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1 INTRODUCTION

With satellite navigation as an enabling technology

for a growing number of applications, maintaining

Global Navigation Satellite Systems’ (GNSS)

Positioning, Navigation, and Timing (PNT) service

has become a necessity. Different GNSS applications

require appropriate quality of PNT (GSA, 2018).

Studies of GNSS positioning performance in different

scenarios of applications thus add to the knowledge

base that empowers risk assessment of GNSS

utilisation (HM Government Office for Science, 2018).

Tropospheric delay of GNSS signal is caused by its

propagation through non-ionised but non-homogenic

medium just above the Earth’s surface (Hopfield,

1972), (Parkinson, Spilker, Jr., 1996), (Teunissen,

Montentbruck, 2017), (Reguzzoni, 2013), (Schueller,

2001). Meteorological parameters, such as air

temperature, air pressure, and water vapour partial

pressure, determines the delay encountered by

satellite signal while propagating through

troposphere (Parkinson, Spilker, Jr., 1996), (Teunissen,

Montentbruck, 2017), (Schueller, 2001). The GNSS

tropospheric delay consists of a dry-air and a wet-air

components, with the latter particularly enlarged

during weather deterioration (Parkinson, Spilker, Jr.,

1996), (Teunissen, Montentbruck, 2017), (Zhou et al,

2017). Tropospheric delay of GNSS signal is then

mapped onto GNSS positioning error using the

geometry matrix (Filić, and Filjar, 2018).

Here we analysed the dynamics of GPS

positioning error due to tropospheric delay for a

selected case of tropical cyclone Marcus (Figure 1)

that stroke the city of Darwin, Australia in 2018, a

devastating tropical cyclone in a coastal region,

affecting a range of maritime GNSS applications

(BOM, 2018). The aim of research was to study GPS

positioning error variations due to tropospheric delay,

Analysis of Tropospheric Contribution to GPS

Positioning Error During Tro

pospheric Cyclone Marcus

in 2018

. Sikirica

Krapina University of Applied Sciences, Krapina, Croatia

. Horvat

Zagreb University of Applied S

ciences, Zagreb, Croatia

. Špoljar & I. Rumora

University of Rijeka, Rijeka, Croatia

ABSTRACT: GNSS positioning performance assessment is essential for sustainable development of a growing

number of GNSS-based technology and socio-economic applications. Case-

studies of GNSS positioning

performance in critical environments and applications scenarios reveals vulnerabilities of the GNSS

Positioning, Navigation, and Timing (PNT) services, and suggest mitigation techniques and GNSS application

risk containment. Here we address the case of GPS positioning performance during a devastating tropical

cyclone Marcus that hit the greater area of the city of Darwin, Australia in 2018. We identified specific statistical

properties of time series of tropospheric contribution to GPS northing, easting, and vertical positioning error

that may contribute to understanding of tropospheric effects on GPS positioning performance during a massive

weather deterioration in maritime and coastal areas, and analysed their adversarial effects on GNSS-based

maritime applications.

http://www.transnav.eu

the

International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 14

Number 2

June 2020

DOI:

10.12716/1001.14.02.10

344

rather than the GPS tropospheric delay itself. In the

approach used, we focused our effort on

understanding the GPS positioning error from the

perspective of (maritime) navigation and the other

GPS applications.

Fast developing and powerful cyclone caused a

massive destruction in the area, with rapid changes of

meteorological parameters, providing essential case-

study to infer GPS positioning performance

degradation in a coastal region. GPS positioning error

due to tropospheric delay was then mapped on

requirements for PNT in maritime sector to estimate

risk of GNSS-based application malfunctioning or

failure in a maritime sector.

2 METHODOLOGY

Tropospheric contribution to GPS positioning error,

which is an amount of GPS positioning error due to

tropospheric delay, may be calculated using

methodology developed by (Filić and Filjar, 2018) and

an additive model, as presented with (1).

tropo uncompensated tropo compensated

TROPOerr Perr Perr

−−

= −

(1)

with:

TROPO

err denotes tropospheric contribution to the

over-all GPS positioning error

Perr

tropo-uncompensated denotes GPS positioning error

without tropospheric corrections applied on GPS

pseudoranges before entering the position estimation

process (Filić, and Filjar, 2018), (Filić, Grubišić, and

Filjar, 2018)

