementation of the Optimization Method
- Range-Global Distance Continuation -
• Smoothed function and gradient in closed-forms
• The first smoothed function is convex
• Random initialization
• Minimization without matrix inversions (BFGS)
• Decreasing smoothing paramters
55

56. Cooperative Positioning
- R-GDC optimization performance -
R-GDC Performance in Large Scale Networks
- cooperative network -
0.65
R-GDC
0.6 PEBLOS
0.55
0.5
Location accuracy, ε [m]
0.45
¯
0.4
0.35 NT = 50
0.3
0.25 NT = 100
0.2 NT = 200
0.15
0.1
0.05
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Meshness ratio, m
Network: Area (14.14 × 14.14) [m2 ], 4 anchors (square location), NT targets (inside the anchors).
Noise: σd = 0.3 [m]. s Location accuracy: ε =
¯ ˆ
E{(Z − Z)2 } [m].
56

57. Weighing Function
- Heuristic strategies -
“Weights are chosen to reflect differing levels of concern
about the size of the squared error terms.
Higher weights to more reliable measurements, less to others
and zero the unmeasured.”
• Inverse of the noise variance (optimal in zero-mean Gaussian model)
• Inverse of the squared-ranging (simple and effective in small scenarios)
• Locally weighted Scatterplot Smoothing (LOESS)-based
(emphasize shorter connections rather than long ones)
• Channel-based (feasible if propagation model is available)
57

58. Ranging in a Realistic Environment
Ranging Error Distribution
25
TF404 eLab LOS d7,12: LOS
NLOS
NLOS2 d2,12: NLOS
7
2
12
d4,12: NLOS
A2
20 Fitting
4
5
15
A1
pdf
8
10
11
6
10
5
y A3
9
x TF407 TF406 TF405
0
−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Ranging error (in meters)
• Ranging statistics are spatial-time variant
• Long distance can be more accurate than short ones, e.g d2,12 vs d4,14
• Distributions are not generally Gaussian (see S-V model)
• Channel-statistics are not practical with off-the-shelf devices
58

59. Stochastic-Geometric Weighing Function
... wij is the confidence that the true distance dij is within a confidence bound
¯
of ±γ of the mean estimate dij , weighted by a penalty Pij on the hypothesis
that the samples {dij,k } are obtained under LOS conditions.
¯ ¯
wij = Pr dij − γ ≤ dij + cij ≤ dij + γ , ∀eij ∈ E
¯ ¯
= Pr dij − γ ≤ dij ≤ dij + γ · Pr {¯ij = 0}
c
¯ij − γ ≤ dij ≤ dij + γ · Pij
= Pr d ¯
D
= Dispersion · Penalty = wij · Pij
where
Pij → 1 Hypothesis of LOS is true
Pij → 0 Hypothesis of LOS is false
59

60. Stochastic (Dispersion) Weighing Function
- The intuition behind: sort categorical data -
Pool of objects Scale
Which unit:? [γ]
Object characteristics
• shape, σ
• density, K
Metric
• weight: w = f (σ, K; γ)
60

61. Maximum Entropy Criteria
Our context:
• Categories → (K, σ )
ˆ
• Sample → zij = (Kij , σij )
ˆ
• Weight of zij → wij
• Population → Z = [Kmin , Kmax ] × [ˆmin , σmax ]
σ ˆ
Diversity of the the objects by the weights is
Kmax ˆ
σmax
H(γ) = w(S, r; γ) · ln (w(S, r; γ)) dS
r=Kmin σ
ˆ min
• Uncertainty analysis: measure wij and compute H (diversity)
• Weight optimization: compute wij that maximizes H (diversity)
γopt = arg max H(γ)
γ∈R+
61

62. Geometric (Penalty) Weights: Concept
- Handling NLOS with scarce information -
Rationale:
• Higher confidence = higher weights
• Pij → 1 ⇒ LOS; Pij → 0 ⇒ NLOS;
˜
• Kij → 1 ⇒ insufficient LOS/NLOS information in {dij }
Concept: Relate likelihood of NLOS with a geometric effect captured by
neighboring nodes, e.g., obtuseness of triangles.
q
q
q
i j
i j
i j
62

63. Experimental Test
63

64. Distance Estimation Indoors
- Experiment with UWB ToA-based ranging -
Localization Test
- network -
12
Anchor
11 Target
p4 p2
10 eLAB p5
9
8 p6
y-coordinate [m]
7
p7
6
5
4 p3
p1
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12
x-coordinate, [m]
CWC/Oulu Installations
64

65. Ranging Statistics
- Experiment with UWB ToA-based ranging -
Link Cluster 1 Cluster 2
i-th node j-th node Ag1 µg1 σg1 Ag2 µg2 σg2
1 5 0.04 0.17 0.03 0.88 0.45 0.09
1 6 1.00 0.78 0.19 - - -
1 7 1.00 0.00 0.02 - - -
2 5 0.96 -0.03 0.005 0.01 -0.02 0.001
2 6 1.00 0.27 0.37 - - -
2 7 1.00 0.49 0.15 - - -
3 5 - - - - - -
3 6 1.00 0.11 0.02 - - -
3 7 0.02 1.29 0.06 0.98 2.03 0.09
4 5 1.00 0.51 0.10 - -
4 6 1.00 0.22 0.06 - -
4 7 1.00 0.62 0.05 - -
5 6 1.00 0.44 0.07 - -
5 7 1.00 0.12 0.04 - -
6 7 0.05 -0.08 0.002 0.88 -0.05 0.09
65

66. Non-Cooperative Positioning
- Experiment with UWB ToA-based ranging -
Localization Test
- non-cooperative -
12
11
p4 p2
10 p5
9
8 p6
y-coordinate [m]
7
p7
6
5
4 p3
p1
3
2
Anchor
Target
C-NLS modified
1 DC-NLS
DC-WC
0
0 1 2 3 4 5 6 7 8 9 10 11 12
x-coordinate, [m]
Metric NLS-DC WC-DC C-NLS modified
Average RMSE [m] 0.29 0.27 0.38
Average CEP-50 [m] 0.24 0.23 0.31
Average CEP-95 [m] 0.41 0.37 0.47
66

67. Cooperative Positioning
- Experiment with UWB ToA-based ranging -
Localization Test
- cooperative -
12
p9
11
p4 p2
10 p7
9
8 p8
y-coordinate [m] p5
7
p10
6
5
4 p3
p1
3
p12
p11
2
Anchor
Target p6
SDP - C
1 SDP - LOESS
R-GDC - DP
0
0 1 2 3 4 5 6 7 8 9 10 11 12
x-coordinate, [m]
Metric R-GDC - DP SDP - LOESS SDP - C
Average RMSE [m] 0.29 0.33 0.40
Average CEP-50 [m] 0.16 0.27 0.37
Average CEP-95 [m] 0.46 0.56 0.63
67

68. Thank You
Ph.D. Thesis “Positioning in Wireless Networks”
Defence: 16/11/2012, Op-Sali L10
Author: Giuseppe Destino, University of Oulu
Advisor: Prof. Giuseppe Abreu, Jacobs Universtiy, Germany
Supervisor: Prof. Jari Iinatti, University of Oulu
68