Real Time Localization Using Receiver Signal Strength Indicator

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Slides from my dissertation defense. Talks about the error in localizing a transmitter by measuring the signal strength. In addition, it presents new techniques for localization using cross-correlation of fading.

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Real Time Localization Using Receiver Signal Strength Indicator

  1. 1. Real Time Localization Systems UsingReceiver Signal Strength IndicatorMohammed Rana BasheerAdvisor: Dr. Jag Sarangapani
  2. 2. Publications Refereed Journal Papers  M.R. Basheer, and S. Jagannathan, "Enhancing Localization Accuracy in an RSSI Based RTLS Using R-Factor and Diversity Combination", in review, International Journal of Wireless Information Networks  M.R. Basheer, and S. Jagannathan, "Receiver Placement Using Delaunay Refinement-based Triangulation in an RSSI Based Localization―, revised and resubmitted, IEEE/ACM Transactions on Networking  M.R. Basheer, and S. Jagannathan, "Localization of RFID Tags using Stochastic Tunneling", accepted, IEEE Transactions on Mobile Computing  M.R. Basheer, and S. Jagannathan, "Localization and Tracking of Objects Using Cross-Correlation of Shadow Fading Noise", minor revision, revised and resubmitted, IEEE Transactions on Mobile Computing  M.R. Basheer, and S. Jagannathan, "Placement of Receivers for Shadow Fading Cross-Correlation Based Localization", to be submitted 2
  3. 3. Publications (contd.) Refereed conference papers  M.R. Basheer, and S. Jagannathan, "R-Factor: A New Parameter to Enhance Location Accuracy in RSSI Based Real-time Location Systems," Sensor, Mesh and Ad Hoc Communications and Networks, SECON 09. 6th Annual IEEE Communications Society Conference on , pp. 1-9, 22-26 June 2009.  M.R. Basheer, and S. Jagannathan, "A New Receiver Placement Scheme Using Delaunay Refinement-Based Triangulation," Wireless Communications and Networking Conference (WCNC), 2010 IEEE, pp.1-6, 18-21 April 2010.  M.R. Basheer, and S. Jagannathan, "Localization of objects using stochastic tunneling," Wireless Communications and Networking Conference (WCNC), 2011 IEEE, pp.587-592, 28-31 March 2011.  M.R. Basheer, and S. Jagannathan, " Localization of Objects Using Cross-Correlation of Shadow Fading Noise and Copulas," Global Communication Conference (GLOBECOM), 2011 IEEE, 6-8 Dec 2011.  M.R. Basheer, and S. Jagannathan, " Placement of Receivers for Shadow Fading Cross-Correlation Based Localization," Submitted to IEEE Local Computer Networks (LCN) 2012. 3
  4. 4. Presentation Outline Introduction and Background Paper 1: Enhancing Localization Accuracy in an RSSI Based RTLS Using R-Factor and Diversity Combination Paper 2: Receiver Placement Using Delaunay Refinement-based Triangulation in an RSSI Based Localization Paper 3: Localization of RFID Tags using Stochastic Tunneling Paper 4: Localization and Tracking of Objects Using Cross-Correlation of Shadow Fading Noise Paper 5: Placement of Receivers for Shadow Fading Cross-Correlation Based Localization Conclusions Future Work 4
  5. 5. Real Time Location Systems (RTLS) Used for locating or tracking assets in places where GPS signals are not readily available Methodologies  Time of Arrival (ToA),  Time Difference of Arrival (TDoA),  Angle of Arrival (AoA) or  Received Signal Strength Indicator (RSSI) RSSI A n log(r ) Boeing factory floor* *http://www.ce.washington.edu/sm03/boeingtour.htm  RTLS using RSSI Uses signal strength of radio signals to locate objects  Classified into  Range Based  Range Free Friis Transmission Equation RSSI vs. Distance 5
  6. 6. RSSI Profile of ERL 114 6
  7. 7. Localization Hardware IEEE 802.15.4 transceiver from XBee Operating frequency 2.45 GHz RTLS Tag MST Mote with 100 MHz Bandwidth 8051 variant microcontroller 8KB RAM and 128 KB code space Spatial diversity with 2 antennas RTLS Receiver 7
  8. 8. Motivation for RTLS using RSSI Time and Angle based methods are costly and require dedicated hardware RSSI information easily accessible through API Localization can be easily deployed on existing wireless infrastructure as a software upgrade Time and Angle based localization achieves better accuracy under LoS condition Coarse grained localization Periodic radio profiling of target area under range free methods or calibration of parameters under range based method is essential 8
