Giải pháp ước lượng thời gian tới để định vị tàu biển dựa trên tín hiệu AIS

́t quả mô phỏng 
chỉ ra các yếu tố ảnh hưởng đến hiệu năng hoạt 
động của phương pháp TOA với tín hiệu AIS. 
Từ khóa: AIS, nhận dạng tự động, phương pháp 
định vị, thời gian tới. 
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communication system and it is not used for 
positioning and navigation purpose. Moreover, the 
shipborne AIS station includes the AIS transmitter 
and the receiver whereas the shore-based station is 
only the receiver. However, the position of the shore-
based station is fixed and could be known in advance. 
If the AIS transmitters are installed at the shore-based 
stations, the vessel can estimate its position based on 
the time of receiving AIS signals. 
In this paper, the method of estimating the range 
between the shipborne station and the shore-based 
station based is researched. The range is estimated 
based on the data of received AIS signals by time of 
arrival (TOA) method. With at least the measured 
ranges of the vessel and 03 shore-based stations, the 
position of the vessel could be caculated via 
triangulation. Then, Cramer-Rao Lower Bound 
(CRLB) criterion for the assessment the measuring 
error of the estimator is formed for the proposed 
method. 
The rest of the paper as follows: Section 2 
analyses the characteristics of the AIS signal. The 
pseudo range measurement using AIS signals between 
the shipborne station and the shore-based station by 
TOA method is presented in Section 3 and Section 4 
assesses the estimator performance and gives out 
discussion. Finally, some conlcusions are shown in 
Section 5. 
2. The characteristics of AIS signals 
In AIS, the information of vessel’s voyage is 
transmitted in the Very High Frequency (VHF) band 
ranging from 156,025MHz to 162,025MHz with the 
bandwidth of 25kHz for each channel. Among them, 
two channels of 87B and 88B which located at 
161,975MHz and 162,025MHz have been designated. 
In order to share the medium for transmitting AIS 
signals in one channel between multi users, the Time 
Division Multiple Access (TDMA) is used. One 
channel in AIS has 2250 time slots, therefore, each 
user uses a time slot of 26,67ms for digital signal 
transmission. Each channel in AIS has a bandwidth of 
25kHz and the modulation is Gaussian Minimum 
Shift Keying (GMSK). In comparison to Mininum 
Shift Keying (MSK), the spectrum of GMSK is 
narrower but has lower side lobes at the same bit error 
performance. The spectrums of MSK and GMSK are 
illustrated in Figure. 1. 
GMSK is the special case of Continuous Phase 
Modulation (CPM) where the Gaussian filter is used. 
The modulated signal of CPM is expressed as: 
2
( ) sin 2 ( )s c k s
ks
E
