165

1 INTRODUCTION

New shipping routes are emerging as a result of

icebergs melting in polar regions, allowing for more

efficient transport of people and goods. The opening

of the Northwest Passage, the maritime route

connecting the Pacific Ocean with the Atlantic Ocean

through the Arctic region, is considered such a

development [8]. The Northwest Passage location in

polar region renders satellite navigation, as a

navigation-supporting technology, vulnerable to

space weather effects [1]. Space weather is defined as

a set of conditions and events of variable energy

transfer originated in the Sun and spread through the

Modelling GPS Positioning Performance in Northwest

Passage during Extreme Space Weather Conditions

D. Špoljar

1,2

, O. Jukić

, N. Sikirica

, K. Lenac

& R. Filjar

1,2,3

University of Rijeka, Rijeka, Croatia

Krapina University of Applied Sciences, Krapina, Croatia

Virovitica University of Applied Sciences, Virovitica, Croatia

ABSTRACT: New shipping routes are emerging as a result of iceberg melting in polar regions, allowing for

more efficient transport of people and goods. Opening of the Northwest Passage, the maritime route connecting

Pacific Ocean with Atlantic Ocean through Arctic region, is considered such a development. The increasing

transport exploitation of the Northwest Passage requires the quality assessment of maritime navigation aids for

compliance with the established requirements. Here we contribute to the subject with addressing the polar

commercial-grade GPS positioning performance in the Northwest Passage in the extreme positioning

environment conditions during the massive 2003 space weather storm, a space weather event similar to the

Carrington Storm of 1859, the largest space weather event recorded. The GPS positioning environment in the

Northwest Passage during the Carrington-like storm in 2003 was reconstructed through the GNSS SDR

receiver-post processing of the experimental GPS observations. The raw GPS dual-frequency pseudoranges and

navigation messages were collected at the International GNSS Service (IGS) reference station at Ulukhaktok,

Victoria Island, Canada. Pseudorange processing and GPS position estimation were performed in three

scenarios of pre-mitigation of the ionospheric effects, known as the single major contributor GPS positioning

error: (i) no corrections applied, (ii) Klobuchar-based corrected GPS positioning, and (iii) dual-frequency

corrected GPS positioning. Resulting GPS positioning error vectors were derived as positioning error residuals

from the known reference station position. Statistical properties of the northing, easting, and vertical

components of the GPS positioning error vector were analyzed with a software developed in the R environment

for statistical computing to select suitable methods for the GPS positioning error prediction model

development. The analysis also identified the most suitable theoretical fit for experimental statistical

distributions to assist the model development. Finally, two competitive GPS positioning error prediction

models were developed, based on the exponential smoothing (reference) and the generalized regression neural

networks (GRNN) (alternative) methods. Their properties were assessed to recommend their use as mitigation

methods for adverse massive space weather effects in polar regions.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 15