  9. 9. Goal and Objectives of the Dissertation Goal—Given a location error threshold, determine the location of a transmitter and track it in a workspace by placing the appropriate number of receivers at the right position in a workspace. Objectives  Develop algorithms for localization and tracking of wireless devices from radio signal strength signals  Develop algorithms for placing wireless receivers around the workspace so that the error in locating a transmitter at any point in this workspace is less than a predefined threshold  Demonstrate the efficacy of the placement and localization algorithms analytically, in simulation environment and experimentally through hardware Both range-based and range free methods are developed 9
  10. 10. Cohesion of completed work Paper 1. M.R. Basheer, and S. Jagannathan, "Enhancing Localization Accuracy in an RSSI Based RTLS Using R-Factor and Diversity Combination", under review at International Journal of Wireless Information Networks Range-Based Paper 2. M.R. Basheer, and S. Jagannathan, "Receiver Placement Using Delaunay Refinement-based Triangulation in an RSSI Based Localization", Revised and resubmitted to IEEE/ACM Transactions on Networking Localization Using RSSI Paper 3. M.R. Basheer, and S. Jagannathan, "Localization of RFID Tags using Stochastic Tunneling", Accepted at IEEE Transactions on Mobile Computing Paper 4. M.R. Basheer, and S. Jagannathan, " Localization and Cross-Correlation Tracking of Objects Using Cross-Correlation of Shadow Fading Noise", Minor revision, revised and resubmitted, IEEE Transactions on Mobile Computing, Paper 5. M.R. Basheer, and S. Jagannathan, "Placement of Receivers for Shadow Fading Cross-Correlation Based Localization", to be submitted, 10
  11. 11. Paper 1: Enhancing Localization Accuracy in an RSSIBased RTLS Using R-Factor and Diversity Combination Weighted least square to the rescue Transmitter location estimation Friis Transmission base station from Signal happens in Transmitter Euclidean distance Equation equation Strength Weights are the radial distancestation Base variance affected by outliers R-Factor and are called the Receivers 11
  12. 12. Paper 1: Enhancing Localization Accuracy in an RSSI Based RTLS Using R-Factor and Diversity Combination Objectives  Derive a statistical parameter called the R-factor to grade radial distance estimates to a transmitter from RSSI values  Non-coherent diversity combination techniques that can improve radial distance estimation Previous efforts involved  Proximity in Signal Space (PSS), a heuristic algorithm that uses signal strength to classify receivers for localization accuracy [Gwon 04]  Chi-square test to classify Line of Sight (LoS) condition at the receiver into Ricean or Rayleigh [Lakhzouri 03]  Binary classification of receivers into good or bad based on a test for Gaussian distribution [Venkatraman 02] 12
  13. 13. Assumptions Received signal amplitude random variable X is Ricean distributed with PDF given by 2 x A2 x 2 Ax f X x | A, X 2 exp 2 I0 2 X 2 X X Radial distance random variable R is related to RSSI X as 1 n l0 R g( X ) X2 where n is the path loss exponent and l0 accounts for antenna geometry, wavelength etc. 13
  14. 14. Mean & Variance of Radial Distance Estimate The mean and variance of the radial distance estimate by a receiver to a transmitter using Friis transmission equation based estimator under Ricean environment is given by 1 1 1 n n 2 2 2l 0 2 n 2 2l 0 1 E(R | K , X ) X 1 K M2 ,1, K 2 1 n 2l 0 1 4 2 X M2 ,1, K 2 X M2 ,1, K 2 2 2 1 n 2 2 8 X 2l 0 1 Var( R | K , X ) 1 K M2 ,1, K n 2l0 2 1 4 2 X M2 ,1, K 2where M , , is the Confluent Hyper-geometric Function (CHF) and K A2 2 2 Xis the ratio of the power in the deterministic LoS component to the NLoSenergy or the signal to noise ratio for localization. 14
  15. 15. Localization Receiver and R - Factor A receiver for RSSI based RTLS, is called a localization receiver if the signal to noise ratio K A2 2 X for the received signals is greater than 9 2 Mean and Variance of radial distance estimate is given by 2n 2 E R | r0 , K r0 r0 Bias n2 K 2 4 2l A n 0 n 2r02 Var ( R | r0 , K ) 2 n K n2 K R-Factor (Receiver Error Factor) measures the variance in radial distance estimate by a localization receiver r02 1 2r0n 2 2 Var( R | r0 , K ) X cr0b 2 X n2 K 2 n 2l0 MSE is proportional to R-Factor r02 MSE 2 2n 2 8n 10 2n 2 8n 10 n K 15
