857
1 INTRODUCTION
Multibeam data includes different error types. These
errors can be classified as systematic errors, gross
errors (outliers) and random errors [1]. The source of
these errors can be humans (hydrographers),
equipment (echosounders) or environment (sea state).
The systematic errors can be corrected using the
functional models utilizing misalignment errors (roll,
pitch and yaw errors) and time delay calibrated by the
patch test in addition to the sound velocity profile
collected by the velocimeter. The random errors are
corrected when the final base surface is produced.
However, the outliers in multibeam data should be
detected and rejected using cleaning methods to obtain
accurate bathymetric surface [2]. Figure 1 shows an
example of different types of multibeam errors. The
main reasons for the outliers could be
cavitation/bubble sweep, loss of bottom on outer
beams, loss of bottom lock and false returns from the
water column [3].
Figure 1. Types of errors exists in multibeam sounding where
five survey lines displayed in different colors and outliers
found in the blue survey line only
Hybrid Machine Learning and CUBE Method
for Multibeam Data Cleaning
M. El-Diasty
1
, R. Abdalla
1
& F. Alsaaq
2
1
Sultan Qaboos University, Muscat, Oman
2
King Abdulaziz University, Jeddah, Saudi Arabia
ABSTRACT: Multibeam data contains different types of errors that are classified as systematic errors, random
errors and gross errors (outliers). Accurate bathymetric base surface production requires efficient cleaning
methods to detect and reject the outliers. The manual cleaning method is tedious and time-consuming method.
The need for automation of data cleaning is essential to reduce the processing time for multibeam data processing
tasks. The newly developed AI-based Machine Learning (ML) method is a promising supervised method for
automatic multibeam outlier detection and rejection. In this paper, a Hybrid ML-CUBE method was introduced
and evaluated using multibeam datasets collected by Kongsberg EM712 and Reson T50-P multibeam
echosounders. It was also found that if the outliers were not successfully detected and rejected, the accuracy of
the produced base surfaces are degraded by 0.61 m and 0.58 m for EM712 and T50-P tests, respectively, which
exceed the International Hydrographic Organization (IHO) special order. The significance of the proposed
Hybrid ML-CUBE method is that it is a rigorous and automatic outlier rejection method for multibeam data
cleaning and a rigorous bathymetric surface generation method for random errors reduction.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 3
September 2025
DOI: 10.12716/1001.19.03.19
858
The manual and automatic cleaning methods can be
used to detect and reject the multibeam data outliers.
The manual cleaning depends on the visual inspection
by the hydrographer to reject any obvious sudden
spikes (outliers) in multibeam data line by line. The
manual cleaning method is certainly tedious, critical
and subjective method. Also, given the huge amount of
data collected by the new generation of current
multibeam acquisition systems, the manual cleaning is
considered as a time-consuming task for hydrographic
offices where the time required for data processing is
almost one-to-one when compared against data
acquisition time [4]. The need for automation of data
cleaning is critical to reduce the processing time for
multibeam data processing. The traditional and simple
automatic methods for data cleaning are the methods
that use the depth limit (based on prior knowledge of
depth range), the nadir angles limit and the beam-to-
beam angle limit [6]. However, these traditional
methods can reject useful multibeam data soundings
where these methods depend on the prior knowledge
of depth limit which in most cases is not known or
depend on the guessing of the nadir angles limit as well
as the beam-to-beam slope angle limit. Therefore,
advanced and more accurate automatic methods are
developed such as AI-based supervised method and
unsupervised methods [5] [7][8]. CARIS AI-based
Sonar Noise Classifier is one of the promising
supervised methods for automatic multibeam data
cleaning and is evaluated in this project [7]. The Caris
AI-based Sonar Noise Classifier uses the machine
learning (ML) three-dimensional convolutional neural
network technique ([3][9][10]. The Caris ML-based
Sonar Noise Classifier method is based on the
estimation of noise confidence level (0-100%) for all
multibeam soundings and recommends the rejection of
the soundings with noise confidence level value above
50% [3][10]. After the correction for systematic errors
and outliers in multibeam data processing, the
remaining outliers and random errors are reduced in
the digital terrain model or base surface production
with different methods such as shoalest depth, swath,
uncertainty, and CUBE methods where CUBE filter is
the most effective method for bathymetric surface
production and random error reduction. Hybrid
Uncertainty and Bathymetry Estimation (CUBE) filter
initially utilizes the soundings and uncertainty of
soundings for high-density multibeam data to create
the CUBE surface. CUBE filter takes the depth of the
CUBE Surface at a location and compares the sounding
depths against the CUBE depth plus a threshold value.
