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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
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
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
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