  16. 16. Localization Error and R-Factor Theorem 1: (Comparison of localization accuracy under LoS and NLoS) For the same amount of NLoS energy at a localization receiver and a receiver under NLoS conditions, the MSE of the radial distance estimate for the localization receiver is lower than that of the receiver under the NLoS condition Theorem 2: (R-factor and localization accuracy) The upper bound of the localization error decreases with R-factor in a Ricean environment for a RSSI based RTLS Theorem 3: (Localization accuracy and receiver count) Localization accuracy using w+1 receivers is better in comparison with deploying w receivers in an RSSI based RTLS system when the maximum R-factor is kept the same in both cases 16
  17. 17. Channel Diversity and R-Factor Diversity is a method to improve certain aspects of the received signal by using two or more communication channels Two commonly used diversity schemes are  Spatial Diversity using multiple antennas  Frequency Diversity For RTLS using RSSI only non-coherent combination is possible Diversity channels were combined using one of the following methods  Selection Combination: Best signal out from all channels  Averaging: Mean of signals from all channels  Root Mean Square: Compute RMS of signal from all channels 17
  18. 18. Simulation of R-Factor vs. Diversity Count Variation of R-Factor with increasing diversity channel count LoS Conditions NLoS ConditionsFrom simulations, combining RSSI from diversity channels using RMSproduced the lowest R-Factor and consequently the best localization accuracy 18
  19. 19. Localization Experiment Receiver layout in ERL 114 22% 28% 22% CDF of Localization Error decrease 26% decreasedecrease 30% 24%Summary of Localization Error Levels decrease decreasedecrease Localization Error (cm) Localization Method Mean Median 90th percentile Std. devTIX + PSS 342 298 432 62.81TIX with R-factor 267 214 335 40.32TIX with R-factor and Spatial Diversity 254 210 329 40.15 *Gwon et al. 2004 19
  20. 20. Conclusions and ContributionsConclusions Contributions Existing localization schemes can  A novel parameter called R- use R-Factor to identify subset of Factor to identify receivers with receivers that will result in better low range estimation errors was location estimation presented R-Factor combined with RMS channel diversity was shown  R-factor for selection theoretically and experimentally combination, averaging and root to improve localization accuracy mean square diversity combination were derived RMS diversity combination was shown to have better localization performance than averaging and selection diversity combination 20
  21. 21. Paper 2: Receiver Placement Using Delaunay Refinementbased Triangulation in an RSSI Based Localization Delaunay refinement Where do I placement is place solution the these receivers? Possible Applications • Locate cellphones to track foot traffic • Coupons for visiting shops • Theft prevention Transmitter being localized with guaranteed accuracy Shopping Mall Layout 21
  22. 22. Paper 2: Receiver Placement Using Delaunay Refinement based Triangulation in an RSSI Based Localization Objective is to find a receiver layout that will locate a transmitter with error less than a preset threshold with least number of receivers Euclidean equation that relates the transmitter location to radial distance between transmitter and receiver is non-linear in xt and yt xt2 yt2 xi2 yi2 ri 2 xi xt y i yt 2 2 Previous effort involved  Delaunay Triangulation based placement that combines heuristics and wireless coverage requirements [Wu 07]  Receiver position based on minimizing the condition number of a linear equation [Isler 06]  Radial errors are assumed to be Gaussian distributed and then receiver positions are selected based on minimization of Fisher information determinant [Martinez 05] 22
  23. 23. Wireless Propagation Model Under far-field conditions between transmitter and receiver However measured signal strength involves noise Pi = Pi*+ei Estimate of di from Pi , represented as ri is 23
  24. 24. Multi-Lateration Using CWLS Constrained Weighted Least Squares provides a method to linearize a non-linear equation and solve for parameters in a linear least square sense2 – Parameter Non-Linear Estimation Problem xt2 yt2 xi2 yi2 ri 2 xi xt yi yt ;i 1,2,  N 2 23 – Parameter Linear Estimation Problem Rs xi2 yi2 ri 2 xi xt yi yt ;i 1,2,  N 2 2 Constraint Rs xt2 yt2 24
  25. 25. Localization Error Under CWLS Theorem 1: For an RTLS setup with N receivers the localization error in estimating the position of the transmitter at location η using CWLS is given by where λ1, λ2 and λ3 are the eigenvalues of the matrix , are the R-factors and ξ≥0 is the Lagrange multiplier and as the cost of violating Rs xt2 yt2 25
