Integrity Performance of Egyptian eLoran System for Maritime Application
Farag M. Bahr Abd El-Aziz
Electrical Eng. Dept.
Military Technical College
Cairo, Egypt
Ezz El-Deen F. Abd-El kawy
Electrical Eng. Dept.
Military Technical College
Cairo, Egypt
Farag_bahr@mtc.edu.eg
ezfarouk@yahoo.com
Abstract— eLoran is considered as the most promising
backup for Global Navigation Satellite System in maritime
applications. A proposal study to establish eLoran
navigation system for Egyptian maritime harbors is
presented to act as an international and national backup to
GPS for marine navigation, and other applications using
MATLAB.
The required levels of Integrity as a
requirement of the International Maritime Organization
had been verified over all the Egyptian harbors.
Key words: eLoran, Integrity, and Horizontal protection level
I. INTRODUCTION
The ability of Global Positioning System (GPS) to provide
high positioning accuracy with high degree of reliability is
well known, so it is widely used as primary navigation system.
The recent concerns about vulnerability of GPS and ability of
jamming on GPS signal have overexcited a renewed concern
in the Loran PNT system. Enhanced Loran “eLoran” is the
latest version of Loran PNT for longstanding and proven
series of low frequency navigation systems which are used to
provide back-up capabilities to GPS in maritime navigation
[1]. eLoran is a terrestrial low-frequency system arranged as
chains each consisting of a master station with two or more
secondary stations. eLoran meets international performance
requirements that permit it to use as alternative system to GPS
in many applications [2]. The primary requirements of concern
for Non Precision Approach (NPA) or Harbor Entrance
Approach (HEA) are the integrity, accuracy, availability and
continuity as depicted in Table (1). The user‟s receiver
estimates the maximum likely error on the position-fix by
calculating the Horizontal Protection Level (HPL), which is
the first common method of providing positioning Integrity. If
HPL is below a certain Horizontal Alert Limit (HAL) then the
fix is verified as „good‟. If the HPL passing the HAL, then the
fix is consider as „bad‟.
Table 1: Primary requirements for eLoran according to NPA and HEA
Performance Requirement
accuracy (m)
Monitor Limit/ Alert Limit (m)
Integrity / hour
Time-to-Alert (sec)
Availability
Continuity
NPA
307
556
107
10
Up to 99.99%
99.9 to 99.99
978-1-5386-9559-3/18/$31.00 ©2018 IEEE

HEA
20
50
3*105
10
99.7%
99.85%
over 3 h
Ahmed Khamis
Guidance & Control Dept.
Military Technical College
Cairo, Egypt
khamahme@isu.edu
Dawid Zydek
Elec & Computer Eng. Dept.
University of Nevada
Las Vegas, USA
dawid.zydek@unlv.edu
II. LEAST-SQUARES POSITIONING
As eLoran is a ranging system, the pseudorange ρ from the
receiver to every eLoran transmitter can be represented as [3]:
(1)
ρ = D + PF + SF + ASF + δ + ε + b
Where:
D
is the true range
PF is Primary Factor
SF is the Secondary Factor
b is the receiver clock bias
ASF is Additional Secondary Factor
δ
is variation in PF, SF and ASF
ε
is remaining measurement errors
In this paper, we have supposed that eLoran positionfixing is obtained by using Least-Squares solution of
pseudorange observations. Since geodetic range measurements
of the ground wave are not linearly related to position, we
linearize the equation of pseudorange, at a nominal position
(xo, yo) to give the linear matrix equation given by [3]:
 G.  p
(2)
Where G is the direction cosine matrix or the geometry
matrix and the correction vector Δp is then used to update the
position solution estimate. Δρ is the vector of corresponding
difference in the measured pseudorange relative to its nominal
value ρ (xo, yo).
The equation (2) can be expanded to:
sin(1 )

sin( 2 )
  


sin( )
n

cos(1 )
cos( 2 )
cos( n )
1

1



1 
 x 
 
 y 
  b 
(3)
G
where  n are bearings of the stations from the receiver.
The differences Δx, Δy and Δb represent corrections
(expressed in meters) to be applied to the current position and
receiver clock bias estimates. If the system contains more than
three stations, we can get the solution by using equation given
by:
 p  (G T G )1G T  
(4)
If the measurement errors are uncorrelated but have
different variance, we use Weighted Least Squares (WLS) in
determination user position (which is usually the case in
practice), the optimum solution is obtained by
1
1
1
p  (G (var( )) G ) G (var( )) 
T
T
III. INTEGRITY CALCULATION
Integrity means that the system able to alert a user through
data channel when Loran signals or solution should not be
used. For Loran, under normal conditions, it can be achieved
by calculating a horizontal protection level (HPL) that limited
by the horizontal position error (HPE) [4]. For position-fixing,
the provision of an HPL is then produced by integrating a
position bound up to the five-nines confidence level. In this
work, we have used a Distance Root-Mean-Square (DRMS)based HPL equation. The position error variance matrix can be
given by


