Localization Studio Product - Localization is not Challenging Task Anymore!
Localization in Networks Based on Log Range …...8 Fredrik Gunnarsson Localization in Networks...
10
1 Fredrik Gunnarsson Localization in Networks Based on Log Range Observations Wireless Systems Workshop 2008 Johannebergs Slott Localization in Networks Based on Log Range Observations Fredrik Gunnarsson Fredrik Gustafsson Fredrik Gunnarsson Localization in Networks Based on Log Range Observations Wireless Systems Workshop 2008 Johannesbergs Slott Outline FOCUS Area Control Sensor Measurement Modeling Nuisance Parameter Elimination Simulations
Transcript of Localization in Networks Based on Log Range …...8 Fredrik Gunnarsson Localization in Networks...
1
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannebergs Slott
Localization in Networks Based onLog Range Observations
Fredrik Gunnarsson
Fredrik Gustafsson
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Outline
� FOCUS Area Control
� Sensor Measurement Modeling
� Nuisance Parameter Elimination
� Simulations
2
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
FOCUS Area Control
� VINNOVA Excellence Center 2007-2009
� Area Control: FOI, LiU, Exensor
� Baseline: Passage control
� UMRA – Underrättelse Multisensor RAdio
� Target: Area Control
10 o
r 20
m
10 o
r 20
m
1 ~ 15 m
1 ~ 15 m
Probe 1Probe 1
Probe 2Probe 2
UMRAUMRA
AntennAntenn
aa
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
UMRA Evolution – UMRA Mini
� UMRA Mini
� Microphone
� Geophone
� GPS
� Self-Healing wireless
mesh network
� 2 months battery time,
normal operation
3
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Sensor Network Modeling
� Problem definition and notation:� \begin{itemize}� \item One target with unknown position $x(t)$ (2D)� \item $N$ sensor nodes with known positions $p_k, k =� 1,\ldots ,N$� \item Each sensor node consists of $M$ sensor types� \item Observations denoted $y_{k,i}(t), k = 1, \ldots ,N$
and� $i = 1, \ldots ,M$� \item Problem: Localization (from one snapshot
$y_{k,i}(t)$)� and tracking of $x(t)$.� \item Assumption: target speed times sampling interval� small compared to network dimensions.� \item Restriction: Communication, sensor calibration and� multi-target localization with data association are� not considered here.� \end{itemize}N
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Sensor Model
4
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Sensor Experiment
� One vehicle passage and one sensor node
� Received power as a function of time for two sensor types.
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Sensor Model Validation
� Log range versus log of received
signal power.
� Good fit to the log range model for all
sensor types
� Non-trivial path loss constants -2.3
and -2.6.
5
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Sensor Network Measurement Model
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Non-linear Least Squares (NLS)
6
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
NLS in x Only
7
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Grid Method to Solve for x
� Tedious to compute
the gradient ...
� Grid method for the lazy ...
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Cramer-Rao Lower Bound
8
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Handling Unknown Noise
Marginalize linear parameters as above.
The maximum likelihood method assuming Gaussian noise gives
which again can be optimizied over x
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Field Trials, Skövde
9
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Point Estimate Example
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Estimation Performance, 2-Stroke MC
-100 0 100 2000
50
100
150
200Track 19
|x0(t
) -
x est(t)
| [m
]
X [m]
-100 0 100 2000
50
100
150
200Track 20
|x0(t
) -
x est(t
)| [
m]
X [m]
-100 0 100 2000
50
100
150
200Track 21
|x0(t
) -
x est(t
)| [
m]
X [m]
-100 0 100 2000
50
100
150
200Track 22
|x0(t
) -
x est(t
)| [
m]
X [m]
10
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Estimation Perforamance, XC90
-100 0 100 2000
100
200
300
|x0(t
) -
x est(t)
| [m
]
Track 01
-100 0 100 2000
50
100
150
200
250Track 02
-100 0 100 2000
50
100
150
200
250
|x0(t
) -
x est(t)
| [m
]
Track 03
X [m]
-100 0 100 2000
50
100
150
200
250Track 04
X [m]
Fredrik Gunnarsson
Localization in Networks Based on
Log Range Observations
Wireless Systems Workshop 2008
Johannesbergs Slott
Some Issues
� Multi-target tracking
� Pre-filtering
� Filtering and marginalization
� Spatial dependency
� Signature correlation
1 2 3 4 5 6-4
-2
0
2
4
6
c1(x)
y 1,1