s t f t m p t kT
T
 (1) 
where 
sE is symbol energy, cf is carrier 
frequency, 1km is binary data in polar NRZ 
form, 
sT is symbol interval and ( )p t is phase 
response of the modulator. The phase response is 
related to the frequency response as: 
( ) ( )
t
p t g x dx
 where ( )g t is the frequency 
response. For GMSK, the frequency response is 
expressed as: 
2 1 2 1
2 2ln(2) ln(2)
( )
2
s s
s
B L B L
Q t T Q t T
g t
T
 (2) 
where 𝐵 is the bandwidth parameter, for AIS, 
0,4SBT ; L is the correlation length, for GMSK, 
4 5L or L and ( )Q x is the Gaussian probability: 
2 /21( )
2
y
x
Q x e dy
 (3) 
There are 27 types of AIS messages as defined in 
ITU M.1371-5 [3]. Each message starts with a training 
sequence of 24 bits, then a 8 bit-start sequence, giving 
32 known bits at the beginning. Finally, it is ended 
with a 8 bit-stop sequence. Moreover, an AIS message 
lasts 256 bits for a single-slot, but there are possible 
for multi-slot message. 
Figure. 1 Spectrums of GMSK and MSK 
TẠP CHÍ KHOA HỌC CÔNG NGHỆ HÀNG HẢI Số - 62 (04/2020) 
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3. Positioning estimation method using AIS 
signals based on TOA 
As above-mentioned, AIS is a communication 
system for providing the identification information 
between the vessels together or between the shore-
based station and the vessel station. For vessel 
positioning purpose, many shore-based stations is 
needed and one a shipborne AIS receiver as shown in 
Figure. 2. In order to determine precisely the position 
of the vessel, the time synchronization is required for 
all shore-based stations. In positioning mode, the 
shore-based stations play as the reference nodes with 
known longitudes and latitudes by the vessel. The 
vessel ultilizes these coordinates and the time of 
receiving AIS message for its position estimation. 
The ship B
The shore-based 
station 2
The shore-based 
station 3
The ship A
The shore-based 
station 1
Figure 2. The structure of AIS for the vessel positioning 
The Message 4 of AIS signals with Universal 
Time Coordinated (UTC) and the postions of shore-
based stations [3] reaching shipborne station from the 
shore-based station is used for the estimation progress. 
Based on received message 4, using TOA method, the 
pseudorange 𝐿𝑚 between the vessel with the 
longitude and the latitude (𝜆, 𝜑) and the 
thm 
shore-based station with the longitude and the latitude 
(𝜆𝑚, 𝜑𝑚) could be estimated as: 
𝐿𝑚̅̅ ̅̅ = 𝐿�̂� +
𝜕𝐿�̂�
𝜕𝜔
Δ𝜔 +
𝜕𝐿�̂�
𝜕φ
Δφ (4) 
Where: 𝐿𝑚̅̅ ̅̅ is the measured range, 𝐿�̂� is the 
estimated range, ( Δ𝜔, Δφ ) is the variations of 
estimated parameters. With the set of 𝑛 shore-based 
stations, the positioning matrix is expressed as: 
1 1
1
ˆ ˆ
ˆ ˆ
n n n
L L
L
L L L
  


