PhD Defence AirportNav

Ecole Nationale

de l’Aviation civile

LTST

LETA

Hybrid Deterministic-Statistical GPS

Multipath Simulator for Airport Navigation

Adrien Chen

PhD Defence – Dec 17th, 2010

Thesis funded by Airbus

Supervised by

LTST and LETA ENAC, France

Navigation Department Airbus Operations SAS

Reviewers

Pr. Emmanuel Duflos Ecole Centrale Lille, France

Pr. Michael Braasch Ohio University, USA

Pr. Fernando Perez-Fontan University of Vigo, Spain

Thesis Director

Dr. Christophe Macabiau ENAC, France

Supervisors

Dr. Alexandre Chabory ENAC, France

Dr. Anne-Christine Escher ENAC, France

André Bourdais Airbus Operations SAS

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LETA

• In civil aviation, satellite navigation is taking precedence over classical

radionavigation means.

It is more independent from the ground infrastructure of each airport,

It may provide a positioning solution for all the flight phases since it has a worldwide

coverage.

• The use of satellite navigation in airport environments raises issues related

to the proximity of the airport buildings

Parasite scattering of the direct signal coming from the satellite called multipath

appears.

• Mutipath may cause positioning errors of the aircraft within the airport, when

taxiing or standing at parking places.

Context of the study (1/2)

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Airbus context

• Satellite navigation is particularly interesting for airport navigation

Onboard Airport Navigation System (OANS) developed by THALES makes use of the GPS

satellites,

Deployed on Airbus A380,

Provides an acceptable indication of the position (situation awareness) despite of multipath.

• For higher requirements levels, such as guidance, a better understanding of these

phenomena is necessary.

Historical context

• Existing prediction tools of multipath

They can be deterministic, statistical or hybrid deterministic statistical,

Most of them are dedicated to telecommunication applications.

• To our knowledge, few models in the literature combine

Context of the study (2/2)

Multipath prediction + Signal processing of the GNSS receiver Realistic estimation of the range error

It is within this context that Airbus has funded this Ph.D.

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Objective of this Ph.D.

2 research goals

1. To develop a deterministic tool for an efficient prediction of the GNSS error due

to multipath in airport environments.

2. To add a statistical component in order to account for the limits of a pure

deterministic prediction.

Objective of the study

To develop a flexible simulation tool to analyze the error due to

multipath in the context of airport navigation with GNSS.

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I. Multipath in GNSS context

II. Comparisons of modeling strategies for the estimation of the

transmission channel

III. PO-based prediction of the transmission channel

IV. Application of the deterministic model to the GNSS context

V. Statistical model

VI. Comparisons with measurements

Conclusion and future works

Presentation Outline

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• Civil aviation context

GPS L1 C/A is currently used from en-route navigation to non-precision approach

We only consider GPS L1 C/A signal.

• Structure of the received GPS L1 C/A signal

• We also ensure the compatibility of the tool we develop with new

constellations

Imminent deployment of new GNSS constellations e.g. Galileo

I. Multipath in GNSS context Civil aviation signal

𝑠𝐶/𝐴 𝑡 = 2𝑃𝑑 𝑡 − 𝜏 𝑐 𝑡 − 𝜏 cos 2𝜋𝑓𝐿1𝑡 + 𝜙

Binary navigation

message

Code delay

Binary code Carrier

frequency

Carrier phase

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Definition of the transmission channel

• Satellite antenna

Emits the GPS signal with a RHCP polarization

• Ionosphere and tropospheric effects

Direct signal and multipath are affected by the same ionospheric and tropospheric effects,

Multipath can be studied independently.

I. Multipath in GNSS context Channel Modeling

Multipath

Receiver antenna

GPS receiver We focus on

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Wideband modeling

• Sum of delayed echoes

I. Multipath in GNSS context Transmission channel Modeling

𝑕 𝑡 = 𝑎𝑚𝛿 𝑡 − 𝜏𝑚 𝑒𝑗 2𝜋𝑓𝑚𝐷 𝑡+𝜙𝑚

𝑀

𝑚=0

Multipath Parameters

𝑎𝑚 the amplitude of the 𝑚th multipath,

𝜏𝑚 the propagation delay of the 𝑚th multipath,

𝜙𝑚 the phase of the 𝑚th multipath,

𝑓𝑚𝐷 the Doppler-shift of the 𝑚th

multipath

Impulse response Spread out over a time delay

range

Frequency response frequency-selective fading

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• Effective height of the antenna

Link between the electromagnetic (EM) fields and the signal at the output of the antenna,

Takes into account the electric field and the direction of arrival to determine the signal phase

and amplitude.