  (G T var(  ) G ) 1

C


 DRMS   x2   y2   
(5)
Where var (∆ρ) is Pseudorange measurement error and it is
composed of variance of Time of Arrival (ToA) and variance
of ASF map and differential Loran correction. The value of
each term will be calculated or estimated, and provided abeforehand to the receiver so that all error sources need to be
distinguished and determined.
 2 
xy  xb
 x

var ( p )   xy  y2  yb

 
 yb  b2
 xb
where H part is dimensionless and depends only on the
transmitter geometry. Hence, we can deduce the HDOP from
the following equation [3]:
(6)
H 1,1  H 2,2
(11)
HDOP
eLoran transmitters are organized into chains where each
chain consist of a single master station and two or more
secondary stations. The time interval between transmitting
successive pulse groups of any one station in the group to the
following transmitted pulse groups of the same station denoted
as Group Repetition Interval (GRI). The value of GRI will be
discussed in the following section. The locations of these new
transmitters in Table (2) are selected depending on the
coverage area to give better HDOP over all harbors as shown
in Figure (1).
Table 2: Egypt Loran stations
GRI
6731
Station
Menia
(Master)
Matrouh
(Secondary 1)
Port-Said
(Secondary 2)
Ash-shaykh
(Secondary 3)
Marsa-Alam
(Secondary 4)
Position
27.5 N
30 E
31.5 N
26.2 E
30.92511 N
32.671567 E
28.15444 N
34.76126 E
24.88699 N
34.19199 E
PWR(KW)
1000
1000
1000
1000
1000
Where  b2 is the variance of the clock bias in eLoran receiver.
The DRMS accuracy can then be expressed simply as:
 DRMS  C (1,1)  C (2, 2)
(7)
HPL EQUATION:
HPL  THEA C (1,1)  C (2, 2)
Egyptian
Harbors
(8)
HDOP
T = 3.3931 in order to multiply up to 99.999% level, 1* 105
Integrity Risk probability [4].
IV. FACTORS AFFECTING DRMS ACCURACY OF POSITION
A. Geometry of the transmitter stations in use
The locations of transmitter stations are generally selected
to give better geometric configuration [3]. The effect of
transmitter geometry on the accuracy is usually represented by
Horizontal Dilution of Precision (HDOP) factor. Assuming the
pseudorange measurement errors are mutually uncorrelated
and have equal variance  2 .
2
var [ ]   
I
(9)
Then, the position error variance matrix can be reduced to
 2 
 xb
xy
 x
2

