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Plans2012 Presentation: Angular PDFs and FootSLAM

Plans2012 presentation without films. Films are available at http://www.kn-s.dlr.de/mobility.

Plans2012 presentation without films. Films are available at http://www.kn-s.dlr.de/mobility.

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Plans2012 Presentation: Angular PDFs and FootSLAM

1. 1. Map-based angular PDFs used as prior map for FootSLAM Susanna Kaiser, Maria Garcia Puyol, Patrick Robertson German Aerospace Center (DLR) Institute of Communications and Navigation Kaiser; PLANS 2012 Slide 1
2. 2. Outline Introduction: FootSLAM and its hexagon map Motivation for using prior maps Angular probability density functions (PDFs) as a basis for prior maps The diffusion algorithm Determining the angular PDFs Mapping of the angular PDFs to the FootSLAM hexagon map Different floor-plan scenarios Experimental Results Conclusions & Outlook Kaiser 04/2012 Slide 2
3. 3. Introduction: Principle of FootSLAM Indoor Navigation is a challenge: GNSS signals are strongly disturbed Foot-mounted IMU sensor  measurements pedestrian odometry FootSLAM: Simultaneous Localization and Mapping for pedestrians with odometry Optionally GPS (absolute coordinate frame) Human motion: First order Markov process FastSLAM factorization: Rao-Blackwellized Particle Filter. Each particle: pose + odometry errors + individual map Kaiser 04/2012 Slide 3
4. 4. Introduction: FootSLAM and its Hexagon map 2D space partitioned into a regular grid of adjacent and uniform hexagons with a given radius Each one of the 6 edges of the hexagons is associated to a transition count that represents the number of times it was crossed Input to FootSLAM: Raw odometry Coordinate System Starting Conditions Prior map, if available Output: Aggregated Posterior Map Best “MAP” Map Kaiser 04/2012 Slide 4
5. 5. Introduction: Integrating a prior map Each particle weight is updated as follows:   i N    e   e  i wk  i wk 1  h  h ,  Nh  h      where i wk is the weight for particle i at time k e Nh   are the transition counts for edge e of the outgoing hexagon  h    e  is the prior value for edge  e h N h   e  0 N h and  h   e  0  h e 5 e e 5 e    Without a prior map, prior values are set to a constant value (e.g. 0.8) Kaiser 04/2012 Slide 5
6. 6. Introduction: Advantages of using a prior map The FootSLAM map converges faster The resulting map is more precise A more precise location of the map in an outer coordinate system can be found Prior maps are also used in FeetSLAM by adding other maps after being transformed to fit the total map. With the use of a prior map from the beginning the transformation will not be necessary anymore The prior map can be strengthened or weakened to control its influence on the FootSLAM map generation process. Kaiser 04/2012 Slide 6
7. 7. Introduction: Changing the strength of a prior map Strengthening: multiplying the counts by a prior strengthening factor If the map is known to be accurate, a high strengthening factor can be used Existing maps are sometimes imprecise, unavailable, obsolete, proprietary, and do not show furniture or other features that significantly limit pedestrian motion If the map is incorrect or only partly known the influence of the map can be lowered by using a low strengthening factor If the map is not available a constant value can be used   h  factor e  Kaiser 04/2012 Slide 7
8. 8. Angular PDFs as a basis for prior maps For each actual waypoint a sliding squared window of size N x  N x is defined, where the waypoint is the middle point of that window Each waypoint represents a source effusing gas Source/waypoint Example for a diffusion matrix For each waypoint  x m , ym  a diffusion matrix D is pre-computed x At start, the diffusion matrix is one at the waypoint and zero else where Kaiser 04/2012 Slide 8
9. 9. Angular PDFs as a basis for prior maps Determining the angular PDF directly out of the diffusion matrix From the diffusion matrix a threshold can be used for obtaining a contour line of the gas distribution Source/waypoint Contour line (dark red) of the diffusion values with threshold value: T=0.0001        c ,..., cN       Resulting in a set C of Nc contour-line points: x1, y ,, xN , y 1   Nc    1  c      c    Kaiser 04/2012 Slide 9