I. Multipath in GNSS context Receiver antenna modeling

At the output of the antenna

𝑎𝑚 =𝐸 𝑚 𝜃𝑚 , 𝜑𝑚 . 𝑙 (𝜃𝑚 ,𝜑𝑚 ),

𝑉0

𝜙𝑚 = Arg 𝐸 𝑚 𝜃𝑚 , 𝜑𝑚 . 𝑙 (𝜃𝑚 , 𝜑𝑚 ) .

(𝜑𝑚 , 𝜃𝑚) azimuth, elevation of the echo,

𝐸 𝑚 𝜃𝑚 , 𝜑𝑚 electric field of the mth echo arriving at the antenna,

𝑉0 a reference voltage

The delays 𝜏𝑚 are the geometric delays of the echoes. For the direct signal, 𝜏0

is the geometric delay between the satellite and the receiver.

𝑙 (𝜃𝑚 ,𝜑𝑚)

Echo

antenna

𝑙

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• The GPS receiver performs a correlation of the incoming signal with a local replica

The local replica is generated with a delay error .

• Two main loops use the correlation outputs to adjust the replica

The delay lock loop (DLL) tracks the delay of the received signal,

The phase lock loop (PLL) tracks the carrier phase of the incoming signal.

• The simulator we use is a correlator output simulator

Available at the ENAC,

We do not process real GPS signals but only the outputs of the correlators (possible since we

know the GPS L1 C/A autocorrelation function),

Good trade-off between realism and efficiency.

휀𝜏 the delay estimation error,

𝐾 휀𝜏 the autocorrelation function of GPS L1 C/A

1 𝐶𝑕𝑖𝑝 = 1 (1023. 106)𝑠

The lock-loop condition is reached when

𝐾𝐸𝑎𝑟𝑙𝑦 = 𝐾𝐿𝑎𝑡𝑒 ⇒ 휀𝜏 = 0,

i.e. for a correct delay estimation.

I. Multipath in GNSS context GPS signal processing

휀𝜏

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• We assume that the received signal is only composed of the direct signal and one

echo

• If the echo varies slowly with respect to the time-loop constant, the resulting

correlation function is modified and becomes

𝑠 𝑡 = 𝑎0𝑑 𝑡 − 𝜏0 𝑐 𝑡 − 𝜏0 cos 2𝜋𝑓𝐿1𝑡 − 𝜙0 𝑑𝑖𝑟𝑒𝑐𝑡 𝑠𝑖𝑔𝑛𝑎𝑙

+ 𝑎1𝑑 𝑡 − 𝜏1 𝑐 𝑡 − 𝜏1 cos(2𝜋𝑓𝐿1𝑡 − 𝜙1) 𝑒𝑐𝑕𝑜 𝑠𝑖𝑔𝑛𝑎𝑙

𝐾𝑀 𝜖𝜏 = 𝐾 𝜖𝜏 + 𝛼1𝐾 𝜖𝜏 + ∆𝜏1 𝛼1 = 𝑎1/𝑎0 the relative amplitude of the multipath,

∆𝜏1 = 𝜏1 − 𝜏0 the relative delay difference.

𝛼1 = 0.5

∆𝜏1 = 0.5 𝑐𝑕𝑖𝑝

The lock-loop condition is reached when

𝐾𝐸𝑎𝑟𝑙𝑦 = 𝐾𝐿𝑎𝑡𝑒 ⇒ 휀𝜏 ≠ 0,

i.e. for an incorrect delay estimation.

Multipath error

(Note that 1 Chip 293m )

I. Multipath in GNSS context Multipath impact

≅

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• Mono channel prediction (1 satellite)

• 2 main blocks

The multipath generator predicts the electromagnetic fields and the multipath parameters,

The GPS receiver simulator predicts the GPS range error associated with one satellite.

