ship trajectory reconstruction from ais sensory data via...

Research ArticleShip Trajectory Reconstruction from AIS Sensory Data via DataQuality Control and Prediction

Xinqiang Chen 12 Jun Ling1 Yongsheng Yang1 Hailin Zheng3 Pengwen Xiong 4

Octavian Postolache5 and Yong Xiong6

1Institute of Logistics Science and Engineering Shanghai Maritime University Shanghai 201306 China2Department of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences Fudan UniversityShanghai 200438 China3Merchant Marine College Shanghai Maritime University Shanghai 201306 China4School of Information Engineering Nanchang University Nanchang 330031 China5ISCTE-Instituto Universitario de Lisboa and Instituto de Telecomunicacoes Lisbon 1649-026 Portugal6Hunan Lianzhi Technology Co Ltd Changsha 410217 China

Correspondence should be addressed to Pengwen Xiong stevenxpwncueducn

Received 28 May 2020 Revised 9 July 2020 Accepted 20 July 2020 Published 17 August 2020

Academic Editor Javier Martinez Torres

Copyright copy 2020XinqiangChen et alis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Accurate ship trajectory plays an important role for maritime traffic control and management and ship trajectory prediction withAutomatic Identification System (AIS) data has attracted considerable research attentions in maritime traffic communitye rawAIS data may be contaminated by noises which limits its usage in maritime traffic management applications in real world Toaddress the issue we proposed an ensemble ship trajectory reconstruction framework combining data quality control procedureand prediction module More specifically the proposed framework implemented the data quality control procedure in three stepstrajectory separation data denoising and normalization In greater detail the data quality control procedure firstly identifiedoutliers from the raw ship AIS data sample which were further cleansed with the moving average model en the denoised datawere normalized into evenly distributed data series (in terms of time interval) After that the proposed framework predicted shiptrajectory with the artificial neural network We verified the proposed model performance with two ship trajectories downloadedfrom public accessible AIS data base

1 Introduction

Maritime transportation occupies over 90 of global tradein terms of goods delivering volume Enhancing traffic safetyattracts huge attention considering that maritime trafficincident can cause significant loss of human life navigationenvironment damage etc [1 2] To avoid potential maritimeaccidents various maritime surveillance data are collectedfor the purpose of navigation environment awareness whichprovides accurate early-warning information to maritimetraffic participants [3] e AIS data involves meaningfulspatial-temporal maritime traffic information which sup-ports various navigation operation decisions More specif-ically the AIS data is a popular data source for analyzing shiptrajectory variation tendency Note that AIS is a type of self-

reporting system originally designed for preventing po-tential accident which is a mandatory facility for cargo ships(ie ship with gross tonnage larger than 300) [4ndash8]Moreover fishing boats with length longer than 15m arerequired to install AIS equipment in the European UnionMember States [9ndash12]

e AIS equipment transmits the static and kinematicship information (eg ship type call sign speed latitudelongitude heading Maritime Mobile Service Identity(MMSI) etc) at a variable refresh rate More specifically theAIS system broadcasts the ship information ranging fromseveral minutes to two seconds based on the ship travellingspeeds (ie the AIS system updates its data at lower fre-quency under larger maneuvering speed) In that mannership (equipped with AIS facility) position can be obtained in

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 7191296 9 pageshttpsdoiorg10115520207191296

real time in coastal area Moreover the large-scale AISdatasets have been stored at regional or national datacenters which can be accessible by users in request (notethat users may need to pay for accessing the AIS data)Previous studies suggested that AIS data quality imposessignificant influence on the maritime traffic safety analysisand thus improving AIS data quality has become an activetopic in the maritime community [13 14]

AIS data anomaly removal studies involve unsupervisedclustering method and neural network based and statisticalmodels [15 16] Liu et al proposed an adaptive Douglas-Peucker framework to suppress AIS data outliers in themanner of data compression [17] Deng introduced a Markovbased model to explore ship movement patterns which werefurther used to identify the abnormal AIS data samples [18]Zhang et al proposed a hierarchical density-based spatialclustering of applications with noise based model to clusterand denoise the raw AIS trajectories [19] Rong et al cleansedthe raw AIS data in the lateral and longitudinal dimensionswith a novel probability trajectory prediction model [20] eneural network relevant models have shown many successesin tackling the AIS trajectory denoising and prediction tasks[21] Hoque and Sharma applied long short-term memoryneural network to forecast ship trajectories which wereemployed to suppress the AIS data anomaly [22] Kim andLee proposed a novel deep neural network model to removeAIS outliers and thus predict both medium- and long-termship trajectory variation tendencies [23] Similar researchescan be found in [8 24ndash28]

We aim to propose a novel AIS denoising and predictionframework with the support of data quality control proce-dure Our main contributions can be summarized as follows(1) we cleansed the raw AIS data with the steps of trajectoryseparation outlier removal and data normalization (2) wepredicted ship trajectory via the denoised AIS data with theartificial neural network (ANN) (3) we testified the pro-posed framework performance on two ship trajectories estudy can help maritime traffic participants forecast accurateship trajectories and thus take early-warning measurementsto enhance maritime traffic efficiency and safety e re-mainder of the paper is organized as follows We introducethe data source used in our study in Section 2 After that themethodology details about the AIS data denoising are il-lustrated in Section 3 and then the ANN model used forpredicting ship trajectories is presented e experimentalresults are shown in Section 4 Section 5 briefly concludes thestudy and illustrates future work

2 Data

e US Marine Energy Administration and NationalOceanic and Atmospheric Administration provides large-scale AIS data which benefits many AIS relevant studies dueto its public accessibility (httpsmarinecadastregovais)[29 30]e original AIS dataset includes both kinematic andstatic information for the ship which contains MMSI Co-ordinated Universal Time (UTC) latitude longitude speedover ground (SOG) heading course over ground (COG)timestamp call sign and so forth We collect the AIS data

from the Gulf of Mexico with latitude ranging from 18degN to31degN and the longitude falls in the interval [75degW 100degW]e minimum time interval for sampling the AIS data is 1 sand the maximum value is 500 s We collect 12813 AIS datasamples on April 11 2017 from the above-mentioned da-tabase (see Figure 1) Following the international standard forrepresentation of latitude and longitude the south latitude(west longitude) is denoted as a negative number while northlatitude (east longitude) is presented with a positive number

