Joint position and LOS-NLOS tracking for mobile location systems

1. Joint position and LOS-NLOS tracking for mobile location systems Josep Vidal, Jose M. Huerta, Signal Processing and Communications Group Universitat Politècnica de Catalunya (UPC)

2. The mobile location problem Objective: Estimate the position of a mobile using the pilot signals sent by several base stations. • Two main problems : • Multipath • Non-Line-Of-Sight • These problems bias the estimates, therefore providing biased positions.

3. Multipath problem • The multipath can bias the ToA estimates • SOLUTION: Use a high-resolution timing estimation

4. NLOS Problem • Always biases timing measures • SOLUTION: LOS/NLOS situation and position are tracked using a coupled Kalman filter

5. sec.) n TOA RMSE ( NLOS Problem • Including the bias in the state vector is possible, but it requires:a) Increasing the number of observationsb) Having a limited number of unbiased observationsc) Knowing which ones are in LOS and in NLOS Effect of Bias tracking in TOA measures 180 TOA RMSE TOA minus estimated bias RMSE TOA RMSE + standard deviation TOA minus estimated bias RMSE + standard deviation 160 140 120 100 80 60 40 20 0 1/4 1/2 1 2 4 Number of slots used for channel estimation

6. Summary • High resolution estimation of delay • Coupled Kalman tracking • Environment description • Measurement campaign • Results and conclusions

7. Delay estimation: NMV method • The DFT of the estimated channels follows the model: • The timing estimation of the first arrival can be computed as the first maximum of the expression:

8. The NMV Algorithm (ii) • Results for a light multipath situation:

9. The NMV Algorithm (iii) • Results for a hard multipath situation:

10. Dealing with NLOS … • The LOS-NLOS situation probability is estimated for each TOA measurement using a Hidden Markov Model • The position is tracked from these measurements using an improved Unscented Kalman Filter • The main objective is to benefit from LOS-NLOS probability estimation in the improved UKF

11. General situation-driven observation model (Position) (LOS/NLOS)

12. p LN p p LOS NLOS LL NN p NL LOS/NLOS: Discrete-state model The transition probabilities are related to the environment and the mobile speed as follows: The expectation depends of the environment (urbal, rural, ...)

13. Pdf of the duration of LOS/NLOS situations LOS pdf NLOS pdf Meters (x10) Meters (x10)

14. Speed coupling General situation-driven observation model (Position) (LOS/NLOS)

15. Range Delay Spread Indicator Prediction Error meters meters PDF of situation events under LOS and NLOS Measurements related to the situation

16. Speed coupling General situation-driven observation model (Position) Prediction error (LOS/NLOS)

17. The position observations equation (I) Non Gaussian noise, depends on the situation Gaussian noise It does not depend on the situation It depends on the situation

18. Comparisson of error PDF between empirical error and ideal model for NLOS 0.04 Error from real data Ideal Rayleigh PDF 0.035 0.03 0.025 Probability Density 0.02 0.015 0.01 0.005 0 0 20 40 60 80 100 120 140 Equivalent meters The model of noise for NLOS assumes a non-symetric, non-zero mean density The position observations equation (II) PDF of observation noises under LOS and NLOS Comparisson of error PDF between empirical error and ideal model 0.09 Error from real data Ideal Gaussian pdf 0.08 0.07 0.06 0.05 Probability Density 0.04 0.03 0.02 0.01 0 -40 -30 -20 -10 0 10 20 30 40 Equivalent meters

19. … computed from the situation tracker LOS NLOS The position observations equation (III)

20. Speed coupling General situation-driven observation model Unscented Kalman tracker (Position) Prediction error (LOS/NLOS) Optimum tracker

21. Unscented Transform (I) The unscented transform is an approach that allows calculating the statistics of random variables undergoing non-linear transformations (the state and observation functions) Input statistics Output sigma set Output statistics Sigma set Pass through a non-linear function

22. Unscented Transform (II) Input Non-linear function Output Twice the number of sigma points are required because of the two possible situations (LOS/NLOS)

23. Unscented Transform (III) Construction of the sigma set: where is a parameter that regulates the of the sigma points spreading This is called Direct Unscented Transform:

24. Unscented Transform (IV) The statistics are obtained as the sample estimates from a sigma set: This is the inverse unscented transform:

25. Unscented Transform (V) Let’s transform a random variable: Pass through a non linear funtion each of the sigma points Finally obtain the output statistics

26. Unscented Kalman filter (I) • It provides an MMSE solution to the Bayesian problem • While EKF approaches the observation statistics to the first order moment, the UKF does it up to the second order moment • No convergence problems

27. Unscented Kalman filter (II) Let the extended state vector be: State State noise Observation noise First, we compute the sigma set associated with the previous iteration extended state vector

28. Unscented Kalman filter (III) Second, we predict the next state: Third, predict the observation:

29. Unscented Kalman filter (IV) Fourth, compute the Kalman gain matrix: Finally, obtain the statistics of the state vector:

30. Measurement campaign • Final goal: evaluate the proposed approach in a real UMTS scenario • Urban conditions: • Four BS available (in NLOS the most of them) • TDOA measures • Use the common pilot downlink channel • Every BS is in NLOS 60% of time (only 2,4% of time the four BS are in LOS)

31. Base Station 3 dB fall LOS zone Multipath zone NLOS zone The environment

32. Multiple BS emulation • The two paths are moved to the same geographical position. This is achieved by rotating, translating the coordinate reference and interpolating to adjust speeds. • The result is one transmission path with two receiving BS.

33. Results using the Common Pilot Channel in Downlink • No power control is used • The SINR is determined from: • The factor a reflects the processing gain due to the pilot sequence correlation, and depends on the number of pilot slots used for the channel estimation

34. Results for different situation trackers Comparison for different state prediction models using the UKF 24 22 Keeping the most likely situation 20 Weighting the pdf of the observations 18 Positioning RMSE (meters) 16 14 Direct function 12 HMP - Dynamic Programming HMP - Fordward iteration Clairvoyant estimation 10 1/4 1/2 1 2 4 Slots used for channel estimation

35. Performance of different location trackers Comparison between trackers 35 30 25 RMSE (meters) 20 15 Particle Filter RMSE + Std. deviation UKF RMSE + Std. Deviation 10 EKF RMSE + Std. deviation Particle filter RMSE UKF RMSE EKF RMSE 5 1/4 1/2 1 2 4 Slots used for channel estimation

36. Convergence speed 250 UKF Particle Filter 200 150 Postioning error (meters) 100 50 0 0 5 10 15 Time (sec.) Convergence

37. Conclusions • Mobile location system in severe multipath and NLOS situations is a hard problem • Multipath can be mitigated with advanced high resolution techniques • The improvement in positioning accuracy achieved by NLOS tracking is significant even in severe conditions, and not far from particle filter approach • A certain knowledge of the propagation environment is required • Improvement is still possible if a tighter coupling of the trackers is done