• Inputs

The satellite position can be defined by its (azimuth, elevation) or derived from the almanacs,

The receiver can be static or dynamic.

• Output

The GPS range error due to multipath

I. Multipath in GNSS context General modeling

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VI. Comparison with measurements



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• One of the main issues of the development of a deterministic multipath

prediction is the choice of an EM computation theory.

• Available EM computation theories

– Method of moments (MoM)

– Geometrical optics (GO)

– Uniform theory of diffraction (UTD)

– Physical optics (PO)

• Strategy

MoM requires too much computation resources MoM

II. Comparison of modeling strategies of the transmission channel Choice of an Electromagnetic theory

Asymptotic

methods

Exact method

High-frequency

Approximations

GO

UTD

PO

?

Comparison of the channel parameters Use of MUSICA (available at the ENAC) for GO and UTD

Development of a PO prediction tool

Comparison of the EM fields Numerical validations with MoM for canonical configurations

Comparison from measurements

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II. Comparison of modeling strategies of the transmission channel Large object

UTD: 1 direct path, 1 reflected, 4 diffracted

GO: 1 direct path, 1 reflected

PO: 1 direct path, many multipath

1 - Time domain comparison

Metallic facade of an ENAC campus building

Satellite

incidence

Receiver antenna

Physically correct but no possible comparison

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II. Comparison of modeling strategies of the transmission channel Large object

Criterion

Computation of the RMS difference of the transfer functions

PO and UTD

match except very

near the reflector

2 - Frequency domain comparison

Metallic facade of an ENAC campus building

Computation on the (x,y) plane

Satellite

incidence

Large differences

between PO and GO

near the reflector and

also near the shadow

boundaries

For large objects

Comparison PO-GO: significant differences

Comparison PO-UTD: good agreement

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II. Comparison of modeling strategies of the transmission channel Small object (3.3m x 1.6m)

EM fields comparison

Computation of the RMS difference of the transfer functions

UTD

PO: 1/r expected decreasing

Near-field limit

GO and UTD cannot be used in the simulator

We choose PO since it is physically acceptable

GO

Criterion

Comparison of the fields reflected by the small metallic plate

For small objects

PO and UTD do not match

Results are non-physical

in the far-field

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• The incident field is a RHCP spherical wave with origin the satellite.

• Definitions

The incident field is the field in the absence of objects,

The scattered field takes into account all the phenomena induced by the

presence of objects,

is the total field.

• Consequence

where the satellite is not in direct visibility.

𝐸𝑖

III. PO-based prediction of the transmission channel Incident / scattered field

𝐸𝑡 = 𝐸𝑖 + 𝐸𝑆

𝐸𝑠

𝐸𝑡

𝐸𝑡 = 0

No a-priori detection of shadowed areas

where the incident field is blocked.

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• First-order interaction

Satellite -> facets -> antenna

• PO computation

We use the Lee and Mittra fast computation technique [Lee et al., IEE AP, vol. 31,1983]

The environment has to be modeled in polygonal facets

• Only the illuminated facets scatter field

Detection: a direct path has to exist between the satellite and the facet.

III. PO-based prediction of the transmission channel First-order interaction

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• The environment is modelled either in oriented rectangular or triangular facets

• The facets can be either metallic or dielectric

III. PO-based prediction of the transmission channel Scene modeling

Initial rectangular meshing Refined meshing

Initial triangular meshing Refined meshing

When modeled as dielectric, a facet is modeled

as a multilayer slab of 𝑁 layers with constant

thicknesses. 𝑑𝑛 = thickness

휀𝑟𝑛 = dielectric coefficient

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III. PO-based prediction of the transmission channel Illustration of the first-order interaction

Satellite incidence

Scattered electric field

Total field = incident field + scattered field

Shadow region

Specular regions

Field scattered

behind

Field scattered in

front

Field scattered by

the roof

Metallic building

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• The simulator can compute multiple interactions up to order 2

For metallic and dielectric multilayer facets.