  26. 26. Receiver Placement Quality Metric Maximum localization error at location η occurs when ξ=0 Receiver placement quality metric is the maximum localization error throughout the workspace G Objective is to attain with least number of receivers 26
  27. 27. Optimal Unconstrained Receiver Placement Theorem 2: A receiver placement strategy whose objective is to span the largest area under localization coverage with least number of receiver while ensuring no coverage holes exists within the placement grid, will have all its receivers placed in an equilateral triangular grid with grid spacing equal to the communication range of the wireless device Bounding walls around a workspace prevents equilateral grid placement of receivers !!!! 27
  28. 28. Constrained Receiver PlacementRequirements Equilateral triangular grid wherever possible Near bounding walls triangular grids that are as close to equilateral triangle as possible Placement should satisfy localization error constraint Should complete in linear time 28
  29. 29. Delaunay Refinement Triangulation Originally developed to generate mesh for Finite Element Modeling and Computer Games Delaunay Refinement satisfies all our receiver placement requirements Delaunay meshing of a 3D object* However, boundary walls results in sub-optimal receiver count * G E O M E T R I C A (http://www-sop.inria.fr/geometrica/ ) 29
  30. 30. Receiver Count Under Delaunay Refinement Placing Theorem 3 (Upper Bound for Receiver Count): For a given workspace G, and a localization error threshold (ϵu), the receiver count generated using Delaunay refinement triangulation on G is suboptimal and is upper bounded by the receiver count for an optimal triangulation of the above receiver placement problem as, where 30
  31. 31. Local Feature Size and Receiver Count Local feature size can be described approximately as a measure of the feature (segments and vertices) density of a graph Removing shorter segments in an input layout resulting in the bound getting tighter Shorter segments in a layout are those segments that are less than twice wavelength 31
  32. 32. Bounded Receiver Count Shopping mall layout Airport layout 32
  33. 33. Experimental Result Localization area is ERL 114 that measures approx. 12m x 12m Upper threshold for localization error set at 1m Layout using (DR) (11 receivers) Layout using DT* (16 receivers) *Wu 07 33
  34. 34. Localization Accuracy Results CDF plot of Localization Error34% 28% 25% decreasedecreasedecreaseSummary of Localization Error Test Points Localization Error (m) Layout 75th Mean Median Std. dev Method percentile DT 1.137 1.038 1.589 0.786 DR 0.808 0.678 1.189 0.657 34
  35. 35. Conclusions and ContributionsConclusions Contributions CWLS Multi-lateration on  CWLS Localization error was receivers placed using Delaunay Refinement achieved derived better localization accuracy  Relationship between R- Better performance of DR due factor and localization error to more triangular regions that under RSSI based RTLS are close to equilateral triangle than comparable method using CWLS Receiver count though sub-  A sub-optimal receiver optimal was lower than placement algorithm with comparable placement algorithm guarantees on localization accuracy presented 35
  36. 36. Paper 3: Localization of RFID Tags using Stochastic Tunneling Multipath fading and shadow fading noise are the primary cause for large localization error in an indoor environment Rx Rx Tx Tx Multipath Fading Shadow Fading 36
  37. 37. Spatial Correlation in Fading Noise 37
  38. 38. RFID Basics  Typically passive device that are energized by radio waves from a tag reader  RFID Tag varies the Radar Cross Section (RCS) to communicate its unique identification to the tag reader 13.56MHz Passive RFID Tag Passive RFID system overview11Nikitin et al. 2006. 38
  39. 39. Application Scenario Movement causes multipath noise Similarity in fading noiseexperienced by neighboring RFID tags is exploited to localize them Anchor nodes Container with placed around the RFID tags reader Displays tag ID and location 39
  40. 40. Objective Objective to derive a RSSI localization method that works under fading noise Localize multiple RFID tags simultaneously from a common transmitter Anchor nodes provide localization correction and reorient the generated location to a global coordinate Localizing RFID tags in a container Past Work  Multi-Dimensional Scaling (MDS) [Ji 04]  Local Linear Embedding (LLE) [Costa 06] 40
  41. 41. RFID Tag Localization Flow Chart 41
  42. 42. Assumptions  In-phase and Quadrature-phase of backscattered signal amplitudes are normally distributed  Distribution of backscattered energy around the tag reader is given by a circular normal distribution called von-Mises Distribution Backscattered signal concentration 42
