![Chart 3
Received Signal Strength - Example 1
Scatter plot
RSS [dBm]
Measured RSS
AP in the corridor
User-AP Distance [m]](https://image.slidesharecdn.com/on-linetrainingofthepath-lossmodelinbayesian-131127073232-phpapp02/85/On-Line-Training-of-the-Path-Loss-Model-in-Bayesian-WLAN-Indoor-Positioning-3-320.jpg)
![Chart 4
Received Signal Strength - Example 2
RSS [dBm]
AP in room
Measured RSS
Scatter plot
User-AP Distance [m]](https://image.slidesharecdn.com/on-linetrainingofthepath-lossmodelinbayesian-131127073232-phpapp02/85/On-Line-Training-of-the-Path-Loss-Model-in-Bayesian-WLAN-Indoor-Positioning-4-320.jpg)
![Chart 8
Observability of Parameters
k=1
k=20
k=5
Simulative scenario:
• 20 RSS i.i.d. at different
User-AP distances
•
RSS Likelihood Function
•
•
•
Distances assumed known
Function of h and a
Depicted at k=1,5,20
Formal proof of observability can be given
Exponent
•
Transmit power [dBm]
L. Bruno and P. Robertson, “Observability of Path Loss Parameters in WLAN-Based Simultaneous
Localization and Mapping”, IPIN 2013](https://image.slidesharecdn.com/on-linetrainingofthepath-lossmodelinbayesian-131127073232-phpapp02/85/On-Line-Training-of-the-Path-Loss-Model-in-Bayesian-WLAN-Indoor-Positioning-8-320.jpg)
![Chart 18
Experiment 1 – Localization Error
Localization error [m] vs. time
CDF of the error [m]
Fixed parameters
Our proposal
Only odometry](https://image.slidesharecdn.com/on-linetrainingofthepath-lossmodelinbayesian-131127073232-phpapp02/85/On-Line-Training-of-the-Path-Loss-Model-in-Bayesian-WLAN-Indoor-Positioning-18-320.jpg)
![Chart 20
Experiment 2 – Localization Error
Localization error [m] vs. time
CDF of the error [m]](https://image.slidesharecdn.com/on-linetrainingofthepath-lossmodelinbayesian-131127073232-phpapp02/85/On-Line-Training-of-the-Path-Loss-Model-in-Bayesian-WLAN-Indoor-Positioning-20-320.jpg)
On Line Training of the Path-Loss Model in Bayesian WLAN Indoor Positioning
- 1. On-Line Training of the Path-Loss Model in Bayesian WLAN Indoor Positioning Luigi Bruno, Mohammed Khider and Patrick Robertson Institute of Communications and Navigation, German Aerospace Center (DLR) Oberpfaffenhofen, Germany
- 2. Chart 2 Received Signal Strength – Why and How? AP 30 m
- 3. Chart 3 Received Signal Strength - Example 1 Scatter plot RSS [dBm] Measured RSS AP in the corridor User-AP Distance [m]
- 4. Chart 4 Received Signal Strength - Example 2 RSS [dBm] AP in room Measured RSS Scatter plot User-AP Distance [m]
- 5. Chart 5 Received Signal Strength - Comparison Even in the same building at the same time and with same receiver, two APs can show different propagation models AP in the corridor AP in the room
- 6. Chart 6 Related Work • RSS based positioning - Fingerprinting • Bahl and Padmanabhan (RADAR, 2000) • Haerleben et al. (2004), Yin et al. (2008), Fang et al. (2011) • RSS based positioning – Adaptivity in path-loss techniques • Li, (2006) • Bose et al. (2007) • Zhang et al. (2012) • Other work relevant to us • Particle filter based positioning: • Transmit power calibration: • RSS model calibration: Arulampalam (2002) Addesso et al. (2010) Nurminen et al. (IPIN 2012)
- 7. Chart 7 Indoor Radio Propagation Model Ex. Least Squares Estimators • RSS Likelihood Gaussian in dBm • Expected power: path-loss model • We require: • • Transmit signal strength Decay exponent In corridor: h=-48 dBm, a=1.4 In room: h=-50 dBm, a=1.8