Perr

tropo-compensated denotes GPS positioning error with the

Saastamoinen tropospheric corrections applied on

GPS pseudoranges before entering the position

estimation process (Filić, and Filjar, 2018), (Filić,

Grubišić, and Filjar, 2018)

Figure 1. (Source: NASA Earth Observatory, available at:

https://eoimages.gsfc.nasa.gov/images/imagerecords/91000/

91876/marcus_vir_2018080_lrg.jpg )

The Filić-Filjar methodology (Filić, and Filjar, 2018)

(Figure 2) involves: (i) experimental GNSS

observations collected by Darwin GNSS reference

station (source: International GNSS Service, at:

ftp://cddis.gsfc.nasa.gov/gnss/data/daily) during the

passage of tropical cyclone Marcus, (ii) post-

processing of observations using an open-source

GNSS Software-Defined Radio (SDR) receiver

RTKLIB (available at: http://www.rtklib.com/) to

estimate GPS positioning error as encountered by a

commercial grade single-frequency GPS receiver with

corrected (compensated)) and uncorrected

tropospheric effects (uncompensated), respectively,

(iv) statistical analysis of the observed contribution of

tropospheric effects of Marcus tropical cyclone to

over-all GNSS positioning error, as derived using (1).

Utilisation of GNSS SDR concept allows for a more

transparent access to GPS position estimation

procedure (Filić, Grubišić, and Filjar, 2018), (Oxley,

2017), (Parknson, Spilker, Jr., 1996), including the

control of the pseudorange correction models applied

(Figure 3).

Figure 2. Methodology of research

Figure 3. RTKLIB GNSS SDR receiver configuration panel,

with available Tropospheric Correction options

Configuration of the GPS SDR RTKLIB framework

in post-processing mode ensured it will behave like a

common maritime commercial-grade single-

frequency GPS receiver. Compensated GPS position

estimates were derived by utilisation of Saastamoinen

tropospheric correction model (GPS Directorate,

2013), (Filić, and Filjar, 2018), (Parkinson and Spilker,

Jr., 1996), (Takasu, 2013), (Teunissen, P J G,

Montentbruck, 2017), as given in Eq (2). Saastamoinen

model (2) estimates tropospheric delay of the satellite

signal, which corrects the raw pseudorange

measurements before those serve as the inputs to the

GNSS position estimation procedure.

( )

0.002277 1255

0.05 tan

cos

T p ez





= ⋅ + ⋅−









(2)

where:

345

z satellite zenith angle in [rad], defined by elevation

angle El

r given with (3):

z El

= −

(3)

p atmospheric pressure in [hPa], defined by standard

Earth atmosphere for the height above the mean

geodetic sea level h as with (4):

( )

5.2568

1013.25 1 2.2557 10ph

−

= ⋅− ⋅ ⋅

(4)

T absolute air temperature in [K], defined by standard

Earth atmosphere for the height above the mean

geodetic sea level h as with (5):

15.0 6.5 10 273.15Th

−

= − ⋅ ⋅+

(5)

e … partial water vapour pressure in [hPa], defined

by standard Earth atmosphere for the relative

humidity h

rel given as with (6):

17.15 4684.0

6.108 exp

38.45 100

rel

⋅−



=⋅⋅



−



(6)

Uncompensated tropospheric effects were

simulated in RTKLIB environment by utilisation of

experimental (observed) GPS pseudoranges with the

selection of GPS SDR receiver tropospheric

corrections switched off (Figure 3), with the rest of

correction models (satellite clocks and ionospheric

errors) operational and the receiver configured as a

commercial-grade single-frequency ones.

The GPS positioning vector was split into three

mutually orthogonal components with roots in the

navigation application context: GPS northing, easting,

and vertical errors, respectively. Time series of

residual GPS positioning errors due to tropospheric

effects (1) were analysed using bespoke software

developed by (Filić, and Filjar, 2018) in the open-

source R environment for statistical computing

(available at: https://www.r-project.org/). The analysis

comprised (i) the essential statistical analysis, (ii)

statistical distribution estimation, through histogram,

and (iii) partial auto-correlation analysis (Shumway,

and Stoffer, 2017).

3 RESEARCH RESULTS

A rapid weather deterioration increased the level of

tropospheric contribution to the over-all GPS

positioning error, as depicted in Figure 4.

Figure 4. Time series of tropospheric contribution to GPS

positioning error components (northing - red, easting - blue,

vertical - green, respectively)

Exploratory statistics of time series of GPS

positioning error components are presented in

Figures 5, 6 and 7, respectively using box-plot

diagrams.

