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Ioannis G. Papageorgiou Charalambos D. Charalambous Christos Panayiotou University of Cyprus

An Enhanced Received Signal Level Cellular Location Determination Method via Maximum Likelihood and Kalman Filtering. Ioannis G. Papageorgiou Charalambos D. Charalambous Christos Panayiotou University of Cyprus WCNC 2005, New Orleans, LA USA 13-17 March 2005. Summary. Problem statement

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Ioannis G. Papageorgiou Charalambos D. Charalambous Christos Panayiotou University of Cyprus

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  1. An Enhanced Received Signal Level Cellular Location Determination Method via Maximum Likelihood and Kalman Filtering Ioannis G. Papageorgiou Charalambos D. Charalambous Christos Panayiotou University of Cyprus WCNC 2005, New Orleans, LA USA 13-17 March 2005

  2. Summary • Problem statement • Drivers • Main obstacles • Proposed solution • Advantages • Assumptions • Initial Estimate • Final Estimate • Conclusions

  3. Problem Statement I • Accurately tracking a cell phone • Other key variables come into play • Consistency • TTFF (Time To First Fix) • Cost (of course) • and more • Main Drivers • Regulatory • E-911, E-112 mandates • Commercial

  4. Problem Statement II • Main Obstacles to Location Estimation • Non Line of Sight (NLoS) conditions • Multipath Propagation • Dynamicity of user and environment • Geometric Dilution of Precision

  5. Proposed Solution I • A two-step CLD method based on Maximum Likelihood and Kalman Filtering Estimation Techniques • First step • RSL method in combination with MLE and triangulation • RSL values from Network Measurement Reports (NMR) are used • Time-invariant lognormal propagation model • Achieves a rough localization

  6. Proposed Solution II • Second and Final Step • Extended Kalman Filtering on instantaneous field measurements is used • The 3D Aulin model used to account for multipath propagation and NLoS conditions • The first-step estimate is incorporated to initialize the filter • A high accuracy is achieved

  7. Proposed Solution III • Advantages • No hardware modifications are needed at the network • Uses current standards and infrastructure • Assumptions • Channel knowledge • Access to the instantaneous received signal

  8. Initial Estimate I • NMR values of RSL are used to estimate the location, through MLE • Lognormal Propagation model where • Parameters ε,d0,and the variance of X should be estimated or selected with care

  9. Initial Estimate II • Sample m from all N BSs, follows the N-variate Gaussian distribution, i.e., where is the mean path loss for each BS. • Assuming iid noise, the likelihood function is the product of the individual likelihood functions

  10. Initial Estimate III i.e., • Maximizing with respect to and solving for using the invariance property of the MLE, we get which is the MLE for the distance of the n-th BS from the MS

  11. Initial Estimate IV • Then, we perform triangulation using the least squares error method to estimate the location where

  12. Initial Estimate V • Simulation Setup • 19(!) cell cluster, BSs equipped with omnidirectional antenna and the number of arranged users in the central cell is 1000 • The simulated environment is designated by the values of d0,σn, εnand cell radius Rn.

  13. Initial Estimate VI • Number of NMR samples is 20, and the number of BSs is 3-7. • Results for urban (R=500m) and suburban (R=2500m) environments

  14. Initial Estimate VII • The FCC mandate is satisfied for urban environments only. Inconsistency of the method • Main error source is triangulation. The error increases as the cell radius increases • Failure as a stand-alone method BUT • Localizes the problem

  15. Final Estimate I • The well-known 3D multipath channel of Aulin is incorporated to better account for channel impairments

  16. Final Estimate II • The electric field at any receiving point consists of N plane waves, and is given by where and n(t) is white Gaussian noise • IMPORTANT: it depends parametrically on the location of the receiver, thus it can be utilized to estimate it

  17. Final Estimate III • Extended Kalman Filtering (EKF) is used to estimate the location. The Initial Estimate initializes the filter estimate • The discretized state-space form is where xkis the system state and wk,vk, are zero-mean independent Gaussian noise processes

  18. Final Estimate IV with covariance , • Clearly, h(.) is non-linear, thus EKF is used:

  19. Final Estimate V where • Simulation Setup: same as for the Initial Estimate but 5 BSs • Results for the worst case suburban environment are depicted • Presenting the case when the location as well as the velocity is unknown, thus the system state is

  20. Final Estimate VI • Assuming zero-mean Gaussian acceleration, the dynamics of the mobile are given by where w1, w2 are white noise processes. In discrete time, the dynamics are given by

  21. Final Estimate VII in which f(.) is a linear and A is a 4x4 identity matrix • For urban areas we take with Rayleigh distributed attenuation. In urban and suburban areas we take N between 2-6 with Nakagami distributed attenuation

  22. Final Estimate VIII Results for rural areas

  23. Final Estimate IX

  24. Conclusions • Triangulation is an obstacle for location estimation • Stand-alone methods are not consistent • The algorithmic part of a method is important for TTFF • A method should be robust against channel knowledge

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