- 8. Chart 8 Observability of Parameters k=1 k=20 k=5 Simulative scenario: • 20 RSS i.i.d. at different User-AP distances • RSS Likelihood Function • • • Distances assumed known Function of h and a Depicted at k=1,5,20 Formal proof of observability can be given Exponent • Transmit power [dBm] L. Bruno and P. Robertson, “Observability of Path Loss Parameters in WLAN-Based Simultaneous Localization and Mapping”, IPIN 2013
- 9. Chart 9 Bayesian Filter • Bayesian algorithm: Compute recursively at each time step k and for each AP j: Path-loss parameters User‟s state RSS measurements • User‟s state: Position and, eventually, velocity of the user • „Predicted‟ by a theoretical user‟s movement model (e.g. NCVM) • „Estimated‟ by step measurements (accelerometers, compass,…) • h and a independently sampled from suitable priors (here uniformartive) • RSS measurements independent over j and k
- 10. Chart 10 Rao-Blackwellized Particle Filter • Implementation based on a Rao-Blackwellized Particle Filter • In our case: User‟s state Path Loss parameters
- 11. Chart 11 Path-Loss Parameters Estimation • We discretize the propagation parameters on a finite grid • A “hypothesis” is a pair of values • Hypothesis probabilities are updated with any new RSS and each particle -40 -38 -36 -34 -32 1.5 2.0 2.5 3.0 3.5
- 12. Chart 12 Localization Algorithm • • Define grid for h and a • Initialize Sample initial state for all particles Uniform prior for h and a Iterations particle i particle 1 • Draw User‟s State • Draw User‟s State • Weight on new RSS • Weight on new RSS • Update parameters pmf • Update parameters pmf Marginalization on hypotheses
- 13. Chart 13 Simulations – RMSE Average parameters 40 x 20 m testbed 5 APs, 1000 particles Movement model: NCVM RSS noise Our proposal h and a ~ Gaussians 100 Monte Carlo trials Best case: known parameters
- 14. Chart 14 Simulations – h Estimation Accuracy
- 15. Chart 15 Simulations – a Estimation Accuracy
- 16. Chart 16 Experiments and Results • Two different office buildings • Data collected by a pedestrian wearing a foot mounted IMU and holding either a laptop or a smartphone • Normal WiFi network of the buildings – no ad-hoc additions • Scenarios: • Building KN – DLR-OP (smartphone – OS Android) • Building TE01 – DLR-OP (laptop – OS Windows XP) • Experiments: • Walks between 4 and 7 minutes long in corridors and offices
- 17. Chart 17 Experiment 1 - Trajectory Final best particle 65 x 20 meters, 4 minutes walk, 4 APs Equipment: • Foot-mounted IMU • Android Smartphone (Hand-held) 1000 particles RSS noise: s=5 dBm
- 18. Chart 18 Experiment 1 – Localization Error Localization error [m] vs. time CDF of the error [m] Fixed parameters Our proposal Only odometry
- 19. Chart 19 Experiment 2 - Trajectory 45 x 25 meters, 7 minutes walk, 4 APs Equipment: • Foot-mounted IMU • Laptop - OS Windows XP 1000 particles RSS noise: s=5 dBm
- 20. Chart 20 Experiment 2 – Localization Error Localization error [m] vs. time CDF of the error [m]
- 21. Chart 21 Opportunistic RSS: Need to Map? Can the building map help? If APs are unknown? L. Bruno and P. Robertson, “Observability of Path Loss Parameters in WLAN-Based Simultaneous Localization and Mapping”, IPIN 2013 Session We1-IUT1: Tomorrow at around 10.45
- 22. Thank you! Contacts: Luigi Bruno, PhD Phone: +49 - 8153 28 4116 Email: luigi.bruno@dlr.de, lbruno236@gmail.com Department of Communication Systems Institute of Communications and Navigation German Aerospace Center Weßling, Germany