Observability of Path Loss Parameters in WLAN-Based Simultaneous Localization and Mapping

Luigi Bruno and Patrick Robertson

Institute of Communications and Navigation, German Aerospace Center (DLR)Oberpfaffenhofen, Germany

30 m

Received Signal Strength – Why and How?

Approaching Leaving

Closest point

• Proximity

• Distance

AP

Chart 2

Chart 3

AP in a room

RS

S [dB

m]

Received Signal Strength – Coverage 1/2

Chart 4

AP in the corridor

RS

S [dB

m]

Received Signal Strength – Coverage 2/2

• Simultaneous Localization and Mapping done in robotics since ~25 years

• Smith, Self, Cheeseman (1990) • Leonard, Durrant-Whyte (1991)

• SLAM for pedestrians

• FastSLAM (Montemerlo, 2002)• FootSLAM (Robertson, since 2009)• ActionSLAM (Hardegger, IPIN 2012/13)

• RSS-based SLAM

• Wifi-SLAM (Ferris, 2007)• WiSLAM (Bruno, 2011)• Walkie-Markie (Shen, 2013)

• RSS model calibration: Nurminen (IPIN 2012)

Related Work

Chart 5

We have:

Dynamic States: user’s pose user’s step colored noise on odometry

Static Maps: Physical environment map M WiFi map W for each AP

Measurements: Odometry (e.g. INS/NavShoe) RSS scan

Dynamic Bayesian Network

Chart 6

Wi(fi-based) SLAM

Chart 7

• Bayesian algorithm: FastSLAM factorization (Montemerlo et al. 2002)

• Implemented by a Rao-Blackwellized Particle Filter

• Proposal Function:

• State is propagated in accordance with odometry

• Likelihood Functions:

• FootSLAM weighting (hexagonal edge crossing counters)

• RSS-based weight per each AP

• Any other in accordance with available sensors (e.g. Magnetic, Gyroscope,

Altimeter)

• WiFi Map: update each particle map at each RSS

• RSS Likelihood Gaussian in dBm

• Expected power: path-loss model

• We require:• AP’s position• Transmit signal strength• Decay exponent

When are known

Indoor Radio Propagation Model

Chart 8

User

AP

r

1 RSS alone Combine 3 RSS …5 RSS

…more RSS

Sequentially multiplying the RSS likelihoods...

Bayesian Method – Known Parameters

Chart 9

Uncertainty of path-loss parameters has a relevant impact

Path-Loss Parameters

Chart 10

Toy case: AP’s and user’s position known, no noise ( = 0 )

Given two measurements, solve:

Circular walk

Constant r

Ambiguity remains

Linear walk

2 RSS sufficient

Exact solution for h and a

Observability of Parameters – Toy Example

Chart 11

Extend to the case of noisy RSS: asymptotic observability

• Claim: Given AP’s and user’s positions, joint asymptotic observability of the path-loss parameters is guaranteed if relevant changes in the user-AP distance are provided

1. Compute CRLB for the vector parameter

a. 1-RSS likelihood

b. K-RSS likelihood

c. Fischer Information Matrix

Observability of Parameters – Known Positions

Chart 12

d. By inverting the FIM, we obtain the CRLB for (unbiased) estimator:

2. ML estimator is efficient: 1/K

Observability of Parameters – Known Positions

Chart 13

• We discretize the propagation parameters on a finite grid

• A “hypothesis” is a pair of values

• Hypothesis probabilities are updated with any new RSS

-40 -38 -36 -34 -32

1.52.02.53.03.5

Hyp 1:

Hyp 2:

Hyp s:

Observability of Parameters – SLAM

Chart 14

• AP’s position, given one hypothesis: Gaussian Mixture Model (GMM)

where

Initialization • GMM learnt from samples of the exact map• Expectation-Maximization algorithm for GMM (developed for speech

processing)• Maximum-likelihood solution with few iterations

Update• At any new RSS update the GMM• Implemented in closed form

Map Model Of AP’s Position

Chart 15

Experiments and Results

Chart 16

• Three different buildings, walks between 4 and 10 minutes

• Data collected by a pedestrian wearing a foot mounted IMU and holding a laptop/smartphone

• Normal WiFi networks of the buildings – no ad-hoc additions

• Scenarios:• Building KN – DLR-OP (smartphone – OS Android)• Building MF - DLR-OP (smartphone – OS Android)• First floor of the building TE01 – DLR-OP (laptop – OS Windows XP)

• Up to 4 APs, no offline calibration

4 minutes walk, 4 APs

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

Contours: AP’s position posterior pdf

1% of maximal value

Experiment 1

Chart 17

Experiment 2 – Open space

Chart 18

7 minutes walk

Equipment:• Foot-mounted IMU• Laptop (to collect RSS)

4 APs

Experiment 3 – Office With Loops

Chart 19

Experiment 3 – Parameters pmf evolution

Chart 20

120 s (1/3 of the walk) 200 s (1/2 of the walk) 420 s (end walk)

Transmit signal strengthTransmit signal strengthTransmit signal strength

Exp

onen

t

Exp

onen

t

Exp

onen

t

• Solving ambiguity in parameter estimation

Chart 21

How many representations does the physical environment have?

WiFi Maps Mag Maps Real Time Position

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

To implement the Bayesian filter we use a Rao-Blackwellized Particle Filter, in which we exploit DBN structure to reduce the complexity of state space sampling

In our case

• : Dynamic states

• : Static maps

RBPF Implementation

Chart 24

What about the WiFi map?