Number 1

March 2021

DOI: 10.12716/1001.15.01.16

166

Earth’s surroundings that can affect space-borne and

ground-based technological systems. Geomagnetic

storms represent extreme forms of space weather that

can affect radio wave propagation across the

spectrum, degrading the positioning performance of

the Global Navigation Satellite System (GNSS) and

reducing the quality of the GNSS-based applications

[1, 7]. Here we address the effects of the 2003

geomagnetic storm on the polar commercial-grade

GPS positioning performance in the Northwest

Passage. The 2003 extreme space weather event, also

known as the ‘Halloween Storm’, is often compared to

the Carrington Storm of 1859, by far the largest solar

storm recorded [1, 2]. Considering the expected

increase in maritime traffic in the Northwest Passage

with the extensive utilization of satellite navigation

on-board the vessels, this study aimed at assessment

of the GPS positioning performance using the

common on-board equipment and compliance with

the requested and required GPS positioning

performance [4]. The study results with the

recommendation proposal to mitigate GNSS

positioning degrading ionospheric delay effects of

massive space weather developments on satellite

navigation performance in the polar region

2 METHOD AND MATERIAL

The GPS positioning environment in the Northwest

Passage during the Carrington-like storm in 2003 was

reconstructed throuvenrgh the GNSS SDR receiver-

post processing of the experimental GPS observations

taken in the region during the space weather event [3,

5, 7]. The research aims at addressing the excess GNSS

ionospheric delay caused by considerable space

weather event, and its contribution to the over-all

GNSS positioning error. As the result, a prognostic

model is to be developed to forecast the GPS

positioning error during a massive space weather

deterioration in the region of Northwest Passage. It

should be noted that we consider the other sources of

GPS positioning errors (multipath, GPS tropospheric

delay etc.) of the unchanged (unaffected) nature.

Additionally, while the research focuses on the GPS

ionospheric delay, we do not consider effects of the

GPS ionospheric scintillation in this research.

Observations were collected of raw (uncorrected) GPS

dual-frequency pseudouranges and GPS navigation

messages broadcast at the International GNSS Service

(IGS) reference station at Ulukhaktok, formerly

Holman, Victoria Island, Canada (latitude:

70.7364000N, longitude: 117.7609000W, 39.5 m above

the mean sea level), and made available through the

IGS internet archives

(ftp://cddis.nasa.gov/gnss/data/daily). The IGS is set to

assist scientists and the other interested parties with

the provision of the GNSS pseudoranges uncorrected

for ionospheric effects to allow for research into the

ionospheric effects on GNSS performance and

operations. Nominally established to provide with

daily records of observed raw (uncorrected) GNSS

pseudoranges at 30 s sampling time, the reference

stations may occasionally provide reduced sets of

observations, and/or present observations in faulty

and inconsistent manner. External events may also

cause tempral suspension of pseudorange collection.

In an approach similar to the essence of differential

GNSS, we consider the GNSS ionospheric delay to be

approximately constant in the bounded region around

the observation site, thus allowing the generalisation

of the observed ionospheric delay effects on GNSS

performance at stationary site to be applicable on the

near-by dynamical environment of mobile maritime

objects (vessels).

We used the Ulukhaktok (Holman) GPS pseudorange

observations from the period DOY298 (25

October) –

DOY315 (11

November) in 2003 to cover the most

intensive phase of the largest space weather event

observed in modern history. Pseudorange processing

and GPS position estimation were performed in three

scenarios of pre-mitigation of the ionospheric effects,

known as the single major contributor to GPS

pseudorange measurement error, and, consequently,

GPS positioning error: (i) GPS positioning exposed to

ionospheric effects, with no corrections applied, (ii)

Klobuchar-based corrected GPS positioning, as

defined with (1) using the GPS-broadcast correction

model parameters (αi,βi,i = 1,…,4) and (iii) dual-

frequency corrected GPS positioning procedure

utilizing pseudorange measurements ρ(f1) and ρ(f2) on

carrier frequencies f1 and f2, respectively, taken

instantaneously, to obtain TEC, and consequently the

GPS pseudorange observations freed from the first-

order ionospheric effects (2).

( ) ( )

( )

( ) ( )

cos , day

iono

n m n m

t t DC A





     



−

= + 







(1)

( ) ( )

40.31

1 cos

Earth

f f STEC b b

TEC STEC E





− =  −  + +









=  − 





(2)

In the Klobuchar model (1), symbols may be

identified as follows: DC = 5e-9 s, A(φ) denotes

amplitude of the day-time cosine component of the

GPS ionospheric delay, determined with the GPS-

broadcast (αi, i = 1, …, 4) parameters and the user

position’s geomagnetic latitude, P(φ) denotes period

of the day-time cosine component of the GPS

ionospheric delay, determined with the GPS-

broadcast (αi, i = 1,…, 4) parameters and the user

position’s geomagnetic latitude, t denotes the time

instant for which the GPS ionospheric delay is

determined in [s], and t0 = 14 hours local time in [s],

and tiono(t) denotes the resulting GPS ionospheric time

delay in [s] at the time instant t.