The threshold value is defined by the parameters set in
the filter. If the difference between the depth of the
sounding and the depth of the CUBE Surface exceeds
the threshold, then the sounding with residual outliers
will be rejected (Calder and Mayer, 2003; Calder, 2003).
The primary aim of the CUBE algorithm is to use as
much information as possible to determine the true
depth at any point in the survey from the noise. CUBE
assumes that you are processing good data which
requires ML-based method to be initially applied to
remove the majority of outliers where only residual
outliers and random errors exist. It is worth noting that
the bathymetric surface can be generated using
uniform grid model or variable gride model [11].
Developing accurate multibeam data cleaning
methods are critical for all hydrographic offices to
achieve bathymetric maps that meet the International
Hydrographic Organization (IHO) standards [12]. The
main objective of this research is to develop an optimal
Hybrid ML-CUBE method for multibeam echosounder
data cleaning where the outliers are rejected using ML-
based method and random errors are reduced using
CUBE method. The proposed method is evaluated and
tested using two multibeam datasets collected from
Kongsberg EM712 and Reson SeaBat T50-P multibeam
echosounders in shallow water case studies areas.
2 HYBRID ML-CUBE METHOD
An optimal method for bathymetric surface creation
using the Hybrid ML-CUBE method is investigated in
this paper to automatically clean multibeam data from
the outliers and rigorously reduce the random errors.
The ML method is developed based on the three-
dimensional convolutional neural network. The three-
dimensional convolutional neural network is the most
popular deep learning model that can learn and extract
the features based on a unique network structure [9]
[13] [14]. The ML method is employed for multibeam
data outliers detection and rejection. Then, the CUBE
method is employed for bathymetric surface
generation where the Kalman filtering is used within
the CUBE algorithm to process high-density
bathymetry data for random errors reductions [15][16].
Therefore, the proposed Hybrid ML-CUBE method is
considered as a rigorous and automatic method for
outliers and random errors reduction in post-
processing phase where systematic errors are corrected
in the pre-processing calibration phase.
The methodology for implementing the proposed
Hybrid ML-CUBE method is shown in Figure 2. In step
1, the high-density multibeam soundings are collected
using two multibeam echosounders (Kongsberg
EM712 and Reson SeaBat T50-P). In step 2, the attitude
and navigation data are cleaned from errors, if
required. In step 3, the multibeam soundings are
georeferenced using the attitude and navigation data.
In step 4, the noisy bathymetric surface is created using
the shoalest depth true position method where the
outliers and random errors are embedded in this
surface. In step 5, the CARIS ML-based sonar noise
classifier using three-dimensional convolutional
neural network technique is employed to clean
multibeam data from outliers. The CARIS ML-based
sonar noise classifier technique includes: 1) the creation
of voxels grids from the high-density multibeam
soundings, 2) send the voxels grids to the Caris AI
cloud computing server, 3) receive the classified voxels
from the Caris AI cloud, 4) map the voxel back to the
soundings and reject the soundings with noise
confidence level values above 50% [3][10]. The ML-
based sonar noise classifier detects and rejects the
outliers embedded in the noisy high-density
multibeam soundings. In step 6, the CUBE bathymetry
is created using the cleaned multibeam high-density
multibeam soundings estimated from second step.
CUBE is an algorithm that rigorously uses the
uncertainty of every cleaned sounding and
simultaneously comparing its depth to its neighbors to
create the best estimate of the bathymetric surface. The
CUBE algorithm reduces the random errors embedded
in the cleaned high-density multibeam soundings
[15][16]. In the last step, the accuracy of Hybrid ML-
859
CUBE method is evaluated for the two EM712 and T50-
P multibeam echosounders using Root Mean Squares
(RMS) errors estimated from the error differences
between the noisy and cleaned bathymetric surfaces.
Then, the RMS errors are compared against the IHO
standards for different hydrographic surveying orders
at 95% confidence level.
Figure 2. Hybrid ML-CUBE method technique and
evaluation
3 DATASETS DESCRIPTIONS
The KAU Hydrography 1 vessel and KAU
Hydrography 2 vessel, owned by faculty of maritime
studies, King Abdulaziz University, were employed to
collect multibeam data. The KAU Hydrography 1
vessel is equipped with Kongsberg EM712 multibeam
echosounder and the KAU Hydrography 2 vessel is
equipped with Reson SeaBat T50-P multibeam
echosounder for multibeam data collection along with
navigation solutions from POS-MV positioning and
orientation system for the georeferencing of the
collected multibeam datasets [17][18][19]. Figures 3
and 4 show the KAU Hydrography 1 vessel along with
the Kongsberg EM712 multibeam echosounder and
KAU Hydrography 2 vessel along with the Reson
SeaBat T50-P multibeam echosounder, respectively.
