CEN/TR 17447:2020
(Main)Space - Use of GNSS-based positioning for road Intelligent Transport System (ITS) - Mathematical PVT error model
Space - Use of GNSS-based positioning for road Intelligent Transport System (ITS) - Mathematical PVT error model
This document is written in the frame of WP1.3 of GP-START project. It discusses several models to provide synthetic data for PVT tracks and the ways to analyse and compare the tracks to ensure these are similar to the reality.
Mathematisches PVT-Fehlermodell
Espace - Utilisation du positionnement GNSS pour les systèmes de transport routier intelligents (ITS) - Modèle d’erreur mathématique PVT
Vesolje - Ugotavljanje položaja z uporabo GNSS za cestne inteligentne transportne sisteme (ITS) - Matematični model za napake PVT
General Information
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Standards Content (Sample)
SLOVENSKI STANDARD
01-april-2020
Vesolje - Ugotavljanje položaja z uporabo GNSS za cestne inteligentne transportne
sisteme (ITS) - Matematični model za napake PVT
Space - Use of GNSS-based positioning for road Intelligent Transport System (ITS) -
Mathematical PVT error model
Mathematisches PVT-Fehlermodell
Espace - Utilisation du positionnement GNSS pour les systèmes de transport routier
intelligents (ITS) - Modèle d’erreur mathématique PVT
Ta slovenski standard je istoveten z: CEN/TR 17447:2020
ICS:
03.220.20 Cestni transport Road transport
33.060.30 Radiorelejni in fiksni satelitski Radio relay and fixed satellite
komunikacijski sistemi communications systems
35.240.60 Uporabniške rešitve IT v IT applications in transport
prometu
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
TECHNICAL REPORT
CEN/TR 17447
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
February 2020
ICS 03.220.20; 33.060.30; 35.240.60
English version
Space - Use of GNSS-based positioning for road Intelligent
Transport System (ITS) - Mathematical PVT error model
Espace - Utilisation du positionnement GNSS pour les Mathematisches PVT-Fehlermodell
systèmes de transport routier intelligents (ITS) -
Modèle d'erreur mathématique PVT
This Technical Report was approved by CEN on 8 December 2019. It has been drawn up by the Technical Committee
CEN/CLC/JTC 5.
CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium,
Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,
Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia,
Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
CEN-CENELEC Management Centre:
Rue de la Science 23, B-1040 Brussels
© 2020 CEN/CENELEC All rights of exploitation in any form and by any means Ref. No. CEN/TR 17447:2020 E
reserved worldwide for CEN national Members and for
CENELEC Members.
Contents Page
European foreword . 3
1 Scope . 4
2 Normative references . 4
3 Terms and definitions . 4
4 List of acronyms . 4
5 Approach . 5
6 Input data . 7
7 Model . 10
7.1 Introduction . 10
7.2 Discussion about models . 11
7.3 AR model . 16
8 Analysis tools . 29
8.1 General . 29
8.2 State of the art on data set similarity assessment . 30
8.3 Validation tool description . 34
9 Conclusions . 48
Annex A (normative) Neural network . 50
A.1 Neuron network concept . 50
Bibliography . 59
European foreword
This document (CEN/TR 17447:2020) has been prepared by Technical Committee CEN-CENELEC/TC 5
“Space”, the secretariat of which is held by DIN.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
1 Scope
This document is written in the frame of WP1.3 of GP-START project. It discusses several models to
provide synthetic data for PVT tracks and the ways to analyse and compare the tracks to ensure these are
similar to the reality.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
EN 16803-1:2016, Space — Use of GNSS-based positioning for road Intelligent Transport Systems (ITS) —
Part 1: Definitions and system engineering procedures for the establishment and assessment of
performances
3 Terms and definitions
For the purposes of this document, the terms and definitions given in EN 16803-1:2016 apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
• ISO Online browsing platform: available at http://www.iso.org/obp
• IEC Electropedia: available at http://www.electropedia.org/
4 List of acronyms
ANOVA Analysis of variance
AR Autoregressive
ARMA Autoregressive moving average
CDF Cumulated distribution function
CET Central european time
DFT Direct Fourier transform
DOP Dilution of precision
FFT Fast Fourier transform
GNSS Global navigation satellite system
GPS Global positioning system
HDOP Horizontal dilution of precision
HPE Horizontal position error
IGS International GNSS service
ITS Intelligent transport systems
KS Kolmogorov–Smirnov
MFNN Multilayer feedforward neural networks
NED Northeast down
NN Neural network
OBU On board unit
PVT Position velocity time
SBAS Satellite based augmentation system
SVM Support vector machine
UTC Universal time coordiante
VDOP Vertical dilution of precision
WGS84 World geodetic system 1984
WP Work package
5 Approach
The objective of the WP1.3 model the PVT tracks similar enough to the reality to be used for application
validation. The approach used is to twofold: to find a model and to build the tools to compare the
simulated data to the real data.
