![Chart 3
Received Signal Strength – Coverage 1/2
AP in a room
RSS [dBm]](https://image.slidesharecdn.com/observabilityofpathlossparametersinwlan-basedsimultaneous-131105115345-phpapp01/85/Observability-of-path-loss-parameters-in-wlan-based-simultaneous-3-320.jpg)
![Chart 4
Received Signal Strength – Coverage 2/2
AP in the corridor
RSS [dBm]](https://image.slidesharecdn.com/observabilityofpathlossparametersinwlan-basedsimultaneous-131105115345-phpapp01/85/Observability-of-path-loss-parameters-in-wlan-based-simultaneous-4-320.jpg)
Observability of path loss parameters in wlan based simultaneous
- 1. Observability of Path Loss Parameters in WLANBased Simultaneous Localization and Mapping Luigi Bruno and Patrick Robertson Institute of Communications and Navigation, German Aerospace Center (DLR) Oberpfaffenhofen, Germany
- 2. Chart 2 Received Signal Strength – Why and How? AP Closest point • Proximity Approaching Leaving • Distance 30 m
- 3. Chart 3 Received Signal Strength – Coverage 1/2 AP in a room RSS [dBm]
- 4. Chart 4 Received Signal Strength – Coverage 2/2 AP in the corridor RSS [dBm]
- 5. Chart 5 Related Work • 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)
- 6. Chart 6 Dynamic Bayesian Network 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
- 7. Chart 7 Wi(fi-based) SLAM • 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
- 8. Chart 8 Indoor Radio Propagation Model • RSS Likelihood Gaussian in dBm When • Expected power: path-loss model User r • We require: • AP’s position • Transmit signal strength • Decay exponent are known
- 9. Chart 9 Bayesian Method – Known Parameters Sequentially multiplying the RSS likelihoods... 1 RSS alone …more RSS Combine 3 RSS …5 RSS
- 10. Chart 10 Path-Loss Parameters Uncertainty of path-loss parameters has a relevant impact
- 11. Chart 11 Observability of Parameters – Toy Example Toy case: AP’s and user’s position known, no noise ( =0) Given two measurements, solve: Circular walk Linear walk Constant r 2 RSS sufficient Ambiguity remains Exact solution for h and a
- 12. Chart 12 Observability of Parameters – Known Positions 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
- 13. Chart 13 Observability of Parameters – Known Positions d. By inverting the FIM, we obtain the CRLB for (unbiased) estimator: 2. ML estimator is efficient:
- 14. Chart 14 Observability of Parameters – SLAM • We discretize the propagation parameters on a finite grid • A “hypothesis” is a pair of values • Hypothesis probabilities are updated with any new RSS Hyp 1: -40 -38 -36 -34 -32 Hyp 2: 1.5 2.0 2.5 3.0 3.5 Hyp s:
- 15. Chart 15 Map Model Of AP’s Position • 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
- 16. Chart 16 Experiments and Results • 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
- 17. Chart 17 Experiment 1 1% of maximal value 4 minutes walk, 4 APs Equipment: • Foot-mounted IMU • Android Smartphone (Hand-held) Contours: AP’s position posterior pdf
- 18. Chart 18 Experiment 2 – Open space
- 19. Chart 19 Experiment 3 – Office With Loops 7 minutes walk Equipment: • Foot-mounted IMU • Laptop (to collect RSS) 4 APs
- 20. Chart 20 Experiment 3 – Parameters pmf evolution • Solving ambiguity in parameter estimation 200 s (1/2 of the walk) Transmit signal strength 420 s (end walk) Exponent Exponent Exponent 120 s (1/3 of the walk) Transmit signal strength Transmit signal strength
- 21. Chart 21 How many representations does the physical environment have? WiFi Maps Mag Maps Real Time Position
- 23. 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
- 24. Chart 24 RBPF Implementation 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 What about the WiFi map?