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Positioning seminar 2012
 

Positioning seminar 2012

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More information on my website www.ee.oulu.fi/~destino/

More information on my website www.ee.oulu.fi/~destino/

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    Positioning seminar 2012 Positioning seminar 2012 Presentation Transcript

    • Positioning in Wireless Networks- Non-cooperative and Cooperative Algorithms - Giuseppe Destino Centre for Wireless Communications University of Oulu October 12, 2012 1
    • Location-Based Service Market - Toward context-awareness - ReveneuPyramidResearch Forecasts 2008-2015 2
    • Location-Based Service Market - Toward a pervasive platform - Navigation devicesPyramidResearch Forecasts 2008-2015 3
    • Geo-Social Network - Location and information sharing -• Find your friend• Get direction• Information sharing 4
    • Shopping - Personalized Advertising -• Real-time sale• Indoor navigation• Find objects• Information sharing 5
    • Smart and Safe Navigation - In-car augmented reality -• Navigation• Localization of accidents• Alert• Information sharing 6
    • Industrial Monitoring - Safety and Security -• Monitoring of the environment• Tracking of personnel• Tracking of assets 7
    • ... 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
    • Location-aware Network Optimization 9
    • Network Planning and Expansion• Location-based RSS map• Use mobile nodes for monitoring• Adaptive network expansion 10
    • 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
    • Positioning System 12
    • System ArchitectureSystem Centric Node Centric • Measurements convey to the • Measurements convey to the radio access network mobile nodes • Centralized calculations • Local calculations 13
    • NetworkNodes • NA anchors, known fixed location A4 A3 • NT targets, unknown locationTopology X • Star-like, non-cooperative scheme • Mesh, cooperative schemeSyncronization A1 A2 • Global, synchronous • Local, asynchronous 14
    • Internode Interaction - Measurement system -Power Profile • Channel Impulse Response (CIR), wideband signal • Power Delay Profile (PDP), wideband signalAngle • Angle-of-Arrival (AoA), multiple-antennaDistance (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
    • Source of Errors - Example of an indoor propagation channel - S-V Indoor Propagation Model III-A we will see, from another point5: 300 ns. Room 1 Room 3 Rate, X individual rays in about 200 powerts 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 thatwith our • Multipaths sensitivity, is measurements Room 2 Room 4ny 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
    • 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
    • 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
    • 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. pathent environ- Fig. 2. RSS measurement in different channels: λ1 , node distance=2m ceiv 19
    • 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
    • Ranging Error6 - 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 20 408 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
    • Fundamentals of Positioning Algorithms 22
    • Positioning via Connectivity - Proximity Positioning -System model • Single target A4 A3 • Connectivity/proximity informationPosition 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
    • Finger-Printing - Signal Space based Positioning -System model • Single target • Measurement phase • Real-time localization A A 1 4 3Position 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
    • Triangulation - Angle-based and Positioning - XSystem model • Single target • AoA measurements A1 H A2Position estimation −1 ˜pML (θ) = pR + GT Σ−1 Gθˆ ˜ Gθ Σ−1 θ − θ R ) θ θ θ − sin(θR1 )/dR1 cos(θR1 )/dR1   . .Gθ . .    . .  − sin(θR1 )/dRNA cos(θRNA )/dRNA 25
    • Multilateration - TDoA-based Positioning -System model A4 A3 Anchor node • NA ≥ η + 1 anchors Target node • Single target • Differential distance estimation • Syncrhonous system Z1Position estimation z − ai F − z − aR F = ∆diR , ∀i ∈ IA R A1 A2 26
    • Trilateration - ToA-based Positioning -System model • NA ≥ η + 1 anchors A4 A3 • Single/Multi-targets NT ≥ 1 Anchor node Target node • Distance estimationPosition 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
    • 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> 2Position 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
    • Positioning Accuracy 29
    • Range-based Position Estimation Problem - System model -Network • NA anchor nodes • NT target nodes • Connectivity range RMAXMeasurement 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
    • Rigid-Bar Model c dGraph f • Connectivity • Distance values a b e Is the graph unique? 31
    • Mirroring Ambiguity - Symmetric ambiguity -The white node is subject to a flip-ambiguity. 32