Position estimates were obtained using the open

source GNSS Software-Defined Radio receiver

RTKLIB (developed by Dr T Takasu, available form:

http://www.rtklib.com). Resulting GPS positioning

error vectors were derived as positioning error

residuals from the known reference station position.

Statistical properties of the northing, easting, and

vertical components of the GPS positioning error

167

vector were analyzed with a tailored software

developed by these authors in the R environment for

statistical computing to improve the understanding of

the positioning error generation process, and to select

suitable methods for the GPS positioning error

prediction model development [3].

We deployed the Cullen and Fray method to

estimate the theoretical statistical distribution of

closest fit to the experimental one, derived from the

GPS position error estimates. Developed by Pearson,

and described later by Cullen and Fray, the method

extend the suggestion for the best fit. We conduct the

actual analysis using the bespoke software developed

in the R environment for statistical computing, and its

external package fitdistrplus [9].

The analysis identified the most suitable

theoretical fit for experimental statistical distributions

to assist the model development. Finally, two

competitive GPS positioning error prediction models

were developed, based on the exponential smoothing

(reference) and the Generalized Regression Neural

Networks (GRNN) [6] (alternative) methods. Model

development and properties assessment were

performed using a tailored software developed in the

R environment for statistical computing to

recommend the utilization for mitigation of

contribution to GPS positioning performance

deterioration of the excessive GPS ionospheric delay

caused by adverse massive space weather effects in

polar regions.

Performance analysis of the models developed was

based on the analysis of residuals, obtained as a

difference between the model-based position forecast

in the particular scenario (i) … (iii) , and th etrue

position of the reference station.

3 RESEARCH RESULTS

The methodology described in the previous Section

was applied on the Ulukhaktok GPS raw pseudorange

data, taken during the Carrington-like space weather

storm of 2003. As a result, insight was gained into

statistical properties of the northing, easting, and

vertical components of the GPS positioning vectors, in

three scenarios of the ionospheric effects mitigation,

as depicted in Figures 1. (for all ionospheric

mitigation scenarios), and 2. (no-corrections

ionospheric mitigation scenario only).

The most suitable theoretical statistical distribution

to fit the experimental one was selected using the

Cullen & Fray diagram, as shown in Figure 3. for the

northing component of the GPS positioning vector in

the no-correction scenario.

A time series of horizontal GPS positioning errors

was constructed from time series of northing and

easting positioning errors. Using the horizontal GPS

positioning error time series, two candidate

prediction model development methods were selected

and tuned, i.e., the exponential smoothing and the

generalized regression neural networks (GRNN), to

develop candidate models of the horizontal GPS

positioning error. The original time series of 2872

single-point horizontal GPS positioning errors was

split into the first 2857 elements training set, and the

remaining 15 elements test set to assess the prediction

models performance.

Figure 1. Exploratory analysis results of the components of

the GPS positioning error vector in the ionospheric effects

mitigation scenarios of (i) no correction (no), (ii) broadcast

Klobuchar corrections (Kl), and (iii) dual-frequency

correction

Figure 2. Experimental statistical distribution density

functions for the northing, easting, and vertical components

of the GPS positioning error vector in the no-correction

ionospheric effects mitigation scenario

The most suitable theoretical statistical distribution

to fit the experimental one was selected using the

Cullen & Fray diagram, as shown in Figure 3. for the

northing component of the GPS positioning vector in

the no-correction scenario.

168

Table 1. The Exponential Smoothing (ES) and the Generalized Regression Neural Networks (GNNR) GPS positioning error

prediction models performance based on residual analysis.

