[EN-004]
Joint target tracking andsystematic error correction
for Wide Area Multilateration
Authors:

Jorge J. ABBUD
Gonzalo DE MIGUELEIWAC 2013

Table of Contents
1. Introduction
2. Characterization of errors in WAM
3. Problem statement
4. Proposed solution
5. Experiments
6. Conclusions

Tokyo, 20.02.2013

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1. Introduction
In order to enable greater optimization in the use ofairspace [1] [2], stricter aircraft positioning requirements
can be expected in the near future.
The trend in Air Traffic Management (ATM) is to rely on
ADS-B as the main source of aircraft positioning.
Wide Area Multilateration (WAM) can be used as aredundant system for ADS-B integrity monitoring.
[1] “Introduction to the Mission Trajectory” EUROCONTROL, ed. 1.0, May 2010.
[2] “EUROCONTROL Speciﬁcation for the application of the Flexible Use of Airspace(FUA)”, EUROCONTROL, ed. 1.1, October 2009.
Tokyo, 20.02.2013

3

1. Introduction(Principle of WAM)
WAM systems are based on the reception of ADS-B
transmissions (or Mode A/C/S replies) by the aircraft.
The emitter (aircraft) position is determined from theTime Difference Of Arrival of the signal obtained in theground stations.

Tokyo, 20.02.20134

2. Characterization of errors in WAM
TDOAji ,1

1= TOA i − TOA = (ρ ij − ρ 1 j )cjj
1ρ ij = R ij + cT e + ∆ Pij + c ∆ Ti + n i(TDOA)
Pseudorange

Where: ij
cTe:
ΔPij :cΔTi:
ni :(SNR)
stands for the base station number
stands for the aircraft number
uncertainty in the signal emission time
propagation error
synchronization error
receiver noise (AWGN)

Goal: to solve the TDOA equation system
Tokyo, 20.02.201352. Characterization of errors in WAM(Propagation error: Slant Range dependency)
Range bias caused by the troposphere propagation (ICAO Standard Atmosphere)100

α1 Rij + α 2 R

2ij

90
80

Range bias, m

70

3km
4km
5km
6km
7km
8km
9km
10km
11km
12km
13km
14km
Limit of applicability(Radio-wave horizon)

60
50

increasing True altitude
40
30
20100050

100

150

200

250
Slant Range, kmTokyo, 20.02.2013

300

350

400

450

500

62. Characterization of errors in WAM(Propagation error: True Altitude dependency)
Ratio between range bias for an aircraft flying at a given altitude
compared to at 14km AMSL but equal slant-range
3km
4km
5km
6km
7km
8km
9km
10km
11km
12km
13km
Limit of applicability(Radio-wave horizon)

Ratio between the Range bias at a given altitude
compared to the Range bias at 14km altitude(equal slant range considered), no unit

1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
15

50

100

150

200

250
300
Slant range, kmTokyo, 20.02.2013

350400450500

72. Characterization of errors in WAM(Propagation error: True Altitude dependency)
Ratio between range bias for an aircraft flying at a given altitude
compared to at 14km AMSL but equal slant-range

 zj 1 + α 3 1 − 
 z0 

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2. Characterization of errors in WAM
The propagation error expression now becomes:

 z j ∆Pij (Rij , z j ) ≈ α 1 Rij + α 2 R 1 + α 3 1 −  
 z0 
where R = (x − x ) + ( y − y ) + (z − z )

(2ij)

2ijji

2ji2jiHence, the pseudorange can be modeled as follows: z j 
ρij = Rij + α1Rij + α R 1+ α3 1−  + c∆Ti + cTe + ni
 z0 
(TDOA)(SNR)(22 ij)