  43. 43. Backscattered Signal PDF Theorem 1: Joint PDF of backscattered RSSI values measured by a tag reader from any two RFID tags separated by radial distance r12 is given by where P1 and P2 are the backscattered RSSI random variables from tag 1 and 2 respectively with p1 and p2 being their realizations, µ1 and µ2 are their average values, 0≤ρ12≤1 and are the backscattered RSSI correlation parameters and I0(◦) is the zeroth order modified Bessel function of the first kind where Θ12 is the azimuth orientation of the tag reader, δθ12 is the concentration of multipath signals around the tag reader orientation Θ12 , , λ is operating wavelength and In(◦) and Jn(◦) are the modified and ordinary Bessel functions respectively of the first kind and order n 43
  44. 44. Localization from Correlation Coefficient Theorem 2: The large sample approximate PDF of ρ12 is given by where is the indicator function that restricts the support of this PDF between [0, 1], and and are the PDF and CDF respectively of a standard normal distribution Pseudo-likelihood method is used to create an approximate likelihood function for M RFID tags from their pair wise PDF 44
  45. 45. Simulation Results Algorithm called LOCUST (Localization Using Stochastic Tunneling) 8 RFID tags and 8 anchor nodes in a 20m x 20m x 20m workspace Wireless tags were positioned randomly i.e. xi, yi and zi of the wireless tags are random variables with continuous uniform distribution in the domain [-10, 10] for i є {1,2,…,m} Total of 50 simulation trials were done to determine the mean, median, standard deviation and 90th percentile of localization errors. 45
  46. 46. Summary of Localization Error Levels Localization Error (m) Localization Error (m) F 90th F 90thMethod Method (MHz) Mean Median percentil Std. dev. (MHz) Mean Median percentil Std. dev. e eLOCUST 0.454 0.429 0.676 0.172 LOCUST 1.359 1.259 1.943 0.485 LLE 20.0 2.764 2.67 4.095 0.949 LLE 20.0 7.90 7.318 11.382 2.652 MDS 2.272 2.136 3.378 0.778 MDS 6.019 5.609 8.486 2.238LOCUST 0.343 0.331 0.518 0.127 LOCUST 0.850 0.804 1.179 0.268 LLE 15.0 1.009 0.969 1.507 0.351 LLE 15.0 2.866 2.831 3.818 0.874 MDS 0.935 0.889 1.429 0.375 MDS 2.92 2.566 4.923 1.490LOCUST 0.233 0.230 0.307 0.056 LOCUST 0.696 0.702 1.067 0.286 LLE 10.0 0.248 0.245 0.326 0.06 LLE 10.0 1.684 1.657 2.509 0.599 MDS 0.194 0.192 0.263 0.05 MDS 1.722 1.652 2.383 0.513LOCUST 0.201 0.189 0.322 0.09 LOCUST 0.274 0.243 0.469 0.135 LLE MDS 5.00 0.270 0.194 Accuracy degrades with LoS 0.260 0.186 0.396 0.308 0.10 0.086 LLE MDS 5.00 0.542 0.477 0.500 0.434 0.791 0.786 0.201 0.207LOCUST 0.195 0.191 0.283 0.066 LOCUST 0.236 0.227 0.323 0.066 LLE 2.50 0.187 0.180 0.272 0.063 LLE 2.50 0.198 0.179 0.287 0.061 MDSLOCUST 0.202 0.111 Accuracy degrades with 0.195 0.103 0.286 0.177 0.062 0.048 MDS LOCUST 0.192 0.131 0.192 0.114 0.256 0.278 0.059 0.060 LLE MDS 1.00 0.198 0.127 increasing frequency 0.191 0.117 0.291 f = 10MHz 0.197 0.07 0.062 LLE MDS 1.00 0.189 0.118 0.185 0.112 0.177 0.159 0.059 0.041LOCUST LLE 0.06 0.105 0.202 0.099 0.197 0.164 0.289 0.048 0.066 f =LOCUST 0.06 20MHz LLE 0.154 0.213 0.170 0.189 0.216 0.327 0.057 0.081 MDS 0.177 0.165 0.281 0.072 MDS 0.178 0.173 0.261 0.062 46
  47. 47. Localization Error and Anchor Node CountAnchor Localization Error (m) Node 90thCount Mean Median Std. dev. percentile 6 0.486 0.432 0.713 0.253 7 0.354 0.378 0.693 0.173 8 0.293 0.278 0.492 0.142 9 0.223 0.244 0.454 0.119 10 0.215 0.210 0.431 0.113 11 0.220 0.216 0.441 0.121 12 0.236 0.225 0.469 0.136 Localization accuracy degraded after 10 anchor nodes due to the large dimension of the estimated variables 47 CDF Of localization error at f=20MHz
  48. 48. Conclusions and ContributionsConclusions Contributions A novel RFID tag localization algorithm  A novel RFID tag localization called LOCUST that estimates the algorithm called LOCUST that position of RFID tags by measuring the estimates the position of RFID correlation between RSSI values tags by measuring the correlation between co-located tags was presented between RSSI values between co-located tags was presented Above 10MHz the non-linear relationship between the correlation coefficient and radial separation results  Joint distribution of backscattered in LOCUST performing better than MDS power from adjacent RFID tags and LLE was derived Localization error under LoS condition was larger in comparison to NLoS  Functional relationship between conditions primarily due to faster drop in backscatterd signal power correlation coefficient with distance correlation, radial separation and under LoS conditions line of sight condition was derived 48
