IPIN2011 Angular PDF

A Maps-Based Angular PDF for Navigation Systems
in Indoor and Outdoor Environments

Susanna Kaiser, Mohammed Khider, Patrick Robertson

German Aerospace Center (DLR)
Institute of Communications and Navigation

Center of Excellence for Satellite Navigation

Folie 1
Vortrag > Kaiser > IPIN2011.ppt > 09.11.2005

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

Indoor Positioning System
Cascaded Bayesian Estimation Architecture:

GNSS
Pseudoranges Likelihood Particles,
Functions: Sensor errors Position and Velocity Output
& Carriers
GNSS, Fusion
Altimeter Outputs Altimeter, Filter Particles
RFID Detections RFID (PF)
Compass, Transition
Model 3D Map
Compass Outputs Step/INS
~1 Hz Database

Fusion Trigger
Step Displacement INS Position and
( P) Velocity PDF
 P PDF (Gaussian) Computer

Gyroscope INS Position and Velocity
Triad Outputs Strapdown +

Accelerometer Inertial Calibration Feedback -
Triad Outputs Computer
~100-500 Hz INS Errors PDF
Extended
Sensors “Foot still” – Detector
Kalman Filter
Triggers ZUPT
(INS Error Space)

3

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 and
transition model to update (for weighting)
4

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

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

Motivation for using angular PDFs:
Example for a Critical Multi-Modal Scenario Based on
Our 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

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

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

Angular PDFs:

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

Angular PDFs:

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

Simulation Results
Simulation 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

Simulation Results
Average Position Error (Errors between the true and estimated pedestrian
positions)

Average Position Error with wall constraints: 1.33m (no angular PDF:
1.5m)
13

Simulation Results
Number 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

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

Many thanks for your interest
&
your questions are welcome!
http://www.kn-s.dlr.de/indoornav
Susanna Kaiser

Date: 22/09/2011

16

IPIN2011 Angular PDF

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