var [ p ]   xy  y  yb


  xb  yb  b2

eLoran
Stations


   2 GT G



H




1
(10)
Fig. 1: HDOP distribution over Egypt using Loran transmitter
stations, new transmitter are denoted by red points and harbors are
denoted by yellow points
var[ ]   2 
c
337.52
 1  c2
N .SNR N
(12)
c1 represent transmitter related noise, which is assumed to be
pseudorange measurements c 2  12 m 2 , the number of pulses
which are used in signal integration denoted as N. Its value
depend on integration time which assumed in this work 5
secounds and time of Group Repetition Interval (GRI) as
depicted in the following equation
N 
8T i
T GRI
(13)
Ground wave field strength is calculated using propagation
curves for different ground conductivities at 100 kHz as
shown in Figure (2). Ground conductivity varies all over the
range from the loran station to the receiver. In this study,
ground wave field strengths will be modeled using the
Millington‟s method as discussed in the ITU-R
Recommendation [5].The signal strength of Loran station is
shown in Figure (3) using data obtained by grwave.exe which
depends on Conductivity, surface permittivity, temperature,
antenna heights above the terrain, frequency and polarization
of the wave [3, 6].
Fig.
Fig. 3: Predicted ground wave field strength for the Ash-Shaykh station
represent other sources of variation in the
2: Ground wave field strength as function of distance for a 1kw
transmission and different grounds types [8].
The prevalent noise source in the band of eLoran is
atmospheric noise. Atmospheric noise is determined at
different percentiles and produced depending on the model
presented in ITU Recommendation P372-9 [7]. The noise
equivalent RMS field strength corresponding to the external
noise power available at the output of an electrically short
monopole antenna during season-time block b (expressed in
dBμV /m) is given by
E  F  20 log f MHZ  10 log B  95.5 dB V / m
(14)
Where F is the external noise figure, B is bandwidth of
eLoran receiver (20 KHz) and f is the frequency of eLoran
(100KHz). Figure (4) shows the distribution of the predicted
average daytime noise over Egypt [3, 7].
Noise Field Strength (dBμV/m)
c1  36 m 2 , c2
Field Strength (dBμV/m)
B. Accuracy of signal Time-of-Arrival (ToA) measurements
Signal to noise ratio (SNR) of the received eLoran signal
strongly determines the accuracy of ToA measurement. As
eLoran signal is in the ground wave band, many error factors
are compromising the noise and interference effects. These
factors include the atmospheric noise, the cross-rate
interference (CRI), sky wave interference, continuous-wave
interference (CWI), and transmitter timing jitter and variations
in the impedance of transmitting antenna [3]. Receiver
processing algorithms can mitigate sky wave interference, CRI
and CWI but the remaining errors from these sources may still
be affecting in certain conditions. The determination of SNR
needs knowledge of the signal strength of the eLoran signal
and the level of external noise at the same position. The main
driver Pseudorange of variance is the signal-to-noise ratio
(SNR) of the received signal because low SNR lead to high
Pseudorange variance and given by:
Fig. 4: Average daytime atmospheric noise over Egypt
SNR is the ratio of the eLoran signal sampling point power to
the power of the noise present in the signal. Fig. 5 shows the
SNR of eLoran station. Under assumption of white noise, we
can get accurate estimation of pseudorange measurement
variance if the SNR range from –10 dB to +40 dB.
GLA Specification
GRI Limits
Interference Database
Interfering GRIs
SNR
Transmitter Configuration
CWI Analysis
CRI Analysis
Loran Field
Strength,
Coverage
Receiver
Model
Other Consideration
List of Candidate GRIs
GRI = 6731
Fig. 6: The overall procedure of GRI selection
Fig. 5: Predicted SNR for the Ash-Shaykh eLoran station
„
GRI value affects on pseudorange measurement error as seen
in equations 12 and 13. To determine the suitable value of
GRI for a chain the following steps are used [8].
1- GRIs value in range of 4000 to 9999 (tens of μs).
2- Determine minimum GRI ( TGRI ,min  58643s )
The minimum time between master and secondary is
. m,s (min) =10900 μs. Minimum time between secondary m
and m+1 is  s,s (min) = 9900 μs and the minimum
separation between the last secondary transmission and
master transmission from the next GRI is  s,m(min) =
9900 μs [8].The minimum GRI can be determined by the
following equation:
TGRI ,min 
N st
  ED ,m   m 1  m ,min  
m 1
N st
rm
(13)
C. Accuracy of the ToA to range conversion
The ground waves are delayed when it is compared to the
predictable propagation time over the same distance in free
space. This delay is the accumulation of three parts or factors
and need to be determined when using measured pseudoranges to fix a position [9].
i. Primary Factor(PF): Due to the refractive index of the
atmosphere  n PF  1.000338 ), the PF speed of the Loran
signal through the atmosphere is given by:
c PF = 299,691,162 m/s
Secondary Factor (SF): Depending on characteristic of Loran
signal, a considerable proportion of the wave will penetrate
earth surface. This part of signal will propagate more delayed
than in atmosphere because of dielectric properties of the
surface. Sea water has the best conducting surface (which has
approximate value 5 S/m). Modeling the SF using the
equations described by P. Brunavs [8], as shown in Figure (7).
prop
where rm is distance between loran stations and  prop is
speed of propagated signal.
3- Determine which Loran stations will interfere with the
proposed chain.
4- CWI result from non-Loran transmitters operating near
to loran band and these interfere to larger or smaller
depending on GRI.