• PO-based technique

The objective is to reduce the computation load,

Illumination of the facets at the second order via ray methods in order to reduce the

number of facets illuminated at the 2nd order.

III. PO-based prediction of the transmission channel Second-order interaction

Propagation is computed as in ray

methods

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III. PO-based prediction of the transmission channel Illustration of the second-order interaction

Satellite

incidence

Scattered field

Total field = incident field + scattered field

Shadow region

Specular regions

Metallic building

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• The impact of the ground is taken into account in the simulator up to second-

order.

• Airport environment context

The ground may be assumed as planar and infinite,

An image source is placed below the ground plane to account for reflections from the

ground plane.

III. PO-based prediction of the transmission channel Ground modeling

1. Satellite -> ground -> antenna

2. Satellite -> ground -> facet -> antenna

3. Satellite -> facet -> ground -> antenna

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• We compare our PO-based prediction with MoM via FEKO in order to

validate our EM prediction with a reference method.

III. PO-based prediction of the transmission channel Numerical validation

Satellite

incidence

Satellite

incidence

First-order interaction Second-order interaction

Results are in good agreement

Our PO-based prediction method can be considered as a reference method in our context

(fundamental for the statistical component)

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IV.1 Antenna mounted on the aircraft

IV.2 Description of the environment

IV.3 Prediction optimization

IV.4 Analysis of the deterministic error

IV.5 Application to Toulouse airport


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• Main issue

Should we model the aircraft on which the antenna is mounted as a 3D element in the scene?

• Measurement campaign performed with an airbus Aircraft [Steingass and al, 2004]

The only source of multipath is the fuselage,

Relative delays are too short to be taken into account: multipath merge with the direct signal.

• Chosen solution

The aircraft on which the antenna is mounted is not modeled as a 3D element in the scene,

The coupling between the antenna pattern and the aircraft structure is taken into account via the

modified gain pattern.

IV. Application of the deterministic model to the GNSS context Antenna mounted on an aircraft (1/2)

Schematic representation of cases where multipath could affect the antenna mounted on the airplane

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• We use measurements of a GPS antenna situated on an Airbus A319

Measurements have been performed for both circular polarizations

IV. Application of the deterministic model to the GNSS context Antenna mounted on an aircraft (2/2)

RHCP polarization pattern LHCP polarization pattern

(dB)

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IV. Application of the deterministic model to the GNSS context Determination of an appropriate description of the environment (1/2)

1. Influence of few-meters elements (windows)

2. Influence of material characteristics

Elements of few-meters have a

significant influence

Different dielectric characteristics for

a same material impact the prediction

of the range error

Satellite

incidence

Segment

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IV. Application of the deterministic model to the GNSS context Determination of an appropriate description of the environment (2/2)

3. Minimal size of objects in the scene

PO prediction limit :

We assess the influence of such objects when isolated

When large objects are present in the 3D scene, isolated objects of size

below 0.8m can be neglected.

20dB

4𝜆 ≃ 80cm

15m

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• Maximal order of interaction

Important issue since the computation of each interaction adds an important work load

IV. Application of the deterministic model to the GNSS context Prediction optimization

Computation of interactions only up to order 2

Inferior to -20dB

Amplitude of the reflected field

as a function of the interaction

order for a concrete wall of

thickness 30cm. ~

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• Multipath reduction process

Each illuminated facet generates a multipath: important computation load in case of 3D

scenes

• We group adjacent multipath in order to reduce their number

Via justified criteria relative to their delays, phase and Doppler,

No impact on the transfer function of the channel (numerically validated).


The number of multipath is drastically reduced

Computation in front of a

70m x 16m facade

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• Multipath area

Area outside which the environment will not affect the position estimation

• The maximum relative delay of multipath which impacts the GPS receiver is known

• Simplification of the problem starting from another geometrical aspect


~ 440m in the worst case,

This does not mean that an object

further than 440 m from the receiver

will not affect the positioning.

We compute the maximum first order

reflection illumination range in function

of the height of a building.