3 Methodology

e raw AIS data may contain different types of outliers dueto instable signal transmission rate data transmissioncongestion etc It is important to suppress such dataanomalies for the purpose of exploiting reliable maritimetraffic kinematic information from the AIS dataset To ad-dress the issue we firstly implement the data quality controlprocedure to remove the trajectory outliers and then predictthe trajectory with artificial neural network e schematicoverview for the proposed framework is shown in Figure 2

31 Data Quality Control for Suppressing AIS OutliersShip trajectory data (ie AIS data) is stored in the databasevia data deliveringreceiving timestamp and thus we need toaggregate trajectory data (from a single ship) before con-ducting ship trajectory analysis relevant researches For thepurpose of thoroughly removing anomalous AIS sampleswe implement the data quality control with steps of shiptrajectory extraction data cleansing and data formatting(ie AIS time interval normalization)

311 Ship Trajectory Extraction e ship trajectory ex-traction can be divided into separating trajectories fromdifferent ships and removing discontinuous ship trajectoriesIt is noted that the ship can be uniquely identified by theMMSI which is thus applied to separate AIS data samplesfrom different shipsen the raw AIS samples are sorted bytimestamp in an ascending manner It is found that an AISsample may be recorded in database for several times Toaddress the issue the repetition samples are removed toavoid being further processed when the constraints inequation (1) are satisfied e outputs from the above stepare the raw ship trajectories We find that several time in-tervals between neighboring samples are very large (eg fourhours) indicating that many AIS data are lost Such AIS datadiscontinuity imposes big challenge for analyzing ship ki-nematic moving state in detail To overcome the disad-vantage we divide the raw ship trajectory into differentsegments when the time interval between neighboringsamples exceeds a threshold (see equation (2))

Ta Tb

Lata Latb

Lona Lonb

⎧⎪⎪⎨

⎪⎪⎩(1)

Ti gtTth (2)

2 Mathematical Problems in Engineering

where Ta and Tb are the timestamps from two AIS recordse ship positions at timestamp Ta are denoted as Lata andLona respectively Latb and Lonb are the counterparts attimestamp Tb Ti is the time interval between neighboringsamples Tth is the threshold which is set to 4 hours bydefault

312 Removal of AIS Data Anomaly After obtaining theAIS data in the above step we implement the anomaly datadenoising procedure to remove AIS data noises Typical AISdata outliers are summarized as follows (a) e longitudeand (or) latitude it is far beyond the reasonable range Wecollect the AIS data in the Gulf of Mexico and the longitude(latitude) is supposed to fall in 75degW (18degN) and 100degW(31degN) e ship trajectory will be considered as outlierswhen the ship spatial data (ie latitude and longitude)exceed the range Moreover sudden longitude (latitude)variation is another type of typical outlier and we employthe moving average method to correct the data outliers (seeequation (3)) (b) Abnormal velocity data after manuallychecking the raw AIS data we find several ship speedsamples are very high (ie larger than 30 knots) It is lesslikely for a ship travelling in inland waterways at such speedfor the purpose of ensuring maritime traffic safety (c) Ship

course outlier ship may change its moving direction incoastal areas to avoid maritime traffic collision But largeship course variation is not permitted in real world Weaverage the neighboring ship courses to remove such dataoutlier Given ship headings C1 C2 and C3 from threeneighboring AIS trajectory samples (with timestamps t1 t2and t3) we consider C2 as the outlier when the condition inequation (4) is satisfiede ship heading C2 is updated as C2primewith equation (5)

lati lat(iminus1) + lat(i+1)

2lati minus lat(iminus1)

11138681113868111386811138681113868111386811138681113868

gt latth and lati minus lat(i+1)

11138681113868111386811138681113868111386811138681113868gt latth

loni lon(iminus1) + lon(i+1)

2loni minus lon(iminus1)

11138681113868111386811138681113868111386811138681113868

gt lonth and loni minus lon(i+1)

11138681113868111386811138681113868111386811138681113868gt lonth

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

C2 minus C11113868111386811138681113868

1113868111386811138681113868gtCth

C2 minus C31113868111386811138681113868

1113868111386811138681113868gtCth

C1 minus C31113868111386811138681113868

1113868111386811138681113868leCth

⎧⎪⎪⎨

⎪⎪⎩(4)

Figure 1 Raw AIS data collected from Gulf of Mexico

Raw AIS data Trajectory prediction with ANN

Trajectory feature exploitation

Ship trajectory prediction

Ship trajectory reconstruction results

Input denoised AIS data

Data quality control

Trajectory separation

Anomaly data removal

Data normalization

Figure 2 Overview for the proposed AIS trajectory reconstruction framework

Mathematical Problems in Engineering 3

C2prime C1 +C1 minus C3

t13times t12 C1 gt C3


t13times t12 C1 lt C3

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)

Here ship latitude and longitude at timestamp i are lati andloni respectively e rule is applicable to lat(iminus1) lat(i+1)lon(iminus1) and lon(i+1) latth and lonth are the thresholds for thelatitude and longitude respectively Cth is the ship headingvariation threshold e parameter t13 is time differencebetween timestamps t1 and t3 and t12 is the time intervalbetween t1 and t2

313 AIS Data Normalization We can obtain noise-freeAIS dataset after implementing the above two steps It isfound that time interval may vary from different datasamples which hinders ship trajectory reconstruction modelfrom accurately extracting AIS intrinsic patterns In thatmanner it is difficult to predict ship trajectory in real-worldapplications To address the issue we employ the cubicspline interpolation and moving average models to nor-malize the AIS data series Given three noise-free AIS tra-jectories A1 A2 and A3 we label and store the AIS samplesA1 and A3 assuming that one of the following conditions ismet (see equations (6) to (9)) Moreover the AIS sample A2is denoted as flag data when the constraints in equation (10)are satisfied We normalize the ship trajectory samplesbetween A1 and A2 with the cubic spline interpolation andfor more details we suggest the reader to refer to [31] eship AIS data between A2 and A3 is normalized with themoving average model and details can be found in [26]

