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

30 m

Received Signal Strength – Why and How?

AP

Chart 2

Scatter plot

User-AP Distance [m]

Mea

sure

d R

SS

Chart 3

AP in the corridor

RS

S [dB

m]

Received Signal Strength - Example 1

Chart 4

Received Signal Strength - Example 2

AP in room

RS

S [dB

m]

Scatter plot

Mea

sure

d R

SS

User-AP Distance [m]

Chart 5

Received Signal Strength - Comparison

AP in the corridorAP in the room

Even in the same building at the same time and with same receiver,two APs can show different propagation models

• 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: Arulampalam (2002)• Transmit power calibration: Addesso et al. (2010)• RSS model calibration: Nurminen et al. (IPIN 2012)

Related Work

Chart 6

• RSS Likelihood Gaussian in dBm

• Expected power: path-loss model

• We require:

• Transmit signal strength• Decay exponent

Indoor Radio Propagation Model

Chart 7

Ex. Least Squares Estimators

In corridor: h=-48 dBm, a=1.4 In room: h=-50 dBm, a=1.8

Observability of Parameters

Chart 8

k=1k=5k=20

Formal proof of observability can be given

L. Bruno and P. Robertson, “Observability of Path Loss Parameters in WLAN-Based Simultaneous Localization and Mapping”, IPIN 2013

• 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

Transmit power [dBm]

Exp

onen

t

Bayesian Filter

Chart 9

User’s state

Path-loss parameters

RSS measurements

• Bayesian algorithm: Compute recursively at each time step k and for each AP j:

• 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

• Implementation based on a Rao-Blackwellized Particle Filter

Rao-Blackwellized Particle Filter

Chart 10

User’s state

Path Loss parameters

• In our case:

• 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

Path-Loss Parameters Estimation

Chart 11

-40 -38 -36 -34 -32

1.52.02.53.03.5

Localization Algorithm

Chart 12

Initialize• Sample initial state for all particles

• Define grid for h and a

• Uniform prior for h and a

Iterations

particle 1 particle i

• Draw User’s State

• Weight on new RSS

• Update parameters pmf

• Draw User’s State

• Weight on new RSS

• Update parameters pmf

Marginalization on hypotheses

40 x 20 m testbed5 APs, 1000 particles

Movement model: NCVM

RSS noise

h and ~ a Gaussians

100 Monte Carlo trials

Simulations – RMSE

Chart 13

Our proposal

Best case: known parameters

Average parameters

Simulations – h Estimation Accuracy

Chart 14

Simulations – a Estimation Accuracy

Chart 15

• 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

Experiments and Results

Chart 16

65 x 20 meters, 4 minutes walk, 4 APs

Equipment:• Foot-mounted IMU• Android Smartphone (Hand-held)

Experiment 1 - Trajectory

Chart 17

1000 particles RSS noise: s=5 dBm

Final best particle

Experiment 1 – Localization Error

Chart 18

Localization error [m] vs. time CDF of the error [m]

Only odometry

Fixed parameters

Our proposal

Experiment 2 - Trajectory

Chart 19

45 x 25 meters, 7 minutes walk, 4 APs

Equipment:• Foot-mounted IMU• Laptop - OS Windows XP

1000 particles RSS noise: s=5 dBm

Experiment 2 – Localization Error

Chart 20

Localization error [m] vs. time CDF of the error [m]

Chart 21

Opportunistic RSS: Need to Map?

If APs are unknown?

Can the building map help?

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

Thank you!

Contacts:Luigi Bruno, PhDPhone: +49 - 8153 28 4116Email: luigi.bruno@dlr.de, lbruno236@gmail.com

Department of Communication Systems Institute of Communications and NavigationGerman Aerospace Center  Weßling, Germany