The following figure shows the overall logic of the work to be undertaken in WP 1.3:
Figure 1 — WP1.3 logic
The blue boxes represent the raw data that can be stored in files. The red boxes are the computations that
need to be carried out to get new data. Finally, the green boxes correspond to the outputs of this work
package that need to be documented.
In some more detail:
— Reference data set: These are the reference trajectories computed with extra sensors and is expected
to have errors at centimetric level or better.
— Real data sets: These are the trajectories computed by the receiver under test.
— Error calculation: The error calculation computes the difference between the position computed by
the receiver and the one from the reference trajectory. Note that this step will be used to define the
parameters to be modelled. For instance in the Ifsttar paper [RD2], the model was based on the
absolute error and its angle. But one could use the position in XYZ (WGS84 coordinates). Since the
behaviour in the vertical axis is usually different, one could use a NED reference system or change
the reference to an axis in the direction of the movement another across the direction of the
movement and the third would be the vertical.
— Real error files: These files should contain the errors for each receiver trajectory.
— Error models: The error models will be described in the documentation and should depict the error
of the position depending on the previous errors, random variables (which can follow any
distribution) and parameters of the distributions.
— it algorithm: The fit algorithm should calculate the parameters that define the models.
— Model parameters: Storage of the models parameters.
— Synthetic error generation: Once the parameters are found, by starting the random variables with
different seed, one will get synthetic errors that should be equivalent to the real ones.
— Error analysis: As can be on the figure, the error analysis box appears twice: for the real errors and
for the synthetic ones. These analysis will be compared to validate the models. So far, the analysis
used have been the CDF (cumulative distribution function) and autocorrelation. As far as the CDF will
be representative for the error distribution in the position domain, in the time domain,
autocorrelation may not be enough to observe the behaviour of the error. It is suggested to compute
the DFT (discrete Fourier transform) to analyse the error in the frequency domain and observe if
there are errors at particular frequencies. Autocorrelation analysis will be kept for comparison with
previous models.
— Comparison: the Error analysis of real and synthetic data are compared to validate the models.
Synthetic data generator: this step adds the synthetic errors with the reference trajectory to create a new
data set that can be used for the sensitivity analysis.
6 Input data
The input data to observe and models has been provided by Q-Free. It contains a header and then the
data with each column separated by a space. The header contains the list of fields
# SAVE Position Export
#
# Equipment: 1, seagull_datalogger_1
# Export Date: Tue Dec 13 13:58:20 CET 2016
#
# Space separated field list
#
# Equipment id (6 is reference)
# Drive id
# Leg id
# Date yyyy-mm-dd (UTC)
# Time hh:mm:ss.fff (UTC)
# Gps week
# Gps time of week, seconds
# OBU Timestamp, seconds
# GNSS Good flag (1 is good, 0 is bad)
# GNSS Fix Type
# Latitude
# Longitude
# Ellipsode height (meters)
# Geoid height, height over sea level (meters)
# Speed over ground (m/s)
# Course over ground (deg)
# Yaw (deg/second)
# Pitch (deg/second)
# Roll (deg/second)
# Horizontal pos error (meter)
# Vertical pos error (meter)
# sN, st.dev of position, in north direction (meters)
# sE, st.dev of position, in east direction (meters)
# sD, st.dev of position, in down direction (meters)
# HDOP
# PDOP
# NED n speed (m/s)
# NED e speed (m/s)
# NED d speed (m/s)
# Number of satellites used in solution
# Average signal quality
# SBAS Active
# rN integrity, north (m)
# rE integrity, east (m)
# rD integrity, down (m)
#
To do the analyses and modelling of the PVT error the outputs computed by the receiver in a specific
proprietary way are not used. For instance, the horizontal and vertical position errors are calculated by
the receiver but one does not know how. Therefore, all the positions in latitude, longitude and height are
compared to the receiver #6 which is the reference. The other fields used are:
— Equipment Id and leg to separate the data sets;
— GNSS good flag and type fix to use only the positions with 4 (four) or more satellites that do not
use additional sensors (i.e.: type of fix 4 or 6).
For more details, the GNSS fix types are:
— NO_FIX = 0, → red
— ONE_SV = 1, → purple
— TWO_SV = 2, → blue
— THREE_SV = 3, → orange
— FOUR_PLUS_SV = 4, → green
— LS_2D = 5, → cyan
— LS_3D = 6, → dark green
— DEAD_RECKONING = 7, → yellow
— PSR_DIFF = 8, → brown
— SENSOR_FUSION = 9 → dark purple
The following figure shows the behaviour one can expect of a receiver (Reference is black) with a tunnel
in the middle of the path:
Figure 2 — Oslo input data plotted
Some other issues have been observed in the input data. The following figure shows the histograms of
the error a data set from Frankfurt. The 6 (six) plots show the same data with different histogram bin
widths:
Figure 3 — Frankfurt errors histograms
As it will be seen in the following clauses, the chosen model tends to a Gaussian distribution for data sets
big enough. However, the errors observed in Frankfurt data set, are not likely to follow a normal
distribution. When one observes the errors in the time domain, one can see that the error distribution
changes during the test. This is, the test starts in small error envir
...
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