 
  
    
   
 (5) 

 
 
R 
Figure. 3 The relationship between (𝝀, 𝝋) and 
(𝜟𝝎, 𝜟𝝋) 
where 𝛿𝐿𝑚 = 𝐿𝑚̅̅ ̅̅ − 𝐿�̂� . The relation between 
(𝜆, 𝜑) and (Δ𝜔, Δφ) is shown in Figure. 3 and could 
be expressed as: 
 1
.
cos
  
 (6) 
Give: 
 
1
1
1
ˆˆ
ˆ ˆ 
ˆˆ
T
T
n
n
T
n
LL
A L L L
LL
B X
 
 
 
     
 
  
 (7) 
The matrix equation (5) could be written in the 
simplized form: 
 L A B X HX (8) 
Matrix H is called the positioning matrix. 
Implementing the Least Square Root algorithm to 
determine the vector X of the estimated position of the 
vessel as: 
1(H H)T TX H L (9) 
Then, the longitude and the latitude of the vessel 
(𝜆, 𝜑) is calculated as (9). 
4. Simulation Results and Discussion 
4.1. Simulation results 
Due to the using TDMA technique in AIS, the 
duration of time slot is 26,67ms and this duration is 
corresponding to the distance of approximated 8000 
km. This distance is extremely futher than the 
maximum range of AIS signals (about 40 km). It 
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TẠP CHÍ KHOA HỌC CÔNG NGHỆ HÀNG HẢI Số - 62 (04/2020) 
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means that the transmission time of propagating AIS 
signals from the shore-based station to the vessel is 
completely within one time slot. Therefore, by using 
GMSK demodulation based on carrier phase tracking 
loop, the estimation of both the time of bit transition 
and carrier phase could be ultilized for the range 
calulation between the vessel and the shore-based 
station. However, almost AIS shore-based stations are 
not located and arranged for positioning purpose. 
Moreover, the AIS signals from the shore-based 
stations reaching to the vessel are the superimposetion 
of many propagation paths beside LOS component 
such as: reflection paths, diffraction paths (commonly 
called NLOS or multipath components). 
Table. 1 Simulation scenario 
Parameter Value 
Number of the shore-based 
stations 
3 to 5 stations 
Number of the vessel 
station 
1 stations 
Carrier frequency 𝑓𝑐 162MHz 
Distances between the 
shore-based stations and 
the vessel station 
From 10km to 
20km 
Channel model AWGN 
Number of path 1 (only LOS path) 
Figure. 4 Vessel’s position estimation and estimation error via TOA method using AIS signals 
with 3 (upper), 4 (middle) and 5 (lower) shore-based stations 
Table. 1 Simulation scenario 
TẠP CHÍ KHOA HỌC CÔNG NGHỆ HÀNG HẢI Số - 62 (04/2020) 
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In order to verify the performance of TOA method 
in vessel positioning with AIS signals, the simulation 
scenario is implemented as shown in Table. 1. There 
are some shore-based stations and 01 shipborne. The 
position errors are illustrated in Fig. 4. As shown in 
the figure, the performance of TOA method is 
degraded due to the arrangement of AIS shore-based 
stations. Since almost AIS shore-based are not located 
and arranged for positioning. They are located along 
the coast-side while the AIS shipborne station is on 
the sea. The arrangement of AIS shore-based station 
can not be surrounding the AIS shipborne station. 
Therefore, the estimation errors are very high in 
comparison to the errors of GPS. Moreover, when the 
number of “visible” AIS shore-based stations 
increases, the performance of the TOA method is 
improved. If re-arranging of AIS shore-based stations 
for positioning with allocating them around the AIS 
shipborne station, the estimation error of TOA method 
is significantly decreased. 
The main contributions of this paper are two-fold. 
First, we recommend a hierarchical framework for 
employee competency with customization for 
logistics sector. Such framework could be used by 
different stakeholders for their own purposes. The 
logistics employers could use the recommended 
criteria to evaluate the strength and weakness of their 
staffs, thereby forming solutions to improve their 
human resource competency. The employee could 
also form a plan to improve their working capabilities 
based on given criteria. From the macro level, the 
evaluation of the human resource competence in the 
logistics sector of an area could be assessed, as proved 
in our empirical research. 
4.2. Performance Assessment and discussion 
The positioning performance of the estimator can 
be measured and assessed by Cramer-Rao Lower 
Bound (CRLB). It is the theoretical lower bound for 
the variation of the desired parameters of the estimator, 
such as positioning parameters in this paper. 
Assuming the channel between the shore-based 
station and the vessel is Additive White Gaussian 
Noise (AWGN) channel with the spectral density 
𝑁0
2
. 
The received AIS signals at the vessel (in complex 
baseband form) is: 
 sin( ) 2 ( ) ( )r t A ft s t n t  (10) 
Where 𝐴 is the signal amplitude; 𝑠(𝑡) is the 
transmitted GMSK AIS signal; 𝑛(𝑡) is the AWGN; 
∆𝑓 is frequency offset; ∆𝜑 is an unknown phase 
(due to the phase mismatch between the receiver’s 
local oscillator and the phase of received signal); 𝜏 is 
an unknown time delay (it is the interested term for 
ranging). With the random of data bit, the CRLB on 
the performance of the receiver estimator for the time 
delay is [4]: 
 0
0
2
,
0
( )
, , ,
T
f
N
CRLB
s t f
dt 

 

  
 
 
 (11) 
where Ε(. ) is the statistical expectation operator; 
0T is the observation time. 
For the GMSK modulation, the CRLB could be 
written as: 
 2 0 0
0
( )
2
(0) 2( 5) ( )
s
s
g g s
T
CRLB
E
L R L R T
N