Radii of the multipath area 𝐷𝑚𝑎𝑥 = 460𝑚

Maximum height 𝐻𝑚𝑎𝑥 = 40𝑚

Mask angle 𝛼 = 5°

𝐷𝑚𝑎𝑥 = 𝐻𝑚𝑎𝑥

tan (𝛼)

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• Spatial variation of the range error in static

IV. Application of the deterministic model to the GNSS context Analysis of results

Satellite

incidence

The range error is highly

dependent on the

position of the receiver

𝜆

The error is null after 180m

as expected

Significant amplitude

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• Static vs. Dynamic

• With dynamic trajectories


Static case

Dynamic case

20m/s

10m/s

The receiver behaves as a low-

pass filter,

The range error is not so much

dependent on the receiver position,

The computation time decreases

(we do not wait at each point the

receiver convergence).

Specular region

19 000 facets

4 hours

19 000 facets

30 min

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• Presentation of the scene

Airbus access to Toulouse-Blagnac (France) airport


Group 1

Group 2

Group3

Weighting

Facility

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• Development of 3D modeling of the airport scene

Buildings and aircraft are modeled with rectangular facets


3D Model of the weighting facility 3D Model of aircraft

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• Large-scale studies

• Small-scale studies

Computation of the error on a segment,

Once the risky areas have been identified by means of a large-scale study it gives precisions on

the range error evolution within these areas.

• Dynamic trajectory studies

Simulation of a trajectory within the airport,

Prediction of the range error affecting a moving aircraft,

Allows comparing simulation results with collected measurements on a moving aircraft.

Satellite

incidence

Risky areas

IV. Application of the deterministic model to the GNSS context Suitable representation of the deterministic prediction

Mapping the range error within the airport,

Determination of risky areas for aircraft

navigation (where the range error is

significant),

It is not possible to display the high

frequency variations of the range error. 132 000 facets

12 hours

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• Illustration of the limits of a pure deterministic prediction

• We compute the GPS range error along the segment

First case: the building is at its initial position,

Second case: the building center is slightly modified of +5cm along the y-axis.

• As expected the range error is highly dependent on the relative position receiver-building

V. Statistical model Limits of the deterministic modeling

Moving the building center of few

centimeters modifies greatly the multipath

phase and thus the GPS range error

Necessity of a statistical component

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• Objective

To obtain the statistical moments of the range error (mean and standard deviation).

• It has been shown that the deterministic prediction could be considered as a

reference method in our context (validation with MoM)

The statistical model may be based on the deterministic model.

• Thus, the accuracy of the deterministic model depends on the uncertainties in the

scene data

A 3D description of a scene, even realistic, may lack of precision.

V. Statistical model Nature of the statistical component

The statistical prediction takes its origins in the

defective scene description

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• We base the statistical simulator on the deterministic simulator via Monte

Carlo (MC) simulations

the uncertainties in the configuration are taken into account via adding a

statistical variability to the 3D scene.

V. Statistical model General principle

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• We have identified eight parameters that we consider as statistical in the Monte Carlo

simulation:

the buildings positions in the horizontal plane,

the buildings orientations in the horizontal plane,

the buildings heights,

the buildings materials,

the buildings materials thicknesses,

the ground material

the height of the antenna.

• These parameters are independent for each building, in order to insure the non-correlation

of the complete geometry.

V. Statistical model Scene generation

Buildings position/height

Buildings/ground materials

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• Small-scale studies

• Parameters set to realistic values

V. Statistical model Analysis of the statistical error

𝜎𝑃 = 1𝑚 (building position)

𝜎𝜃 = 1° (building orientation)

𝜎𝐻 = 5% (building height)

Deterministic prediction is only a realization of the possible error

Statistical prediction gives a more realistic representation of the error.

Deterministic prediction

Statistical prediction

19 000 facets

12 hours

19 000 facets

30min

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• Large-scale studies

• Dynamic trajectory studies

Prediction of the statistical moments of the range error affecting a moving aircraft,

Allows comparing simulation results with collected measurements on a moving aircraft.

Satellite

incidence

V. Statistical model Analysis of the statistical error

Standard deviation of the predicted range error

Indication of the same risky areas as for the

deterministic predictions,

More complete information:

the variance value takes into account the

important variations of the error

132 000 facets

7 days

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VI. Comparison with measurements Objectives

• For one trajectory of an aircraft within Toulouse Blagnac airport

We have extracted the range error due to multipath (plus noise).