Figures 5 and 6 show the survey lines in two different
shallow waters case study areas for test 1 using KAU
Hydrography 1 vessel and for test 2 using KAU
Hydrography 2 vessel data, respectively.
Figure 3. KAU Hydrography 1 vessel (3.a) along with
Kongsberg EM712 multibeam echosounder (3.b) and POS-
MV positioning and orientation system (3.c) [17][19]
Figure 4. KAU Hydrography 2 vessel (4.a) along with Reson
SeaBat T50-P multibeam echosounder (4.b) and POS-MV
positioning and orientation system (4.c) [18][19].
Figure 5. KAU Hydrography 1 vessel test 1 survey lines
(Sharm Obhur)
Figure 6. KAU Hydrography 2 vessel test 2 survey lines
(Alrayes)
4 RESULTS AND DISCUSSIONS
The high-density multibeam soundings collected from
test 1 (EM712 multibeam echosounder) and test 2 (T50-
P multibeam echosounder) were about 1,134,026
soundings and 3,493,434 soundings, respectively. The
multibeam soundings from test 1 and test 2 were
georeferenced using the Caris HIPS and SIPS software
and the base surfaces for test 1 and test 2 data were
produced using the shoalest depth true position
method without applying any cleaning method.
Figures 7 and 8 show the produced base surfaces for
test 1 and test 2 which include the outliers and we call
these surface noisy bathymetries for test 1 and test 2.
860
The ML-based cleaning method was implemented
using the CARIS Sonar Noise Classifier processor for
test 1 and test 2 high-density multibeam soundings.
The ML-based CARIS Sonar Noise Classifier processor
works using the Caris AI Mira authentication service
and the selected options for Sonar Noise Classifier
processor to clean the soundings confidence noise level
value was above 50%. Figure 9 and 10 show examples
of the ML-based CARIS Sonar Noise Classifier results
in swath editor and subset editor windows,
respectively, for selected number of soundings which
lists the values of the noise confidence level value (0-
100%) for each sounding and the rejected soundings
with the noise confidence level values above 50%. The
Hybrid ML-CUBE method was implemented and
Figures 11 and 12 show the cleaned bathymetries for
test 1 and test 2, respectively, where the ML-based
Sonar Noise Classifier method was implemented for
outliers rejection and CUBE method was implemented
for random errors reduction. To test the performance
of Hybrid ML-CUBE method, the error differences
between the noisy and Hybrid ML-CUBE based
cleaned bathymetries for tests 1 and 2 were estimated
and shown in Figures 13 and 14. Also, the bathymetric
error differences from test 1 and test 2 were used to
generate the histograms distributions and cumulative
distributions plots as shown in Figures 15, 16, 17 and
18, respectively. The error differences from test 1
ranges from -10.61 m to 6.77 m with mean value around
-0.12 m and error differences from test 2 ranges from -
15.74 m to 8.31 m with mean value around -0.09.
Then, the bathymetric error differences from test 1
and test 2 were used to estimate the summery statistics
as listed in Tables 1. The RMS errors at 95% confidence
level listed in Table 1 are estimated using the absolute
means and the RMS errors at 68% confidence level
using the following formula [20]:
95% 68%
1.96*=+RMS mean RMS
(1)
where the mean and RMS68% are estimated from the
error differences the error differences between the
noisy and Hybrid ML-CUBE based cleaned
bathymetric surfaces for tests 1 and 2.
The estimated RMS errors at 95% confidence level
caused by the outliers and random errors are 0.61 m
and 0.58 m for test 1 and test 2, respectively, which
exceed IHO special order requirement of maximum
allowed total vertical uncertainty that equal 0.34 m but
meets IHO order 1a requirement of maximum allowed
total vertical uncertainty that equal 0.63 m both were
estimated using the average depth of the area (30 m in
the tests 1 and 2) at 95% confidence level.
Therefore, the rejection of the outliers and reduction
of random errors using the proposed Hybrid ML-
CUBE method are essential and critical to produce
bathymetric maps with accuracy within the IHO
special order level when multibeam data is processed.