(12) 
where (.)gR is the autocorrelation function of the 
frequency pulse; 𝛼 the scaling factor related to 𝐵𝑇𝑠 
[3]; with AIS: 𝐵𝑇𝑠 = 0,4, 𝛼 = 0,68. For GMSK, we 
have [3]: 
(0) 0,1597 /
( ) 0,0443 /
g s
g s s
R T
R T T
 (13) 
Assuming 
0 5L and substituting in for (.)gR : 
2
0
0
( )
2
2,48
s
s
T
CRLB
E
L
N

 (14) 
0L is the number of bits, 0 0 sT L T . In AIS, with 
the bit rate of 9600bps, we have 1/ 9600( )sT s . 
In Figure. 5, the results of standard deviation of 
time delay according to the values of symbol energy 
per noise ratio (𝐸𝑠/𝑁0) for various observation times 
are shown. It can be seen that the higher the 𝐸𝑠/𝑁0 
is, the smaller the measuring error is. On the other 
hand, the longer the observation time is, the smaller 
the measuring error is. Assuming the typical noise 
power of AWGN channel is set as -114dBm [5]. With 
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the received signal level of AIS receiver is -107dBm, 
then, the ratio (𝐸𝑠/𝑁0) is 7dB, it could result in the 
time delay error is 750ns, equivalently 225m in 
pseudo-range error for 𝐿0 = 1280𝑏𝑖𝑡𝑠 (5 time slots) 
and the time delay error is 1570ns, equivalently 470m 
in pseudo-range error for 𝐿0 = 256𝑏𝑖𝑡𝑠 (single time 
slot). A single time slot is used with message 4 and 5 
time slots are used with message 8. However, the 
typical received signal level at AIS receiver is -
75dBm, therefore, the ratio (𝐸𝑠/𝑁0) is 39dB. Finally, 
the time delay error is only 18ns or pseudo-range error 
is 5,65m and 40ns or pseudorange error is 12m for 
𝐿0 = 1280𝑏𝑖𝑡𝑠 and 𝐿0 = 256𝑏𝑖𝑡𝑠, respectively. 
Figure. 5 Time Delay Error Standard Deviation versus 
Signal Power 
5. Conclusions 
For resilent PTN in maritime navigation, AIS 
can be used as an alternative system of GNSS in the 
vessel’s positioning. The position of the vessel is 
estimated based on receiving AIS signals from at least 
03 shore-based stations via TOA method. However, 
the variation of measuring parameters is suffered from 
many error sources. The measuring error of TOA 
method is assessed by CRLB. From the results, the 
measuring error of TOA method is acceptable in 
comparison to the vessel dimensions as well as the the 
accuracy of GNSS. Thefefore, the vessel position 
estimation based on AIS signals is feasibility for e-
navigation in the future. Finally, more error 
supression methods needed being researched and 
proposed for improving the accuracy of positioning 
based on AIS signal. This issue could be focus in the 
futher research. 
REFERENCE 
[1] Williams, P., et al. "Resilient PNT for e-
navigation." Proceedings of the ION 2013 Pacific 
PNT Meeting. 2013. 
[2] Grant, Alan, et al. "Understanding GNSS 
availability and how it impacts maritime safety." 
Proceedings of the Institute of Navigation 
International Technical Meeting. 2011. 
[3] Recommendation ITU-R M.1371-5. Technical 
characteristics for an automatic identification system 
using time division multiple access in the VHF 
maritime mobile band International 
Telecommunications Union. Retrieved 2017-08-07. 
[4] Hosseini E, Perrins E. “The Cramer-Rao bound for 
training sequence design for burst-mode CPM”. 
IEEE Transactions on Communications. 2013 Apr 
30; 61(6):2396-407. 
[5] Seybold, John S. “Introduction to RF 
propagation”. John Wiley & Sons, 2005. 
Received: 25 December 2019 
Revised: 10 January 2020 
Accepted: 15 January 2020