  49. 49. Paper 4: Localization and Tracking of Objects Using Cross-Correlation of Shadow Fading Noise Objectives  Increase the frequency of operation of cross- correlation based RSSI localization  Resilient to pedestrian or machinery traffic  Improve the convergence speed of cross-correlation based localization Past work  Network Shadowing [Agarwal 09]  Large scale correlation model [Gudmundson 91]  Multi-Dimensional Scaling (MDS) [Ji 04]  Local Linear Embedding (LLE) [Costa 06] 49
  50. 50. Localization from Shadow FadingCorrelation Neighboring receivers experience similar shadow fading noise 50
  51. 51. Flowchart of Shadow Fading Cross-CorrelationBased Localization 51
  52. 52. Shadow Fading Wireless Channel Model Geometrically Based Single Bounce Elliptical Model (GBSBEM) Wireless Channel Model is assumed under shadow fading Any radio signal that reaches the receiver after bouncing off of a scatterer in the localization region can affect signal fading if and only if its ToA satisfies GBSBEM Wireless Channel Model where r is the radial separation between the transmitter and receiver, c is the speed of radio and τm is the signal integration time at the reciever IEEE 802.15.4 receivers integrate the signal for 128us before computing the signal strength resulting in τm = 128us 52
  53. 53. Shadow Fading Correlation Coefficient Pedestrian traffic is modelled as Poisson process Shadow fading attenuation is normally distributed Theorem 1: Correlation coefficient under GBSBEM given by Overlapping of scattering regions causing cross-correlation in shadow fading where |·| is the area operator, S1 and S2 are the elliptical scatterer regions surrounding receivers R1 and R2 respectively, S12 is overlapping region between scattering regions S1 and S2. 53
  54. 54. Extraction of Shadow Fading Residuals Ornstein Uhlenbeck stochastic model usually applied for high volatility stock trading is used to extract shadow fading residuals from RSSI Autoregressive Model (AR) for Xs(t) to separate path loss from shadow fading residuals where ϵs(t)=σs(t)Zs Generalized Auto Regressive Conditional Heteroskedasticity (GARCH) for to account for fast changes in pedestrian traffic 54
  55. 55. Localization Using Student-t Copula Copula function helps to create joint distributions from marginal CDFs and their inter-dependency  Gaussian & Student-t Copula models linear dependency  Gumbel, Frank and Clayton Copulas model tail dependency Theorem 2: For an M receiver localization system, Student-t copula was used since shadow fading correlation coefficient is a linear dependencywhere is the inverse CDF or quantile function vector of a student-t distributionwith degree of freedom v, is an M-variate student-t copula density with vdegree of freedom, P is an MxM correlation coefficient matrix given by Ρ={ρkl}; k,l ϵ{1,2,…,M} and ρkl is the correlation coefficient between receiver k and l and 55
  56. 56. Tracking Using Divergence Divergence arise in classification problem when a measurement x has to be categorized into two possible groups C1 or C2 Miss-classification occurs when x is assigned to C1 while it should have been in C2 or vice versa α-Divergence is a measure of the upper bound in Bayes error in classification problems where C1||C2 implies divergence operation between groups C1 and C2, f(x|Ci) is the PDF of random variable X given that it belongs to group Ci;iϵ{1,2}, x is a single realization of random variable X and the integration is over the entire range of random variable For velocity estimation the hypothesis being tested is that the RSSI values that a receivers measures is from a stationary transmitter 56
  57. 57. α-Divergence for a Mobile Transmitter Theorem 3: For a mobile transmitter operating under GBSBEM wireless channel model, α-divergence of RSSI measured between two time instances n and n-1 is given byθn-1 is the azimuth angle of arrival of LoS radio signal atthe receiver with respect to the direction of motion of thetransmitter while rn-1 is the radial separation between thetransmitter and receiver at time instance n-1, Δrn is thedistance the transmitter travelled between time instances Tracking an IEEE 802.15.4n-1 and n and rm=cτm and ω is the average scatterer Transmitterdensity 57