Note that appropriate time interval is crucial for shiptrajectory analysis due to the fact that large time interval canlead to ship kinematic information loss and smaller timeinterval may introduce trivial ship moving patterns Aftercarefully exploiting time interval distributions via the col-lected AIS data samples (see Figure 3) we find the majorityof time for interval samples is 60 s which is set as defaultvalue in our study without further specifications

d12

d23gtdt1 (6)

t12 gt tt1 (7)

v1 minus v21113868111386811138681113868

1113868111386811138681113868gt vth (8)

d12 ltdt2 (9)

t23 lt tt2

d12 gt dt3

d23 gt dt4

⎧⎪⎪⎨

⎪⎪⎩(10)

where d12 middot (d23) is the ship displacement between positionsA1 middot (A2) and A2 middot (A3) (A3) Parameter t12 middot (t23) is timecost for the ship travelling from position A1 middot (A2) to po-sition A2 middot (A3) e speed recorded in the trajectory sample

A1 is v1 and the rule is applicable to v2 dt1 tt1 vth dt2 tt2dt3 and dt4 are the thresholds with the default settings being5 360 5 10 160 30 and 30

32 Ship Trajectory Prediction with the ANN Model eartificial neural network model has shown great success-fulness in many roadway traffic flow prediction applicationswhich demonstrates its potential in ship trajectory predic-tion taskemain advantages of the back-propagation (BP)neural network are strong nonlinear curve fitting capabilitylow complexity and self-learning ability which can easilyidentify and predict ship trajectory variation tendencyMoreover the ANN model can output ship trajectoryprediction results in real-time manner due to the lowcomputational cost which can provide instant maritimetraffic information for tackling time-demanding maritimetasks Based on the above reasons we employ the ANNmodel to predict AIS trajectories e ANN model exploitsintrinsic relationship between input training (and testing)data and the output samples with the human-like infor-mation perception rule

For the given gth neuron node we denote by Aj (j 1 2 J) the input ship AIS trajectory wj ( j 1 2 J) rep-resents the weight for each ship trajectory Based on that theinput AIS data for the gth neuron node is obtained by equation(11) Note that the hidden layer in a BP neural network playsthe role of extracting ship travelling patterns from the AIS dataWith the help of transfer function the BP neural network canlearn the nonlinearity patterns among the input ship AIS datasamples and the sigmoid transfer function used in our study isshown in equation (12) e BP network measures differencebetween the predicted AIS trajectories and ground-truth datawhich is returned back to network to adjust the modelstructure and neuron settings for the purpose of obtainingoptimal ship trajectory prediction results

Ng

in 1113944

J

j1wlowastj Aj (11)

f sjg1113872 1113873

11 + exp minuss

jg1113872 11138731113872 1113873

(12)

where Ng

in is the input for the gth neuron node and sjg is the

state of the gth neuron of the hidden layer with the jth AISsample

000

200000000

400000000

600000000

800000000

1000000000

1200000000

1 51 101 151 201 251 301 351 401 451 501

Sam

ple n

umbe

r

Time interval (s)

Figure 3 Time interval distribution for the collected AIS samples


33 Evaluation Metrics To quantify the ship trajectoryprediction performance we compare the predicted AIS datawith ground truth data with typical statistical measurementsFollowing the rule in previous studies [26 27] we employthe root mean square error (RMSE) mean absolute error(MAE) Frechet distance (FD) and average Euclidean dis-tance (AED) to measure the prediction goodness For anygiven ship trajectories the prediction accuracy is quantifiedwith the above-mentioned statistical indicators (see equa-tions (13) to (16)) e smaller RMSE MAE FD and AEDindicate more accurate ship trajectory prediction accuracyand vice versa Note that both the RMSE and MAE indi-cators are implemented to quantify the ship trajectoryprediction accuracy in terms of longitude and latituderespectively

RMSE

1n

1113944

n

i1pi minus gi( 1113857

2

11139741113972

(13)

MAE1n

1113944

n

i1pi minus gi

11138681113868111386811138681113868111386811138681113868 (14)

FD maxiε[1n]

pi(x) minus gi((x)( 11138572

+ pi(y) minus gi(y)( 11138572

1113969

(15)

AED1113936

ni1

pi(x) minus gi(x)( 11138572

+ pi(y) minus gi(y)( 11138572

1113969

n (16)

where n is the number of AIS data samples pi is the ithpredicted AIS data sample and gi is the ith ground truth AISdata samples e parameters pi(x) and pi(y) are the lat-itude and longitude for the ith predicted AIS data sampleand gi(x) and gi(y) are the counterparts for the ith groundtruth AIS sample

4 Experiment

For the purpose of evaluating framework performance wehave collected two typical ship trajectories (ie two groupsof AIS data samples) from the observed navigation regioneAIS data for the ship withMMSI No 357234000 andNo367715380 were collected from the above-mentioned database which were denoted as Case 1 and Case 2 respectivelye ship trajectory for Case 1 was sampled from 24 January2017 to 25 January 2017 e data samples for Case 2 werecollected on 6 January 2017 e framework was imple-mented on Windows10 OS with 16GB RAM and 4GHzCPUWe employed Python (35 version) to perform the dataquality control and prediction procedure on the ship tra-jectory data