The results show that the Hybrid ML-CUBE method
can significantly improve the overall accuracy of the
produced final bathymetric maps. The advantage of
the Hybrid ML-CUBE method that is based on the use
of the AI-based sonar noise classifier subscription is
that it is a very efficient and accurate automatic
cleaning method in detecting and rejecting the outliers.
Figure 7. Noisy bathymetry for test 1 (EM712 multibeam
echosounder) referenced to the WGS84 ellipsoid (units in
meters)
Figure 8. Noisy bathymetry for test 2 (T50-P multibeam
echosounder) referenced to the WGS84 ellipsoid (units in
meters)
Figure 9. ML-based CARIS Sonar Noise Classifier Results for
selected soundings located inside the yellow box using
CARIS swath editor
Figure 10. ML-based CARIS Sonar Noise Classifier noise
confidence values for soundings using subset editor where
the grey color shows the rejected soundings and the red-to-
blue color soundings shows the accepted soundings
861
Figure 11. Hybrid ML-CUBE based cleaned bathymetry for
test 1 (EM712 multibeam echosounder) referenced to the
WGS84 ellipsoid (units in meters)
Figure 12. Hybrid ML-CUBE based cleaned bathymetry for
test 2 (T50-P multibeam echosounder) referenced to the
WGS84 ellipsoid (units in meters)
Figure 13. Error differences between the noisy and Hybrid
ML-CUBE based cleaned bathymetries for test 1 (EM712
multibeam echosounder)
Figure 14. Error differences between the noisy and Hybrid
ML-CUBE based cleaned bathymetries for test 2 (T50-P
multibeam echosounder)
Figure 15. Histogram distribution for test 1 (EM712
multibeam echosounder) bathymetric error differences
Figure 16. Cumulative distribution for test 1 (EM712
multibeam echosounder) bathymetric error differences
Figure 17. Histogram distribution for test 2 (T50-P multibeam
echosounder) bathymetric error differences
Figure 18. Cumulative distribution for test 2 (T50-P
multibeam echosounder) bathymetric error differences
Table 1. Summary of statistical results of the error difference
between noisy and the Hybrid ML-CUBE cleaned
bathymetries produced from test 1 and test 2
Test 1
(EM712 multibeam
echosounder)
Test 2
(T50-P multibeam
echosounder)
6.77 m
8.307 m
-10.61 m
-15.743 m
1,134,026
3,493,434
-0.12 m
-0.09 m
0.25 m
0.25 m
0.12+1.96*0.25 =
0.61 m
0.09+1.96*0.25 =
0.58 m
862
5 CONCLUSION AND RECOMMENDATIONS
The objective of this paper is to evaluate the proposed
Hybrid ML-CUBE method for outliers rejections and
random error reduction using high-density multibeam
soundings collected by Kongsberg EM712 and Reson
SeaBat T50-P multibeam echosounders. The noisy
bathymetries were produced using the shoalest depth
method from the noisy Kongsberg EM712 and Reson
SeaBat T50-P multibeam datasets. Afterwards, the
Hybrid ML-CUBE method was employed to reject
outliers and reduce random errors in the Kongsberg
EM712 and Reson SeaBat T50-P multibeam datasets
and produce the cleaned bathymetries. The difference
surfaces between the noisy and cleaned bathymetries
showed that outliers in Kongsberg EM712 and Reson
SeaBat T50-P datasets can successfully be detected and
rejected using the ML-based CARIS Sonar Noise
Classifier automatic cleaning method and the random
errors can successfully be reduced using the CUBE
method. It was found that if the outliers were not
successfully rejected and random errors were not
successfully reduced by Hybrid ML-CUBE method, the
accuracy of the produced bathymetries are degraded
by 0.61 m and 0.58 m in the tests conducted by EM712
and T50-P, respectively, which exceed the IHO special
order but meet order 1a requirements. Therefore, it is
recommended to use Hybrid ML-CUBE method for the
bathymetric mapping with multibeam echosounders.
The significance of the Hybrid ML-CUBE method is
that it is an automatic outlier rejection method for
multibeam data cleaning and a rigorous bathymetric
surface generation method for random errors
reduction.
ACKNOWLEDGMENTS
The authors acknowledge the financial support of deanship
research fund, Deanship of Research, Sultan Qaboos
University, Oman, grant number RF/ENG/CAED/22/02. The
data was provided to the authors by the Research and
Consulting Institute (RACI), King Abdulaziz University. The
author, therefore, gratefully acknowledges RACI’s support.
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