10. 10. Angular PDFs as a basis for prior maps Determining the angular PDF directly out of the diffusion matrix For each angle  the distance from the middle waypoint to the contour point is determined and the maximum distance is used: 0° bci  ( xm  k )2  ( ym  l ) 2 ρ b Source/waypoint f (  )  max bci ci  ( k , l )  ( k ,l )   f ( ) Normalizing: f ( )  2  f ( ) 0 Kaiser 04/2012 Slide 10
11. 11. Angular PDFs as a basis for prior maps Determining the angular PDF directly out of the diffusion matrix Resulting Polar Plot of the angular PDF for that specific waypoint: This location dependant angular PDF can be used as prior information for FootSLAM Kaiser 04/2012 Slide 11
12. 12. Angular PDFs as a basis for prior maps Mapping angular PDFs on the FootSLAM Prior Map r e of edge e     Range r e  (rmin , rmax )  ( e e e , e ) 6 3 6 3 0° 0 r0 5 1 270° 90° 4 2 x 3 180° Hexagon centre = source of gas e rmax Values for the prior map:  e e  h f (  )d  rmin Kaiser 04/2012 Slide 12
13. 13. Angular PDFs as a basis for prior maps Mapping angular PDFs on the FootSLAM Prior Map White/yellow -> high values Black -> low values Totally white hexagons: No angular PDF (position of hexagon centre is on wall) Kaiser 04/2012 Slide 13
14. 14. Different Floor-Plan scenarios: 2: The complete and correct 3: The complete and correct 4: A plan with only the plan plan including furniture outer building walls 5: A plan with only corridors 6: A plan missing a long wall 7: A plan with an additional, incorrect wall Kaiser 04/2012 Slide 14
15. 15. Experimental Results Sensor: Foot-mounted Inertial Measurement Unit (IMU) with Zero Velocity Updates (ZUPTs) processed with an extended Kalman Filter for pedestrian dead reckoning [Foxlin] A prior map is generated for the 7 floor-plan scenarios To emulate a GPS anchor when entering a building we assumed that starting conditions of the walk were not exactly known:  X / Y  2.0m,    2.0 3 walks of 5-14 minutes duration 10 evaluation runs of the PF with different seeds for every data set (walk) Evaluation criterion: Ratio of violated walls and furniture ground- truth by the resulting FootSLAM map (smaller is better …) Kaiser 04/2012 Slide 15
16. 16. Experimental Results Results for different prior strengthening factors -1 10 FootSLAM with complete prior map (1) Crossed Wall Ratio [%] -2 10 -3 10 0 20 40 60 80 100 Prior Strengthening Factor Kaiser 04/2012 Slide 16
17. 17. Experimental Results Results for different floor plan scenarios -1 10 Raw FootSLAM PSF 40 Only outer walls PSF 20 Crossed Wall Ratio [%] Outer and -2 Corridor walls Missing wall 10 Complete plan Incorrect wall Complete plan including furniture -3 10 1 2 3 4 5 6 7 Index of Floor Plan Scenario Kaiser 04/2012 Slide 17
18. 18. Experimental Results Das Bild k ann zurzeit nicht angezeigt werden. Odometry Kaiser 04/2012 Slide 18
19. 19. Conclusions & Outlook A prior map can be applied to FootSLAM and is a useful additional information that can enhance the position estimation. The advantages of using prior maps are: Reaching faster convergence Better accuracy of the map More accurate positioning if the starting condition are not exactly known A prior map represented as angular PDFs is combined with FootSLAM. The angular PDFs are calculated using the diffusion algorithm and are mapped on the hexagon edge transitions Experiments: The use of angular PDFs as prior map in FootSLAM performs better than using no prior map It doesn’t matter if the prior map is only partly available or contains some errors: The influence of the map can be controlled via the prior strenghtening factor Knowing only the trunk of the building is almost as good as knowing the entire map Further work should focus on Additional data sets Different wall situations / map errors Evaluation of the resulting position accuracy Information theoretic evaluation of map similarity Kaiser 04/2012 Slide 19
20. 20. Many thanks for your interest & your questions are welcome! http://www.kn-s.dlr.de/indoornav Susanna Kaiser Date: 24/04/2012 Kaiser 04/2012 Slide 20
21. 21. Evaluation Results Results for different walks -1 Crossed Wall Ratio [%] 10 -2 10 1: No Prior 1: Complete Plan 2: No Prior 2: Complete Plan 3: No Prior 3: Complete Plan -3 10 1 2 3 Index of Walk Kaiser 04/2012 Slide 21