__________________________________________________________________________________________________

Scenario (i): No corrections Scenario (ii): Klobuchar corrections Scenario (iii): Dual-frequency corrections

Mean Median Max Mean Median Max Mean Median Max

__________________________________________________________________________________________________

ES 0.2208 0.0527 2.5948 0.1208 0.0515 2.6363 -0.1390 0.3251 2.4469

GRNN 0.0527 -0.1154 2.4266 0.0292 -0.0401 2.5448 -0.1128 0.3212 2.4648

__________________________________________________________________________________________________

A time series of horizontal GPS positioning errors

was constructed from time series of northing and

easting positioning errors. Using the horizontal GPS

positioning error time series, two candidate

prediction model development methods were

selected and tuned, i.e., the exponential smoothing

and the generalized regression neural networks

(GRNN), to develop candidate models of the

horizontal GPS positioning error. The original time

series of 2872 single-point horizontal GPS positioning

errors was split into the first 2857 elements training

set, and the remaining 15 elements test set to assess

the prediction models performance. The reduction of

number of GPS pseudorange observations in

comparison with the nominal determination for

provision of 30 s-sampled data was not explained by

IGS.

The most suitable theoretical statistical

distribution to fit the experimental one was selected

using the Cullen & Fray diagram, as shown in Figure

3. for the northing component of the GPS positioning

vector in the no-correction scenario.

The model performance analysis was conducted

on the basis of residuals between the estimated

positions and the true position of the IGS reference

station. Two candidate models extend similarly in

their performance, as evident from the performance

assessment results outlined in Table 1.

Figure 3. Cullen & Fray diagram for the northing

component of the GPS positioning vector in the no-

correction scenario.

We suggest the preference should be given to the

GRNN model for its ability to accommodate a larger

variance in GPS positioning performance during the

extended period of observations, and for the

method’s ability to learn from new cases.

4 DISCUSSION

The commercial-grade GPS positioning performance

in the Northwest Passage was assessed in three

scenarios of the ionospheric effects mitigation. In

general, the GPS positioning performance observed

during a massive deterioration of space weather does

not meet the requirements for maritime navigation

and non-navigation applications. Notable biases and

variations were identified in three components of the

GPS positioning error vector in all three scenarios of

presumed GPS use in the Arctic region of the

Northwest Passage during a massive space weather

disturbance. Deterioration of the GPS positioning

error was understood to result from the inadequate

GPS receiver design, as well as from the unaccounted

space weather deterioration of the unknown

statistical properties, thus its effects were not being

accounted when using common correction models

and procedures. Those were exploited for the GPS

positioning error prediction model development

based on the observed northing, easting, and vertical

positioning errors, and on two competing model

development methods: the exponential smoothing,

and the Generalised Regression Neural Networks

(GRNN). Based on this study results, a set of

recommendations on the GNSS receiver design and

the standalone and assisted GNSS use in the newly

opened and emerging transport routes in polar

regions are proposed for improvement of safety,

accuracy, and sustainability of maritime navigation.

The recommendations are as follows:

GNSS receiver design that benefits from dual-

frequency GNSS ionospheric effects corrections is

recommended for use in the Northwest Passage.

Use of the Klobuchar correction model is not

recommended in the Northwest Passage during the

periods of intensive space weather disturbance,

and/or geomagnetic and ionospheric storm.

Use of the Generalised Regression Neural

Networks (GRNN) GPS positioning error prediction

model on either un-corrected, or dual frequency-

corrected GPS pseudoranges-based position estimates

is a recommended practice in the Northwest Passage

during a period of intensive space weather

disturbance and/or geomagnetic and ionospheric

storm.

Utilisation of recommended GRNN model may

lead to the transition from infrastructure-assisted

mitigation of the GNSS ionospheric effects towards

the adaptive GNSS positioning process, capable of the

GNSS positioning environment awareness, as

proposed in [10]. The adaptive GNSS positioning

process is particularly suitable for maritime vessels,

which may offer power stability and sufficiency, as

well as required computational capacity.

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