IPIN2011 Angular PDF

1,518 views

Published on

IPIN2011 Presentation without films. Films are available at http://www.kn-s.dlr.de/mobility

Published in: Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,518
On SlideShare
0
From Embeds
0
Number of Embeds
1,012
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

IPIN2011 Angular PDF

  1. 1. A Maps-Based Angular PDF for Navigation Systemsin Indoor and Outdoor EnvironmentsSusanna Kaiser, Mohammed Khider, Patrick RobertsonGerman Aerospace Center (DLR)Institute of Communications and NavigationCenter of Excellence for Satellite Navigation Folie 1 Vortrag > Kaiser > IPIN2011.ppt > 09.11.2005
  2. 2. Outline Indoor Positioning System Motivation for Using Angular PDFs Algorithm for Determining Angular PDFs Calculation of the Diffusion Matrix Determining the angular PDF directly from the diffusion matrix Simulation Results Conclusions & Outlook 2 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  3. 3. Indoor Positioning SystemCascaded Bayesian Estimation Architecture:GNSSPseudoranges Likelihood Particles, Functions: Sensor errors Position and Velocity Output& Carriers GNSS, FusionAltimeter Outputs Altimeter, Filter ParticlesRFID Detections RFID (PF) Compass, Transition Model 3D MapCompass Outputs Step/INS ~1 Hz Database Fusion Trigger Step Displacement INS Position and ( P) Velocity PDF  P PDF (Gaussian) ComputerGyroscope INS Position and VelocityTriad Outputs Strapdown +Accelerometer Inertial Calibration Feedback -Triad Outputs Computer ~100-500 Hz INS Errors PDF ExtendedSensors “Foot still” – Detector Kalman Filter Triggers ZUPT (INS Error Space) 3 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  4. 4. Bayesian Filter Algorithm Two stages: Prediction, transition model is used to predict the state PDF from one time-step to the next p(xk | z1:k 1)   p(xk | xk 1) p(xk 1 | z1:k 1)dxk 1 Update, measurement model is used to update the prediction PDF according to the latest measurement p ( xk | z1:k )   k p ( z k | xk ) p ( xk | z1:k 1 ) Several types of Bayesian filters results in different accuracy, robustness,efficiency, sensor variety and complexityLikelihood Particle Filter: uses measurements for importance sampling andtransition model to update (for weighting) 4 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  5. 5. Motivation for Using Angular PDFs Likelihood Particle Filter is used -> We need the Transition Model for weighting the Particles. (But: The angular PDF can also be used as a movement model!) The main problem of the whole system is the heading drift, therefore, we concentrate our focus on the heading. The heading of a walking pedestrian is correlated with maps or floor- plans. Floor-plans are used in a binary way: if a particle crosses a wall it‘s weight is set to zero. This may lead to estimation failures in multi-modal scenarios (e.g. the “Y-problem”) How can we find a weighting function that uses floor-plans in a non binary way? A transition model will not just eliminate particles that cross walls but rather reward those that follow a trajectory compatible with the building layout. Advantages to the previous used Diffusion Movement Model: No destination points, no path finding algorithm, smaller area 5 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  6. 6. Motivation for using angular PDFs: The „Y-Problem“: Building Building Part A Part B True track Particles Split Point Particles in A will be eliminated after time due to the wall constraints 6 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  7. 7. Motivation for using angular PDFs:Example for a Critical Multi-Modal Scenario Based onOur Own Office Environment x ground truth point path of the test user x6 Location where the x7 particle cloud splits x5 into two groups x8 x4 x9 x3 Large room x2 x1 Start/End Particles will be split into 2 groups at GTP4. Particles that enter the large room will dominate due to the wall constraints when using binary weighting. 7 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  8. 8. Angular PDFs:Calculation of the Diffusion Matrix For each actual waypoint a sliding squared window of size Nx  Nx 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. 8 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  9. 9. Angular PDFs: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        Resulting in a set C of Nc contour-line points:  c1,..., cN      x1, y1  ,, xN , yN      c      c c    Contour Points (dark red) are included in the set if The direct line from the source to the contour point is not crossing a wall. At least one neighboring value is greater than the threshold. 9 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  10. 10. Angular PDFs: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° b  (xm  k )2  ( ym l)2  C(k,l) Source/waypoint b w( )  max bC (k ,l )  C (k ,l )  (k ,l ) Normalizing: w( )  w( )  2  w( )   0 Adapting to the speed S: w( )  w( )S 10 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  11. 11. Angular PDFs:Determining the angular PDF directly out of the diffusion matrix Resulting Polar Plot of the angular PDF for that specific waypoint: By using this weighting function within the LPF angles in the possible direction without wall constraints are favored. 11 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  12. 12. Simulation ResultsSimulation Environment Sequential Bayesian Positioning Estimator: Based on a Particle Filter fusion engine. Integrates the new angular PDFs. Using the following sensors: Commercial GPS Electronic compass A foot-mounted Inertial Measurement Unit (IMU) with Zero Velocity Updates (ZUPTs) processed with an extended Kalman Filter for pedestrian dead reckoning [Krach and Robertson]. The ground truth points (GTRP) were measured to the sub- centimeter accuracy using a tachymeter (Leica Smart Station (TPS 1200), employing optical distance, angular measurements, differential GPS (initial positioning)). 100 runs for a single walk (playback mode) 12 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  13. 13. Simulation ResultsAverage Position Error (Errors between the true and estimated pedestrianpositions) Average Position Error with wall constraints: 1.33m (no angular PDF: 1.5m) 13 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  14. 14. Simulation ResultsNumber of Failures Rates of wrong position estimations of the scenario Location of wrong position estimation Algorithm Wrong position in first loop Wrong position in second/third loop Angular PDF 0% 8% No angular PDF 100% 50% 14 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  15. 15. Conclusions & Outlook A transition model for pedestrians that uses a known building layout to construct an angular PDF for a pedestrian’s step direction. A simple Likelihood Particle Filter (using binary weighting) can diverge if the particles distribution is multi-modal and a competing, erroneous particles group is in an area with few limiting walls in their vicinity. It has been shown that weighting with the angular PDF performs better than using no transition model in critical scenarios. Further work should focus on More data sets Different wall situations The use of different accessibility levels in indoor and outdoor environments. 15 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011
  16. 16. Many thanks for your interest &your questions are welcome! http://www.kn-s.dlr.de/indoornav Susanna Kaiser Date: 22/09/2011 16 A Maps-Based Angular PDF … > Kaiser > IPIN2011 > 22.09.2011

×