41 Ship Trajectory Reconstruction on Case 1 We firstpresented the ship trajectory reconstruction results onCase 1 (ie the ship with MMSI No 357234000) and thenverified the model performance on the AIS data from theship with MMSI No 367715380 e spatial-temporalship trajectory distribution shown in Figure 4 indicated

that the ship was travelling back and forth in small areaconsidering that both ship longitudes and latitudesvaried in small range But several obvious outliers werefound in the raw ship trajectory data More specificallythe anomalous ship positions from several AIS datasamples were far away from their neighbors whichshowed unreasonable ship displacement After carefullychecking the raw AIS data we found that average shipmoving speed was quite slow (ie smaller than 4 knots)e main reason is that the ship is a special surveyseismic vessel which was towing on the water surface at alarge area (eg towing a dozen of sensors connected byhydrophone streamer cables) Moreover the shiprsquos in-stant speed reached 20 knots when the ship position wasconsidered as obvious outlier (eg abnormal ship lati-tude andor longitude) It can be inferred that the shipfinished the task in the current coastal region and thusspeeded up to another sea area Besides the abnormalship longitude positions were different from those of thelatitude counterparts (see Figures 4(a) and 4(b) re-spectively) In that way anomaly ship trajectory samplewas observed when latitude (or latitude) was interferedby neighboring ship positions

e denoised ship trajectory showed that abnormal datasamples were successfully removed by the proposedframework considering that no outliers were observed in thespatial-temporal trajectory distributions e denoised shiplatitude and longitude distributions shown in Figures 5(a)and 5(b) confirmed the above analysis It is observed that thedenoised ship longitude varied from minus896deg to minus898deg and thelatitude data varied from 278deg to 28deg It can be inferred thatthe ship travelled in an area with a radius about 2 km andthus the ship was indeed in mooring state We observed thatship trajectory samples were not evenly distributed con-sidering that many data discontinuities are found in Fig-ure 5 To alleviate such discontinuity we have normalizedthe ship trajectory samples which are shown in Figure 6 eraw denoised ship trajectories were interpolated into evenlydistributed data series and discontinuous data samples weresuccessfully removed (see Figures 6(a) and 6(b)respectively)

e ship trajectory reconstruction results were fur-ther evaluated by ship trajectory prediction accuracywhich can be found in Table 1 (note that our proposedframework is denoted as DANN) We have implementedanother popular trajectory prediction model (ie thelong short-term memory model (abbreviated as LSTM))[32] for the purpose of prediction performance com-parison From the perspective of MAE the longitudeerror of our proposed framework was approximatelyone-tenth to that of LSTM which is 394 times 10minus3 elatitude MAE obtained by our model is 207 times 10minus3 whichis about 1 to that of the LSTM counterpart e RMSEindicators for the longitude and latitude obtained by theproposed framework were both 541 times 10minus4 whichshowed similar variation tendency to those of MAE Boththe FD and AED indictors demonstrated distance be-tween predicted and ground truth data samples whichshowed similar tendency to those of MAE and RMSE


42 Ship Trajectory Reconstruction on Case 2 e modelperformance of the proposed framework was validated onanother trajectory with ship MMSI No 367715380 Weapplied the same procedure to improve the AIS dataquality and thus ship trajectory prediction was furtherimplemented We observed several sudden variations inboth latitude and longitude data samples (see Figures 7(a)and 7(b) respectively) Moreover the maximum distancebetween neighboring ship latitudes was over 1000 kmwhich is quite impossible in real world Figures 7(c) and

ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

142400 213600 44800 120000 191200

Long

itude

(deg

ree)

Time

(a)

142400 213600 44800 120000 191200Time

278

2785

279

2795

28

Latit

ude (

degr

ee)

(b)

Figure 4 Raw ship trajectory distributions via AIS data for Case 1 (a) Raw longitude data distribution (b) Raw latitude data distribution

Table 1 Ship trajectory prediction performance results for Case 1

DANN LSTMMAE (LON)lowast 394 times 10minus3 200 times 10minus2

MAE (LAT) 207 times 10minus3 249 times 10minus1

RMSE (LON) 541 times 10minus4 669 times 10minus4

RMSE (LAT) 541 times 10minus4 172 times 10minus2

FD 983 times 10minus2 305 times 10minus1

AED 516 times 10minus3 251 times 10minus1

lowastNote MAE (LON) is the MAE value for longitude data and the rule isapplicable to MAE (LAT) RMSE (LON) and RMSE (LAT)

ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 213600 44800 120000 191200Time

(a)

278

2785

279

2795

28

142400 213600 44800 120000 191200

Latit

ude (

degr

ee)

Time

(b)

Figure 5 Denoised ship trajectory distributions via AIS data for Case 1 (a) Denoised longitude data distribution (b) Denoised latitude datadistribution

ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 19120012000044800213600Time

(a)

278

2785

279

2795

28

142400 191200 00000 44800 93600 142400 191200

Latit

ude (

degr

ee)

Time

(b)

Figure 6 Normalized ship trajectory distributions via AIS data for Case 1 (a) Normalized longitude data distribution (b) Normalizedlatitude data distribution


7(d) demonstrated the AIS data after implementing thedata quality control procedure It is demonstrated thatship trajectory outliers were successfully removed by ourproposed framework e ship trajectory prediction re-sults indicated that our proposed framework obtainedhigher accuracy compared to the LSTM model For in-stance the MAE indicators for the DANN latitude andlongitude were 223 times 10minus3 and 260 times 10minus3 respectivelywhich were both approximately one-tenth to those of theLSTM counterparts (see Table 2) e RMSE FD andAED indicators showed similar variation tendency tothose of the MAE

5 Conclusion

It is not easy to obtain accurate ship trajectory informationvia historical AIS data due to unpredicted noises Weproposed a novel framework by integrating steps of datadenoising data normalization and trajectory predictione proposed framework firstly identified different shiptrajectories via time interval between neighboring datasamples which is the first substep in the data quality controlprocedure of the proposed framework en the dataoutliers in the raw AIS data were determined with a group ofconstraints which were further corrected by the movingaverage method After that the denoised AIS data werenormalized into data samples for the purpose of ship tra-jectory analysis applications en we predicted ship tra-jectory with the ANN model for the purpose of furtherevaluating model performance e experiments wereimplemented on two ship trajectories (ie typical outlierswere observed in the raw data)e statistical results showedthat our proposed framework can successfully remove ab-normal AIS data outliers and obtained satisfying ship tra-jectory prediction performance (ie the average MAE

ndash912

ndash909

ndash906

ndash903

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(a)

0

10

20

30

33600 60000 82400 104800

Latit

ude (

degr

ee)

Time

(b)

ndash9122

ndash9112

ndash9102

ndash9092

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(c)

319

321

323

325

327

35024 61424 83824 110224

Latit

ude (

degr

ee)

Time

(d)

Figure 7 Ship trajectory distributions via AIS data for Case 2 (a) Raw longitude data distribution (b) Raw latitude data distribution (c)Normalized longitude data distribution (d) Normalized latitude data distribution