    • 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 dEquivalent graphs with incongruent nodes Notice the distances between (c,e) and (c,f) 33
    • Higher-dimensional Ambiguity - Folding in higher dimension - 2D Network Representation 3D Network Representation1.4 0.35 0.31.2 0.25 0.2 1 0.15 0.10.8 0.050.6 0 1.50.4 10.2 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
    • Position InformationTheorem: Generalized Information Matrix Decomposition (Destino, ’12)In a network with NA = η + 1 anchors, NT targets and connectivity C, theposition 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 informationwhere 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
    • Equivocation MatrixTheorem: Decomposition of the Equivocation Matrix (Destino, ’12)Consider a network with NA anchors and NT targets, the equivocation matrixof 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 uncertaintywhere ma = NA + 1 and sa = max (i, j) + 1. 36
    • 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
    • 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
    • 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
    • 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 5y 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
    • 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. ˆMetric: MSE = E{(Z − Z)2 } 41
    • 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
    • Maximum-Likelihood - Weighted Least Squares • Independent measurements • Anchor-to-target ranging • Gaussian modelNon-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-targetNon-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
    • Illustration of the Log-Likelihood Function - 2-D, 4-Anchors and 1-Target -Perfect Measurements Noisy Measurements 44
    • The Least-Square Formulation RevisedNA 2 NA ˜ di − ai − z ˆ F = ( ai − z F + ρi − ai − z F )2 ˆi=1 i=1 When the variables ρi s are not harmful? 45
    • Linear Algebra Intuition - The null space -Property: Noise in the Null-spaceLet n denote a perturbation vector and assume that n lies in thenull-space of A, i.e. n ∈ N (A). Then, A(x + n) = Ax 46
    • 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 4y-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 4y-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
    • 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
    • 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
    • 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, pNLOSNetwork: 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
    • Cooperative Algorithm Scenario of Cooperative Positioning 8 Anchor node Target node 6 4y-coordinate, [m] 2 0 −2 −4 −6 −8 −8 −6 −4 −2 0 2 4 6 8 x-coordinate, [m] 51
    • Maximum-Likelihood - Weighted Least Squares • Independent measurements • Target-to-target cooperation • Gaussian modelCooperative Maximum Likelihood Formulation:     NA N ˜ N N ˜ (dij − ai − zj 2 )2 ˆ (dij − zi − zj 2 )2 ˆˆz = 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-targetCooperative Weighted Least-squares Formulation: NA N N N 2 2ˆz = 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
    • Facts of the WLS Optimization ProblemNumber 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
    • 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
    • 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
    • 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, mNetwork: 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
    • 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
    • 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 5y 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
    • 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 · Pijwhere Pij → 1 Hypothesis of LOS is true Pij → 0 Hypothesis of LOS is false 59
    • Stochastic (Dispersion) Weighing Function - The intuition behind: sort categorical data - Pool of objects Scale Which unit:? [γ]Object characteristics • shape, σ • density, KMetric • weight: w = f (σ, K; γ) 60
    • Maximum Entropy CriteriaOur context: • Categories → (K, σ ) ˆ • Sample → zij = (Kij , σij ) ˆ • Weight of zij → wij • Population → Z = [Kmin , Kmax ] × [ˆmin , σmax ] σ ˆDiversity 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
    • 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 byneighboring nodes, e.g., obtuseness of triangles. q q q i j i j i j 62
    • Experimental Test 63
    • 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
    • Ranging Statistics - Experiment with UWB ToA-based ranging - Link Cluster 1 Cluster 2i-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
    • 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 modifiedAverage RMSE [m] 0.29 0.27 0.38Average CEP-50 [m] 0.24 0.23 0.31Average CEP-95 [m] 0.41 0.37 0.47 66
    • 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 - CAverage RMSE [m] 0.29 0.33 0.40Average CEP-50 [m] 0.16 0.27 0.37Average CEP-95 [m] 0.46 0.56 0.63 67
    • Thank YouPh.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