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,d 0,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 d 0,σ n, ε n and cell radius R n.

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 x k is the system state and w k,v k, 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 w 1, w 2 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