DANN LSTMMAE (LON) 223 times 10minus3 164 times 10minus1







RMSE FD and AED are 271 times 10minus3 677 times 10minus4665 times 10minus2 and 471 times 10minus3)

We can expand our work by conducting further studiesin the following aspects First we applied our proposedframework to cleanse and predict ship trajectories on the AISdata from two special-purpose ships which is more chal-lenging due to the irregular and unpredicted spatial-tem-poral movements In future we can employ the proposedframework to denoise and forecast ship trajectories forgeneral-purpose merchant ships (eg oil tankers and con-tainer ships) to further testify the model performanceSecond it is noted that the ANN module in the proposedframework may suffer from the overfitting disadvantagewhich may degrade the model performance We can employadditional bio-inspired models to further enhance the modelprediction accuracy ird we can obtain more holisticmodel performance by comparing it against other popularship trajectory prediction models Fourth we can test themodel robustness on the AIS data collected under morecomplicated navigation environment interferences (egship sailing at narrow and busy channels) Last but not leastwe can implement maritime situation awareness task (egship behavior analysis and prediction) by exploiting theobtained historical AIS data

Data Availability

All data generated or analyzed during this study can beobtained from the corresponding author upon request byemail

Conflicts of Interest

e authors declare no conflicts of interest

Authorsrsquo Contributions

Conceptualization was performed by Xinqiang Chen andJun Ling methodology was contributed by Xinqiang ChenJun Ling and Yongsheng Yang original draft preparationwas done by Xinqiang Chen Jun Ling Hailin Zheng andYong Xiong review and editing were carried out byYongsheng Yang Pengwen Xiong Octavian Postolache andYong Xiong funding acquisition was done by YongshengYang and Pengwen Xiong

Acknowledgments

is work was jointly supported by the National NaturalScience Foundation of China (51709167 51579143 and61663027) and Shanghai Committee of Science and Tech-nology China (18040501700 1829501100 and 17595810300)

References

[1] R Zhen Y Jin Q Hu Z Shao and N Nikitakos ldquoMaritimeanomaly detection within coastal waters based on vesseltrajectory clustering and naıve bayes classifierrdquo Journal ofNavigation vol 70 no 3 pp 648ndash670 2017

[2] J Xue P H A J M VanGelder G Reniers E Papadimitriouand C Wu ldquoMulti-attribute decision-making method forprioritizing maritime traffic safety influencing factors of au-tonomous shipsrsquo maneuvering decisions using grey and fuzzytheoriesrdquo Safety Science vol 120 pp 323ndash340 2019

[3] Y Zhou W Daamen T Vellinga and S HoogendoornldquoReview of maritime traffic models from vessel behaviormodeling perspectiverdquo Transportation Research Part CEmerging Technologies vol 105 pp 323ndash345 2019

[4] X Chen S Wang C Shi H Wu J Zhao and J Fu ldquoRobustship tracking via multi-view learning and sparse represen-tationrdquo Journal of Navigation vol 72 no 1 pp 176ndash192 2019

[5] X Chen X Xu Y Yang H Wu J Tang and J ZhaoldquoAugmented ship tracking under occlusion conditions frommaritime surveillance videosrdquo IEEE Access vol 8 no 1pp 42884ndash42897 2020

[6] Z Fang L Jian-yu T Jin-jun W Xiao and G Fei ldquoIden-tifying activities and trips with GPS datardquo IET IntelligentTransport Systems vol 12 no 8 pp 884ndash890 2018

[7] X Chen Y Yang S Wang et al ldquoShip type recognition via acoarse-to-fine cascaded convolution neural networkrdquo Journalof Navigation vol 73 no 4 pp 813ndash832 2020

[8] X Chen Z Li Y Yang L Qi and R Ke ldquoHigh-resolution vehicletrajectory extraction and denoising from aerial videosrdquo IEEETransactions on Intelligent Transportation Systems pp 1ndash13 2020

[9] G Pallotta M Vespe and K Bryan ldquoVessel patternknowledge discovery from AIS data a framework for anomalydetection and route predictionrdquo Entropy vol 15 no 6pp 2218ndash2245 2013

[10] X Chen L Qi Y Yang et al ldquoVideo-based detection in-frastructure enhancement for automated ship recognition andbehavior analysisrdquo Journal of Advanced Transportationvol 2020 Article ID 7194342 12 pages 2020

[11] X Chen ldquoRobust visual ship tracking with an ensembleframework via multi-view learning and wavelet filterrdquo Sensors(Basel) vol 20 no 3 2020

[12] Y Zou X Zhong J Tang et al ldquoA copula-based approach foraccommodating the underreporting effect in wildlife‒vehiclecrash analysisrdquo Sustainability vol 11 no 2 p 418 2019

[13] R J Bye and P G Almklov ldquoNormalization of maritimeaccident data using AISrdquo Marine Policy vol 109 Article ID103675 2019

[14] C Iphar C Ray and A Napoli ldquoData integrity assessment formaritime anomaly detectionrdquo Expert Systems with Applica-tions vol 147 Article ID 113219 2020

[15] L Zhao and G Shi ldquoMaritime anomaly detection usingdensity-based clustering and recurrent neural networkrdquoJournal of Navigation vol 72 no 4 pp 894ndash916 2019

[16] J Tang F Gao F Liu and X Chen ldquoA denoising scheme-based traffic flow prediction model combination of ensembleempirical mode decomposition and fuzzy C-means neuralnetworkrdquo IEEE Access vol 8 pp 11546ndash11559 2020

[17] J Liu H Li Z Yang K Wu Y Liu and R W Liu ldquoAdaptivedouglas-peucker algorithm with automatic thresholdi`ng forAIS-based vessel trajectory compressionrdquo IEEE Access vol 7pp 150677ndash150692 2019

[18] F Deng ldquoVessel track information mining using AIS datardquo inProceedings of the International Conference on MultisensorFusion and Information Integration for Intelligent Systems(MFI) Beijing China September 2014

[19] S-K Zhang G-Y Shi Z-J Liu Z-W Zhao and Z-L WuldquoData-driven based automatic maritime routing frommassiveAIS trajectories in the face of disparityrdquo Ocean Engineeringvol 155 pp 240ndash250 2018