5- Use the minimum GRI and the list of stations that may
interfere to obtain a list of GRIs that are relatively prime
to all GRIs that may interfere with the proposed chain.
6- Eliminate all GRIs that would result in exceeding the
maximum transmitter pulse rate 700 p/s.
7- The need to space into GRI for presence of signal from
Loran simulators.
Fig. 7: Secondary Factor Delay from Brunavs‟ equations
GRI selection can be executed by the following procedures
which can be summarized in Figure (6) [3, 7].
(14)
Additional Secondary Factor (ASF): If the propagated signal
passes over land with surface conductivity lower than sea
water, it delays even further and this additional delay is
denoted as ASF. In Figure (8), the phase delay for dry ground
and seawater is depicted with respect to distance from
transmitter. Neglecting ASF values into determination can
lead to error in range up to 2 km. Experimental work has
indicated that it is necessary to calculate ASF by modeling
with accepted accuracy for navigation applications [10, 11].
Over time, there are some variations in ASF from the
fixed ASF values stored in the receiver due to Seasonal. It is
known as temporal variations. Its effect appears on loran
2
2
position accuracy in terms temp
which represent bias
,  temp
and variance in temporal variation respectively. So we can
represent Pseudorange measurement error in meters [3].
V a r [ ]   2 
c
337.52
2
2
 1   A2 SF   temp
  temp
N . SNR
N
(15)
ToA to Range conversion
ToA measurement
When all the data arrays are calculated, each grid point
will be tested using algorithms within the software to specify
whether the eLoran signals fulfill certain acceptance criteria.
With data at each point on the map, the integrity using HPL is
calculated and plotted as shown in Figure (10). It is shown that
error is below a prescribed Horizontal Alert Limit (HAL)
(20m) then the fix is validated as „good‟ over all Egyptian
harbor.
Fig. 8: Phase delay of dry land and sea water
HPL
The current method depends on the proposed data format is a
grid with specified values of ASF at regular spacing
everywhere the harbor and approach channel area for each
eLoran transmitter. Practical test in the USA [10, 12] has
shown that ASF maps with grid size of 500 m are generally
agreeable for marine applications. The current procedure for
calculating ASF data includes an overall measurement
campaign of an area, with the surveyed data then uploaded to
the eLoran receiver. This survey will have been executed on a
certain day to specify the ASF values once and for all as
shown in Figure (9). Since ASF depends on the ground
conductivity along the propagation path, any changes in
conductivity will change the ASF and it is known as temporal
variation which can be provided to eLoran receiver by using
differential eLoran stations.
Fig. 10: Predicted Integrity of proposed eLoran chain
ASF delay (μs)
V. CONCLUSION AND FUTURE WORK
Fig.9: Port Said Basic ASF grid of the data at 500m spacing measured at Suez
port
In this paper we presented a simulation-based proposal to
establish the eLoran navigation system for the Egyptian
marine sector according to its positioning accuracy. We have
generated integrity plot for Egypt by installation of eLoran
stations at candidate locations. We use HPL equation to
determine integrity over Egyptian harbors. This technique is
critically dependent on transmitter geometry and having an
over-determined position-solution. The simulation results for
this proposal of Egyptian eLoran achieved the IMO's integrity
requirement over most of Egyptian‟s coastal borders and
harbors. The future work will be intended into studying the
other factors affecting on the eLoran performance as a
positioning system for Egyptian harbors including continuity
and availability.
REFERENCES
[1] Grant A., Williams P., Ward N., and Basker S., GPS Jamming and the
Impact on Maritime Navigation, The Journal of Navigation, 2009, Vol.
62, pp. 173–187.
[2] International Loran Association, Enhanced Loran (eLoran) Definition
Document, 2007. v. 1.0.
[3] Jan Šafáˇr: Analysis, Modelling and Mitigation of Cross-Rate Interference
in Enhanced Loran, Ph.D thesis, Czech Technical University in Prague,
August 2014.
[4] Mr. Chris Hargreaves, Williams, P. “A Method of Providing Integrity for
eLoran” International Technical Meeting of The Institute of Navigation,
ITM 2014.
[5] Hargreaves, C, Williams, P. “Use of an HPL Equation to assess the
Integrity performance of the eLoran System” ENC 2012
[6] International Telecommunication Union, ITU-R Rec. 368-9, GroundWave Propagation Curves for Frequencies between 10 kHz and 30 MHz,
2007.
[7] International Telecommunication Union, ITU-R P.372-9, Radio Noise,
2007.
[8] R. W. Nutting, Loran-C Rate Selection Process. United States Coast
Guard, 1988.
[9] Brunavs P., Phase lags of 100 kHz radio frequency ground wave and
approximate formulas for computation, 1997.
[10] Last, J.D., Williams, P., Peterson, B. and Dykstra, K., „Propagation of
Loran-C Signals in Irregular Terrain – Modelling and Measurements Part
1: Modelling‟, 29th Annual Convention and Technical Symposium,
International Loran Association, Washington DC, Washington USA, 1315 November 2000.
[11] A. Khamis, et al. "Control system design based on modern embedded
systems." International Conference on Computer Aided Systems Theory.
Springer, Berlin, Heidelberg, 2013, doi: 10.1007/978-3-642-53862-9_62
[12] Millington, G, “Ground-wave Propagation over an Inhomogeneous
Smooth Earth”, Proceedings of the IEE, Series 96, Number 3, 1949
[13] G. Borowik, T. Łuba, and D. Zydek. "Features reduction using logic
minimization techniques." International Journal of Electronics and
Telecommunications 58.1, 2012, pp. 71-76, doi: 10.2478/v10177-0120010-x.