Figure 5. Box-plot summary of GPS northing positioning

error component

Figure 6. Box-plot summary of GPS easting positioning

error component

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Figure 7. Box-plot summary of GPS vertical positioning

error component

Statistical distribution estimation was conducted

through histogram analysis, with histograms

presented in Figures 8, 9 and 10, respectively.

Figure 8. Histogram-based statistical distribution estimates

for GPS northing positioning error component

Figure 9. Histogram-based statistical distribution estimates

for GPS easting positioning error component

Figure 10. Histogram-based statistical distribution estimates

for GPS vertical positioning error component

Figures 11, 12 and 13, respectively, show the

Quantile-Quantile (Q-Q) diagrams of time series, for

further analysis of statistical distribution of GPS

positioning residuals.

Figure 11. Q-Q diagrams of GPS northing positioning error

component

Figure 12. Q-Q diagrams of GPS easting positioning error

component

Figure 13. Q-Q diagrams of GPS vertical positioning error

component

Finally, Figures 14, 15 and 16, respectively, depicts

results of partial auto-correlation analysis of residual

GPS positioning error components due to

tropospheric effects of tropical cyclone Marcus,

derived using partial auto-correlation method.

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Figure 14. Partial auto-correlation analysis of GPS northing

positioning error component

Figure 15 Partial auto-correlation analysis of GPS easting

positioning error component

Figure 16. Partial auto-correlation analysis of GPS vertical

positioning error component

4 DISCUSSION AND CONCLUSION

The aim of this research was to identify and assess the

contribution of the rapidly degrading weather

conditions to the GPS positioning error budget of a

commercial-grade single-frequency receiver, and

address potential implications of neglecting the

tropospheric effects for maritime GNSS-based

applications.

Based on experimental GPS pseudoranges taken

during development of a tropical cyclone, time series

of tropospheric contributions to the over-all GPS

positioning error vector components (northing,

easting, and vertical) were estimated and analysed

statistically.

Box-plot diagrams of GPS positioning error

components (Figures 5, 6 and 7, respectively) reveal

slightly lowered (negative mean) GPS northing and

easting positioning error, and enhanced GPS vertical

positioning error. GPS easting error box-plot shows

an imbalance between mean and median values of the

derived time series, with a number of positive

outliers.

Histograms and Quantile-Quantile (Q-Q)

diagrams (Figures 11, 12, and 13, respectively)

(Sumway, and Stoffer, 2017) reveal interesting

statistical properties of GPS northing and easting

positioning error components. While the histogram of

GPS northing positioning error component is

suggestive towards normal distribution, the Q-Q plot

provides the cues on the contrary. The GPS easting

positioning error component time series, although

with slightly skewed statistical distribution, yields the

Q-Q diagram suggesting good fit with normal

distribution. Statistical distribution of GPS vertical

positioning error component time series does not

follow normal distribution, as it is usually the case in

disturbed tropospheric condition (Filić, Filjar, 2018),

(Rumora, Jukić, Filić, Filjar, 2018).

Partial auto-correlation-based analysis (Figures 14,

15, and 16, respectively) revealed processes that may

be modelled using simple auto-regressive (AR)

models, AR(1) for residual GPS positioning northing

and vertical errors, and AR(2) for residual GPS

positioning easting errors (Shumway, and Stoffer,

2017).

Observed statistical properties will assist in

development of appropriate models of GPS

positioning performance degradation during rapidly

developing and massive weather deterioration,

without consideration of the actual GPS tropospheric

delay. It should be noticed that we did not analyse the

weather deterioration itself, but assessed the

consequences on GPS positioning performance only.

Considering required GPS positioning

performance in maritime segment (GSA, 2018), we

identified a potential issue in utilisation of

uncorrected GPS tropospheric delay during a tropical

cyclone for port and inland waterways applications.

However, the increasing utilisation of unmanned

robots (UAVs, autonomous vessels in particular), and

the need for relief operation during and in the

aftermath of a devastating tropical cyclone in coastal

areas may suffer from degraded GPS positioning

performance.

We continue our research in examination cases of

different weather conditions impact on GNSS

positioning performance in maritime areas and for

maritime-related navigation and non-navigation

applications (Oxley, 2017), (GSA, 2018), in which we

will also examine the correlation between the way the

weather deterioration develops and the impact on

particular components of GPS positioning error vector

(Kačmarik et al, 2019).

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348

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