[20] H Rong A P Teixeira and C Guedes Soares ldquoShip trajectoryuncertainty prediction based on a Gaussian Process modelrdquoOcean Engineering vol 182 pp 499ndash511 2019

[21] L Du F Goerlandt and P Kujala ldquoReview and analysis ofmethods for assessing maritime waterway risk based on non-accident critical events detected from AIS datardquo ReliabilityEngineering amp System Safety vol 200 Article ID 106933 2020

[22] X Hoque and S K Sharma ldquoEnsembled deep learning ap-proach for maritime anomaly detection systemrdquo in Pro-ceedings of the ICETIT 2019 Springer InternationalPublishing Cham Switzerland 2020

[23] K I Kim and K M Lee ldquoDeep learning-based caution areatraffic prediction with automatic identification system sensordatardquo Sensors (Basel) vol 18 no 9 2018

[24] M Gao and G-Y Shi ldquoShip-handling behavior patternrecognition using AIS sub-trajectory clustering analysis basedon the T-SNE and spectral clustering algorithmsrdquo OceanEngineering vol 205 p 106919 2020

[25] L Zhang Q Meng Z Xiao and X Fu ldquoA novel ship tra-jectory reconstruction approach using AIS datardquo OceanEngineering vol 159 pp 165ndash174 2018

[26] X Chen ldquoAnomaly detection and cleaning of highway ele-vation data from google earth using ensemble empirical modedecompositionrdquo Journal of Transportation Engineering PartA Systems vol 144 no 5 Article ID 04018015 2018

[27] X Chen ldquoTraffic flow prediction at varied time scales viaensemble empirical mode decomposition and artificial neuralnetworkrdquo Sustainability vol 12 no 9 2020

[28] R J Bye and A L Aalberg ldquoMaritime navigation accidentsand risk indicators an exploratory statistical analysis usingAIS data and accident reportsrdquo Reliability Engineering ampSystem Safety vol 176 pp 174ndash186 2018

[29] E Tu G Zhang L Rachmawati E Rajabally andG-B Huang ldquoExploiting AIS data for intelligent maritimenavigation a comprehensive survey from data to method-ologyrdquo IEEE Transactions on Intelligent Transportation Sys-tems vol 19 no 5 pp 1559ndash1582 2018

[30] V F Arguedas G Pallotta and M Vespe ldquoMaritime TrafficNetworks from historical positioning data to unsupervisedmaritime traffic monitoringrdquo IEEE Transactions on IntelligentTransportation Systems vol 19 no 3 pp 722ndash732 2017

[31] H Behjat Z Dogan D Van De Ville and L SornmoldquoDomain-informed spline interpolationrdquo IEEE Transactionson Signal Processing vol 67 no 15 pp 3909ndash3921 2019

[32] S Dai L Li and Z Li ldquoModeling vehicle interactions viamodified LSTM models for trajectory predictionrdquo IEEE Ac-cess vol 7 pp 38287ndash38296 2019


real time in coastal area Moreover the large-scale AISdatasets have been stored at regional or national datacenters which can be accessible by users in request (notethat users may need to pay for accessing the AIS data)Previous studies suggested that AIS data quality imposessignificant influence on the maritime traffic safety analysisand thus improving AIS data quality has become an activetopic in the maritime community [13 14]

AIS data anomaly removal studies involve unsupervisedclustering method and neural network based and statisticalmodels [15 16] Liu et al proposed an adaptive Douglas-Peucker framework to suppress AIS data outliers in themanner of data compression [17] Deng introduced a Markovbased model to explore ship movement patterns which werefurther used to identify the abnormal AIS data samples [18]Zhang et al proposed a hierarchical density-based spatialclustering of applications with noise based model to clusterand denoise the raw AIS trajectories [19] Rong et al cleansedthe raw AIS data in the lateral and longitudinal dimensionswith a novel probability trajectory prediction model [20] eneural network relevant models have shown many successesin tackling the AIS trajectory denoising and prediction tasks[21] Hoque and Sharma applied long short-term memoryneural network to forecast ship trajectories which wereemployed to suppress the AIS data anomaly [22] Kim andLee proposed a novel deep neural network model to removeAIS outliers and thus predict both medium- and long-termship trajectory variation tendencies [23] Similar researchescan be found in [8 24ndash28]

We aim to propose a novel AIS denoising and predictionframework with the support of data quality control proce-dure Our main contributions can be summarized as follows(1) we cleansed the raw AIS data with the steps of trajectoryseparation outlier removal and data normalization (2) wepredicted ship trajectory via the denoised AIS data with theartificial neural network (ANN) (3) we testified the pro-posed framework performance on two ship trajectories estudy can help maritime traffic participants forecast accurateship trajectories and thus take early-warning measurementsto enhance maritime traffic efficiency and safety e re-mainder of the paper is organized as follows We introducethe data source used in our study in Section 2 After that themethodology details about the AIS data denoising are il-lustrated in Section 3 and then the ANN model used forpredicting ship trajectories is presented e experimentalresults are shown in Section 4 Section 5 briefly concludes thestudy and illustrates future work

2 Data

e US Marine Energy Administration and NationalOceanic and Atmospheric Administration provides large-scale AIS data which benefits many AIS relevant studies dueto its public accessibility (httpsmarinecadastregovais)[29 30]e original AIS dataset includes both kinematic andstatic information for the ship which contains MMSI Co-ordinated Universal Time (UTC) latitude longitude speedover ground (SOG) heading course over ground (COG)timestamp call sign and so forth We collect the AIS data

from the Gulf of Mexico with latitude ranging from 18degN to31degN and the longitude falls in the interval [75degW 100degW]e minimum time interval for sampling the AIS data is 1 sand the maximum value is 500 s We collect 12813 AIS datasamples on April 11 2017 from the above-mentioned da-tabase (see Figure 1) Following the international standard forrepresentation of latitude and longitude the south latitude(west longitude) is denoted as a negative number while northlatitude (east longitude) is presented with a positive number