  58. 58. Speed Estimation Using α-divergence For slow moving (≤1m/s) IEEE 802.15.4 transmitter, α- Divergence is related to transmitter’s velocity as Bhattacharyya coefficient where α=0.5 is used for velocity estimation Fully functional dead-reckoning based tracking system can be realized from velocity and transmitter heading measured using either a gyroscope or an antenna array 58
  59. 59. Copula Smoothing Using Bayesian Particle Filter Dead reckoning based tracking method results in incremental position error over time Bayes particle filter is a stochastic filter that generates multiple random points or particles around the position estimated from dead reckoning method Student-t Copula likelihood function computes the likelihood of each generated particle which forms the weight of that particle The copula smoothed position is the weighted average of all the generated particles Copula smoothing will generate an accurate solution as long as the dead- reckoning generated position is close to the global maxima of the Likelihood function 59
  60. 60. Static Localization Experimental Results Localization area approx. 1250 sq. m with an average of 1000 people moving in this area during peak lunch hour traffic on a weekend between of 10AM and 1PM 8 Receivers R1 through R8 localizing a transmitter Localization Errors At Various Locations Transmitter Localization Error (m) Location Mean Median 90th Perc. Std. Dev T1 2.458 2.329 3.962 1.727 T2 2.378 2.267 3.628 1.221 T3 3.537 3.496 77% 5.234 82% 2.377 83% T4 2.739 2.912 decrease decrease decrease of food court area with dark lines 4.138 1.839 Layout showing physical boundary Summary of Localization Errors Localization Error (m) Method Mean Median 90th Perc. Std. Dev MDS 12.343 15.925 25.358 6.464 Proposed Method 2.778 2.751 4.2405 1.791 60
  61. 61. Tracking Experimental Results Tracking experiment performed at ERL 114 8 wireless receivers R1 through R8 tracking a transmitter 3DM-GX2 Attitude Heading Reference System (AHRS) from Microstrain attached to the transmitter Top view of ERL 114 with tracked points Summary of Tracking Errors Tracking RMSE (m) Method Mean Min Max Std. Dev α-divergence 0.3859 0.0464 0.8652 0.2944 INS 0.2466 0.0025 0.6719 0.1972 Copula 0.1777 0.0105 0.4379 0.1505 Smoothing Comparison of Tracking Errors 61
  62. 62. Conclusions and ContributionsConclusions Contributions Extended the operating frequency  Derived the correlation in shadow fading range of cross-correlation based noise between adjacent receivers localization from 20MHz to 2.15GHz  Developed a stochastic filtering method At small velocities α-Divergence to isolate shadow fading residuals from based velocity estimation performed RSSI better than accelerometer based velocity estimation  Developed a transmitter velocity estimation technique that measures α- divergence of RSSI values  Copula smoothing algorithm using Bayesian particle filter was implemented to prevent the accumulation of tracking error over time 62
  63. 63. Paper 5: Placement of Receivers for Shadow Fading Cross-Correlation Based Localization Objectives  Provide a receiver placement algorithm for cross- correlation based localization  Resilient to pedestrian and machinery traffic Past Work  Sub-optimal receiver placement using Delaunay Refinement [Basheer 10]  Optimal receiver placement algorithm [Isler 06]  Placement based on maximizing the condition number [Martinez 05] 63
  64. 64. Shadow Fading Wireless Channel Model Geometrically Based Single Bounce Elliptical Model (GBSBEM) Wireless Channel Model is assumed under shadow fading Any radio signal that reaches the receiver after bouncing off of a scatterer in the localization region can affect signal fading if and only if its ToA satisfies GBSBEM Wireless Channel Model where r is the radial separation between the transmitter and receiver, c is the speed of radio waves, r/c is the ToA of LoS signal and τm is the signal integration time at the reciever IEEE 802.15.4 receivers integrate the signal for 128us before computing the signal strength resulting in τm = 128us 64
  65. 65. Optimal Unconstrained Receiver Placement Theorem 1: (Equilateral Triangular Grid for Receiver Placement) A receiver placement strategy whose objective is to span the largest area under localization coverage with least number of receiver while ensuring no coverage holes exists within the grid will have all its receivers placed in an equilateral triangular grid. Equilateral grid is not possible near bounding walls 65
  66. 66. Receiver placement near bounding wallsLocalization coverage hole near bounding walls 66