• We compare one measurement with statistical predictions

Comparison of predicted statistical moments for each point of the trajectory with the

measured range error due to multipath,

Remind that one measurement is one measured realization.

• A rigorous validation of our statistical prediction would require having access to

the statistical moments of the measurements for each point of the trajectory,

This requires to have many measurements on exactly the same trajectory and for the

same position of satellite,

Requires to have and to process a huge database.

• Synthesis

Such a comparison does not validate the simulator,

It illustrates its relevance in regards to measurements.

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• From the measurement database we have the satellite position, the receiver

position, and the range errors.

• We do not have information regarding the presence of other aircraft in the scene

at the date at which the measurements were collected

VI. Comparison with measurements Collected measurements

Satellite

incidence

17°

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• The magnitude of the predicted sigma is of the same order of the measured range error

(excepted in the pointed regions).

• The predicted mean is almost null for the complete trajectory

• The predicted variance remains almost constant of value around 0.2m

VI. Comparison with measurements Results without aircraft in the scene

Unpredicted error Unpredicted peak error

According to our predictions, the buildings and the ground seem to

have a weak influence on the range error in this particular scenario.

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• We introduce 10 aircraft in the scene at realistic parking places

VI. Comparison with measurements Results with 10 aircraft in the scene

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• The introduction of the aircraft in the scene impacts the variance prediction

The presence of aircraft in proximity impacts the range error due to multipath.

Prediction and measurement fit better.

• For such a trajectory for which multipath reaching the receiver antenna are essentially due

to the presence of other aircraft, it is important to have information regarding the location of

surrounding aircraft.

VI. Comparison with measurements Results with aircraft in the scene

Predicted error

Predicted peak error

The perturbation is

predicted at the right place

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• Regarding the deterministic prediction

Development of a deterministic tool for the prediction of GNSS multipath error for airport

navigation,

Geometrical optics (GO) and the uniform theory of diffraction (UTD) cannot be employed

for multipath prediction in GNSS context,

The use of physical optics (PO) for GNSS multipath prediction is numerically validated by

means of comparison with the method of moments (MoM),

The prediction of the interactions with the scene up to order 2 is sufficient.

• Regarding the addition of a statistical component

We have developed a hybrid deterministic-statistical tool based on the deterministic

prediction combined with Monte-Carlo simulations.

Conclusion Main results (1/2)

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• In order to ensure the efficiency of the prediction tool, we have proposed

Criteria for a suitable modeling of a 3D environment,

Techniques to improve the computation efficiency of the GNSS errors due to multipath

in environments as large as an airport.

• We have proposed suitable deterministic and statistical descriptions of the

GNSS error due to multipath in environments at the scale of an airport

• We have shown that for an aircraft maneuvering at the surface of an airport, the

presence of other aircraft in proximity may be a source of GNSS positioning

error.

• By means of comparisons with measurements we have illustrated the results of

the hybrid deterministic-statistical model and found coherent results.

Conclusion Main results (2/2)

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• Conduction of studies regarding the impact of periodic small elements of size below

0.8m which repeat themselves a great number of times

E.g. metallic window frames in a façade or corrugated metal walls of a building beyond PO limits.

• Assessing in details the impact of the temporal variability of the scene

Influence of meteorological phenomena,

A statistical description of the presence of mobiles in the scene, e.g. aircraft, could also be

proposed.

• Computation of the statistical moments of the multipath error observed within airports in

order to perform a complete validation of our tool

More measurements should be extracted.

• Efforts of simplification into a more high level model

Development of a simpler prediction model of the multipath error which settings would be based

on simulations performed with our tool,

Thesis launched by Airbus on GNSS singular effects including multipath in airports.

Conclusion Future works (1/2)

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LETA

• The multipath prediction simulator may be used for other applications than airport

navigation with GNSS

Other signals e.g. mobile telecommunications,

Other environments e.g. urban environment.

Conclusion Future works (2/2)

Position of the emitter

Movement of the receiver

Achieved in the framework of a student project

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LETA

Thanks for your attention

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LETA

Urban Environment PDP

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Documents

PhD Defence AirportNav