3 Methodology

e raw AIS data may contain different types of outliers dueto instable signal transmission rate data transmissioncongestion etc It is important to suppress such dataanomalies for the purpose of exploiting reliable maritimetraffic kinematic information from the AIS dataset To ad-dress the issue we firstly implement the data quality controlprocedure to remove the trajectory outliers and then predictthe trajectory with artificial neural network e schematicoverview for the proposed framework is shown in Figure 2

31 Data Quality Control for Suppressing AIS OutliersShip trajectory data (ie AIS data) is stored in the databasevia data deliveringreceiving timestamp and thus we need toaggregate trajectory data (from a single ship) before con-ducting ship trajectory analysis relevant researches For thepurpose of thoroughly removing anomalous AIS sampleswe implement the data quality control with steps of shiptrajectory extraction data cleansing and data formatting(ie AIS time interval normalization)

311 Ship Trajectory Extraction e ship trajectory ex-traction can be divided into separating trajectories fromdifferent ships and removing discontinuous ship trajectoriesIt is noted that the ship can be uniquely identified by theMMSI which is thus applied to separate AIS data samplesfrom different shipsen the raw AIS samples are sorted bytimestamp in an ascending manner It is found that an AISsample may be recorded in database for several times Toaddress the issue the repetition samples are removed toavoid being further processed when the constraints inequation (1) are satisfied e outputs from the above stepare the raw ship trajectories We find that several time in-tervals between neighboring samples are very large (eg fourhours) indicating that many AIS data are lost Such AIS datadiscontinuity imposes big challenge for analyzing ship ki-nematic moving state in detail To overcome the disad-vantage we divide the raw ship trajectory into differentsegments when the time interval between neighboringsamples exceeds a threshold (see equation (2))

Ta Tb

Lata Latb

Lona Lonb

⎧⎪⎪⎨

⎪⎪⎩(1)

Ti gtTth (2)







11138681113868111386811138681113868111386811138681113868


11138681113868111386811138681113868111386811138681113868gt latth



11138681113868111386811138681113868111386811138681113868


11138681113868111386811138681113868111386811138681113868gt lonth

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

C2 minus C11113868111386811138681113868

1113868111386811138681113868gtCth

C2 minus C31113868111386811138681113868

1113868111386811138681113868gtCth

C1 minus C31113868111386811138681113868

1113868111386811138681113868leCth

⎧⎪⎪⎨

⎪⎪⎩(4)










Data normalization







⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)




d12

d23gtdt1 (6)

t12 gt tt1 (7)

v1 minus v21113868111386811138681113868

1113868111386811138681113868gt vth (8)

d12 ltdt2 (9)

t23 lt tt2

d12 gt dt3

d23 gt dt4

⎧⎪⎪⎨

⎪⎪⎩(10)





Ng

in 1113944

J

j1wlowastj Aj (11)

f sjg1113872 1113873

11 + exp minuss

jg1113872 11138731113872 1113873

(12)

where Ng



000

200000000

400000000

600000000

800000000

1000000000

1200000000

1 51 101 151 201 251 301 351 401 451 501

Sam

ple n

umbe

r

Time interval (s)




RMSE

1n

1113944

n


2

11139741113972

(13)

MAE1n

1113944

n

i1pi minus gi

11138681113868111386811138681113868111386811138681113868 (14)

FD maxiε[1n]

pi(x) minus gi((x)( 11138572

+ pi(y) minus gi(y)( 11138572

1113969

(15)

AED1113936

ni1


+ pi(y) minus gi(y)( 11138572

1113969

n (16)


4 Experiment








ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

142400 213600 44800 120000 191200

Long

itude

(deg

ree)

Time

(a)

142400 213600 44800 120000 191200Time

278

2785

279

2795

28

Latit

ude (

degr

ee)

(b)










ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 213600 44800 120000 191200Time

(a)

278

2785

279

2795

28

142400 213600 44800 120000 191200

Latit

ude (

degr

ee)

Time

(b)


ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 19120012000044800213600Time

(a)

278

2785

279

2795

28

142400 191200 00000 44800 93600 142400 191200

Latit

ude (

degr

ee)

Time

(b)




5 Conclusion


ndash912

ndash909

ndash906

ndash903

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(a)

0

10

20

30

33600 60000 82400 104800

Latit

ude (

degr

ee)

Time

(b)

ndash9122

ndash9112

ndash9102

ndash9092

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(c)

319

321

323

325

327

35024 61424 83824 110224

Latit

ude (

degr

ee)

Time

(d)












Data Availability






Acknowledgments


References








































11138681113868111386811138681113868111386811138681113868


11138681113868111386811138681113868111386811138681113868gt latth



11138681113868111386811138681113868111386811138681113868


11138681113868111386811138681113868111386811138681113868gt lonth

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

C2 minus C11113868111386811138681113868

1113868111386811138681113868gtCth

C2 minus C31113868111386811138681113868

1113868111386811138681113868gtCth

C1 minus C31113868111386811138681113868

1113868111386811138681113868leCth

⎧⎪⎪⎨

⎪⎪⎩(4)










Data normalization







⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)




d12

d23gtdt1 (6)

t12 gt tt1 (7)

v1 minus v21113868111386811138681113868

1113868111386811138681113868gt vth (8)

d12 ltdt2 (9)

t23 lt tt2

d12 gt dt3

d23 gt dt4

⎧⎪⎪⎨

⎪⎪⎩(10)





Ng

in 1113944

J

j1wlowastj Aj (11)

f sjg1113872 1113873

11 + exp minuss

jg1113872 11138731113872 1113873

(12)

where Ng



000

200000000

400000000

600000000

800000000

1000000000

1200000000

1 51 101 151 201 251 301 351 401 451 501

Sam

ple n

umbe

r

Time interval (s)




RMSE

1n

1113944

n


2

11139741113972

(13)

MAE1n

1113944

n

i1pi minus gi

11138681113868111386811138681113868111386811138681113868 (14)

FD maxiε[1n]

pi(x) minus gi((x)( 11138572

+ pi(y) minus gi(y)( 11138572

1113969

(15)

AED1113936

ni1


+ pi(y) minus gi(y)( 11138572

1113969

n (16)