  67. 67. Receiver Placement Quality Metric Theorem 2: Cramer-Rao Lower Bound for the variance in estimating the transmitter at Cartesian coordinate from receivers that are under localization coverage with a transmitter using cross-correlation of shadow fading residuals between receiver pairs is given by Receiver placement quality metric is for workspace G Objective is to attain with least number of receivers 67
  68. 68. Flowchart of Receiver Placement Algorithm Localization Coverage Localization Error Coverage Grid Equilateralholes 68
  69. 69. Simulation Results Delaunay Refinement was used to search for receiver positions in linear time Receiver count for cross- correlation coverage placement was lower than using Delaunay Refinement search Delaunay refinement generates more receivers near sharp edges Receiver count vs. communication range Improvement in receiver count was at the expense of search time 69
  70. 70. Simulation Results Localization Error (m) No. of Tx. rx. in Media 90th Std.Location Mean range n Perc. Dev T1 4 0.894 0.792 1.579 0.466 T2 3 0.926 0.883 1.526 0.472 T3 4 0.792 0.828 1.377 0.418 T4 4 0.779 0.698 1.534 0.481 T5 4 0.879 0.927 1.445 0.407 T6 3 0.955 1.100 1.693 0.562 T7 5 0.652 0.690 1.076 0.325 T8 6 0.677 0.550 1.401 0.484 T9 3 0.907 0.943 1.484 0.475 T10 4 0.712 0.762 1.167 0.360 70
  71. 71. Conclusions and ContributionsConclusions Contributions Developed a receiver placement  Derived the optimal unconstrained algorithm for cross-correlation – placement for cross-correlation based based localization localization  Derived the Cramer-Rao lower bound Average localization error was for transmitter location estimation well under the designed 1m error variance under cross-correlation based localization method This method generated lower receiver count for a given  A receiver placement algorithm was communication range when developed for the cross-correlation compared with a Delaunay method that ensures the localization refinement based placement accuracy within the workspace is less than a pre-specified threshold. 71
  72. 72. Conclusions and Future Work--DissertationConclusions Future work Localization from cross-  Explore techniques that can correlation of RSSI is suited for measure transmitter heading from multipath rich environment such RSSI values so that the as factory floor, food court etc. requirement for compass or Our technique takes advantage gyroscope can be removed of the temporal correlation in RSSI that arise in co-located  Improve the execution time for receivers due to the movement receiver placement algorithm for of people or machinery in its cross-correlation based localization vicinity Performance of our proposed  Improve the accuracy of shadow algorithms were validated using fading correlation by better hardware experiments on IEEE modeling of the shadow fading 802.15.4 receivers cross-correlation likelihood 72
  73. 73. Questions Thank you! 73
  74. 74. References [Costa 06] J. A. Costa , N. Patwari, and A. O. Hero, ―Distributed weighted-multidimensional scaling for node localization in sensor networks,‖ ACM Trans. on Sensor Networks, vol.2, No.1, pp.39-64, Feb. 2006. [Gwon 04] Y. Gwon and R. Jain, ―Error characteristics and calibration-free techniques for wireless LAN-based location estimation,‖ Proc. of ACM MobiWac, pp. 2-9, October 2004. [Isler 06] V. Isler, ―Placement and distributed deployment of sensor teams for triangulation based localization,‖ In Proc. IEEE ICRA, pp. 3095-3100, May, 2006. [Ji 04] X. Ji, and H. Zha, ―Sensor positioning in wireless ad-hoc sensor networks using multidimensional scaling,‖ 23rd Annual Joint Conf. of the IEEE Computer and Commun. Soc. , vol.4, pp. 2652- 2661, Mar. 2004. [Lakhzouri 03] A. Lakhzouri, E. S. Lohan, R. Hamila, and M. Renfors, ―Extended kalman filter channel estimation for line-of-sight detection in WCDMA mobile positioning,‖ EURASIP Journal on Applied Signal Processing, vol. 2003, no. 13, pp. 1268-1278, 2003. [Martinez 05] S. Martínez, and F. Bullo, ―Optimal sensor placement and motion coordination for target tracking,‖ Proc. of the inter. Conf. on Robotics and Automation, Barcelona, Spain, pp. 4544-4549, April 2005. [Venkatraman 02] S. Venkatraman and J. Caffery Jr., ―Statistical approach to nonline-of-sight BS identification,‖ Proc. of the 5th International Symp. on Wireless Personal Multimedia Comm., vol. 1, pp. 296–300, Hawaii, USA, October 2002. [Wu 07] C. Wu, K. Lee, and Y. Chung, ―A Delaunay Triangulation based method for wireless sensor network deployment,‖ Computer Communications, Volume 30, Issue 14-15, pp. 2744-2752, Oct 2007. 74

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