Tokyo, 20.02.20139

3. Problem statement
The aim is to dynamically estimate the effect of systematicerrors, in order to mitigate them when calculating thetarget positions.
Hence, for each instant, the following values have to becomputed:
State vector of all aircrafts (position, velocity, acceleration)
Covariance matrix associated to the aircraft state vectors
State vector of the systematic errors (α1, α2, α3, cΔTi)
Covariance matrix associated to the systematic errors

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4. Proposed solution (Concept)
Use of opportunity traffic to obtain a set of new
independent equations [4], thus avoiding an indeterminate
equation system.
Joint tracking and systematic error estimation [7]:Decoupling the systematic error estimation from the target
position estimation in the prediction phase
Combination of tracking and systematic error information in theupdate phase[4] “Correction of systematic errors in Wide Area Multilateration”,
J.Abbud, G. De Miguel, J.A.Besada, Proceedings of the ESAV2011.
[7] "Multitarget-Multisensor tracking: Applications and Advances,Volume II",
Y. Bar-Shalom, (Ed.), Artech House Inc., 1992.
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4. Proposed solution (Design)
TDOA
measurementsX(k-1│k-1)

Px(k-1│k-1)

X(k│k-1)
Prediction(UKF)

X(k│k)
Update(UKF)

Px(k│k-1)

E(k-1│k-1)

Px(k│k)E(k│k-1)
Prediction(EKF)

Pe(k-1│k-1)

E(k│k)
Update(EKF)

Pe(k│k-1)

Pe(k│k)X: Target state vector
Px: Covariance matrix associated to X
E: Systematic error vector
Pe: Covariance matrix associated to E
Tokyo, 20.02.201312

5. Experiment
Procedure:Monte Carlo experiments involving a hypothetical WAM
scenario with 8 aircrafts and 6 base stations.

Assumptions:
All aircrafts have constant groundspeed along a specified
bearing and a specified height AMSL.
Range bias due to propagation effects has been modeled
following the path integration method presented in [9].
Clock synchronization errors and receiver noise have beenmodeled via zero-mean Gaussian distributions.
[9] "Radar System Analysis and Modeling", D. K. Barton, Artech House Inc., 2005.
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5. ExperimentSettings:
Each aircraft transmits every 4 seconds
1000 runs of 15-minute scenarios
Aircraft maneuvering model (Singer acceleration model)

Assessment:
Calculation of the mean and standard deviation of thepositioning error (Horizontal and Vertical).
Performance comparison of the proposed method versus
hyperbolic location, in terms of mean and standard deviation(best, median, worst).

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5. Experiment+ Aircraft trajectory
Movement direction
x Base station

100806040y (km)200-20-40-60-80-100-100 -80-60-40-20

020x (km)40Tokyo, 20.02.2013

608010015

H oriz o ntal po s ition - M ea n erro r R M S (m )5. Experiment
Mean of the positioning error (m) - Horizontal

310210

1100

100

100

200

300

400

500

600

700

800

900

800

900

Time (s)V e rtic a l p os itio n - M ea n error R M S (m )Mean of the positioning error (m) - Vertical
3102101

100100

100

200

300

400

500

600

700

Time (s)Tokyo, 20.02.2013

16V e rt ic a l p o s it io n - S t a n d a rd d e v ia t io n R M S (m ) H o riz o n t a l p o s itio n - S ta n d a rd d e v ia tio n R M S (m )5. ExperimentStandard deviation of the positioning error (m) - Horizontal

3102101

100100100

200

300

400

500

600

700

800

900

Time (s)Standard deviation of the positioning error (m) - Vertical

3102101100100100

200

300

400500

600

700

800

900

Time (s)Tokyo, 20.02.201317

6. Conclusions
The method presented in this paper tracks
the systematic errors in order to mitigate
their effect.
The necessary amount of equations isobtained via opportunity traffic.
Significant gains in accuracy and precision
are obtained in target tracking with WAM,
especially in scenarios with poor GDOP.
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Joint target tracking andsystematic error correction
for Wide Area Multilateration

Thank you for your attention.
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