4 Experiment








ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

142400 213600 44800 120000 191200

Long

itude

(deg

ree)

Time

(a)

142400 213600 44800 120000 191200Time

278

2785

279

2795

28

Latit

ude (

degr

ee)

(b)










ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 213600 44800 120000 191200Time

(a)

278

2785

279

2795

28

142400 213600 44800 120000 191200

Latit

ude (

degr

ee)

Time

(b)


ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 19120012000044800213600Time

(a)

278

2785

279

2795

28

142400 191200 00000 44800 93600 142400 191200

Latit

ude (

degr

ee)

Time

(b)




5 Conclusion


ndash912

ndash909

ndash906

ndash903

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(a)

0

10

20

30

33600 60000 82400 104800

Latit

ude (

degr

ee)

Time

(b)

ndash9122

ndash9112

ndash9102

ndash9092

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(c)

319

321

323

325

327

35024 61424 83824 110224

Latit

ude (

degr

ee)

Time

(d)












Data Availability






Acknowledgments


References







































⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)




d12

d23gtdt1 (6)

t12 gt tt1 (7)

v1 minus v21113868111386811138681113868

1113868111386811138681113868gt vth (8)

d12 ltdt2 (9)

t23 lt tt2

d12 gt dt3

d23 gt dt4

⎧⎪⎪⎨

⎪⎪⎩(10)





Ng

in 1113944

J

j1wlowastj Aj (11)

f sjg1113872 1113873

11 + exp minuss

jg1113872 11138731113872 1113873

(12)

where Ng



000

200000000

400000000

600000000

800000000

1000000000

1200000000

1 51 101 151 201 251 301 351 401 451 501

Sam

ple n

umbe

r

Time interval (s)




RMSE

1n

1113944

n


2

11139741113972

(13)

MAE1n

1113944

n

i1pi minus gi

11138681113868111386811138681113868111386811138681113868 (14)

FD maxiε[1n]

pi(x) minus gi((x)( 11138572

+ pi(y) minus gi(y)( 11138572

1113969

(15)

AED1113936

ni1


+ pi(y) minus gi(y)( 11138572

1113969

n (16)


4 Experiment








ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

142400 213600 44800 120000 191200

Long

itude

(deg

ree)

Time

(a)

142400 213600 44800 120000 191200Time

278

2785

279

2795

28

Latit

ude (

degr

ee)

(b)










ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 213600 44800 120000 191200Time

(a)

278

2785

279

2795

28

142400 213600 44800 120000 191200

Latit

ude (

degr

ee)

Time

(b)


ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 19120012000044800213600Time

(a)

278

2785

279

2795

28

142400 191200 00000 44800 93600 142400 191200

Latit

ude (

degr

ee)

Time

(b)




5 Conclusion


ndash912

ndash909

ndash906

ndash903

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(a)

0

10

20

30

33600 60000 82400 104800

Latit

ude (

degr

ee)

Time

(b)

ndash9122

ndash9112

ndash9102

ndash9092

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(c)

319

321

323

325

327

35024 61424 83824 110224

Latit

ude (

degr

ee)

Time

(d)












Data Availability






Acknowledgments


References




































RMSE

1n

1113944

n


2

11139741113972

(13)

MAE1n

1113944

n

i1pi minus gi

11138681113868111386811138681113868111386811138681113868 (14)

FD maxiε[1n]

pi(x) minus gi((x)( 11138572

+ pi(y) minus gi(y)( 11138572

1113969

(15)

AED1113936

ni1


+ pi(y) minus gi(y)( 11138572

1113969

n (16)


4 Experiment








ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

142400 213600 44800 120000 191200

Long

itude

(deg

ree)

Time

(a)

142400 213600 44800 120000 191200Time

278

2785

279

2795

28

Latit

ude (

degr

ee)

(b)










ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 213600 44800 120000 191200Time

(a)

278

2785

279

2795

28

142400 213600 44800 120000 191200

Latit

ude (

degr

ee)

Time

(b)


ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 19120012000044800213600Time

(a)

278

2785

279

2795

28

142400 191200 00000 44800 93600 142400 191200

Latit

ude (

degr

ee)

Time

(b)




5 Conclusion


ndash912

ndash909

ndash906

ndash903

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(a)

0

10

20

30

33600 60000 82400 104800

Latit

ude (

degr

ee)

Time

(b)

ndash9122

ndash9112

ndash9102

ndash9092

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(c)

319

321

323

325

327

35024 61424 83824 110224

Latit

ude (

degr

ee)

Time

(d)












Data Availability






Acknowledgments


References




































ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

142400 213600 44800 120000 191200

Long

itude

(deg

ree)

Time

(a)

142400 213600 44800 120000 191200Time

278

2785

279

2795

28

Latit

ude (

degr

ee)

(b)










ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 213600 44800 120000 191200Time

(a)

278

2785

279

2795

28

142400 213600 44800 120000 191200

Latit

ude (

degr

ee)

Time

(b)


ndash9005

ndash8995

ndash8985

ndash8975

ndash8965

Long

itude

(deg

ree)

142400 19120012000044800213600Time

(a)

278

2785

279

2795

28

142400 191200 00000 44800 93600 142400 191200

Latit

ude (

degr

ee)

Time

(b)




5 Conclusion


ndash912

ndash909

ndash906

ndash903

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(a)

0

10

20

30

33600 60000 82400 104800

Latit

ude (

degr

ee)

Time

(b)

ndash9122

ndash9112

ndash9102

ndash9092

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(c)

319

321

323

325

327

35024 61424 83824 110224

Latit

ude (

degr

ee)

Time

(d)












Data Availability






Acknowledgments


References




































5 Conclusion


ndash912

ndash909

ndash906

ndash903

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(a)

0

10

20

30

33600 60000 82400 104800

Latit

ude (

degr

ee)

Time

(b)

ndash9122

ndash9112

ndash9102

ndash9092

33600 60000 82400 104800

Long

itude

(deg

ree)

Time

(c)

319

321

323

325

327

35024 61424 83824 110224

Latit

ude (

degr

ee)

Time

(d)












Data Availability






Acknowledgments


References





































Data Availability






Acknowledgments


References



































ship trajectory reconstruction from ais sensory data via...

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