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Studies in Surveying and Mapping Science (SSMS) Volume 3, 2015
TPEC Algorithm and Its Application in Lau Basin Multi-Beam Echo-Sounder Data Processing Li-Shoujun1,2, Wu-Ziyin*1, Zhou-Mengjia1 Second Institute of Oceanography, Key Lab of Submarine Geosciences, SOA, Hangzhou, 310012, China
1.
Graduate Department, China University of Geosciences, Wuhan, 430074, China
2.
0911guang@163.com Abstract Currently, multibeam automatic filtering algorithm in processing gross errors has some defects. For example, in trend surface model, we can easily mark obvious gross errors, but it’s hard to identify small gross errors. Median filter model can filter abnormal data well, but it also will lead to the loss of the terrain details. The biggest problem is that the existing filtering algorithms are mostly based on statistical characteristics of the data, without considering the size of the error in the data itself. In this paper, we introduce Total Propagated Error Computation (TPEC) algorithm to improve the efficiency of Multi-Beam Echo-Sounder data (MBES) processing and to avoid losing terrain details in trend surface model and median filter model. The workflow of TPEC algorithm can be summarized as follows: Firstly, compute the Total Propagated Error of MBES data. Next, according to the IHO standard, eliminate noises automatically. Further, generate a plurality of depth and associated uncertainty estimation of grid nodes. Finally, construct “the best” Digital Terrain Model (DTM) based on the principles of density and neighborhood. To evaluate the efficiency and quality of the TPEC algorithm, TPEC algorithm and conventional method are used respectively to process the same MBES data in Lau Basin. The conventional method uses man-machine editor to reject gross errors and construct DTM by beam inverse weighting algorithm. TPEC algorithm removes gross errors automatically by filter based on the computation of Total Propagated Error, and builds DTM by the combined estimation of the depth and related uncertainty.The data processing speed of TPEC algorithm is 5 times of the conventional method. Furthmore, the TPEC model shows much more terrain details than the man-machine model. TPEC model has a better robustness, and is suitable for the research of complex seabed terrain environment, such as Lau Basin. TPEC algorithm provides a possible technological method for the study of terrain features in submarine hydrothermal area. Keywords Total Propagated Error Computation Algorithm; Multi-Beam Echo-Sounder; Density Principle; Neighborhood Principle; Lau Basin
Introduction Due to the influence of the instrument’s noise, waves, sound velocity and other factors, Multi-Beam Echo-Sounder data exists gross errors inevitably. These gross errors make it difficult to reflect the topography accurately, and even leads to the whole data invalid. The traditional method of eliminating the gross error of Multi-Beam EchoSounder data is based on man-machine interaction editing for each line processing, which is less efficient and easily affected by the subjective judgment [1]. Under the assumption of seabed topography continuous change, many researchers proposed some automatic filtering algorithms to eliminate abnormal soundings. The simplest method is setting the maximum and minimum depth threshold; Varma et al. presented the median and standard deviation estimation to exclude abnormal soundings [2]; Eeg used multivariate hypothesis testing to process multibeam data [3]; Du, Wells et al. wrote a program simulating artificial filtering data editing [4]; Lirakis, Bongirvanni et al. rejected the abnormal data by using PFM systems [5]; He Yibin put forward a trend surface model and robust filter based on M-estimation to detect abnormal data [6]; Yang Fanlin et al. combined median filter with local variance estimation and wavelet analysis to remove outliers and noises [7]. Multibeam data automatic filtering algorithms are mostly based on statistical characteristics of the data, or a priori regional topography, without the consideration of data errors. Strict filter settings will cause the loss of terrain detail, while loose settings are eliminating the gross error inefficiently. University of New Hampshire Calder put forward a combined estimation of the depth and related uncertainty by MBES to process multibeam data [8, 9]. According to
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the International Hydrographic Organization (IHO) standards, this paper will use the total propagation error computation to eliminate multibeam gross error automatically, then construct seabed Digital Terrain Model (DTM) by using the combined estimation of the depth and related uncertainty of the MBES data. Definition and filtering of the Total Propagated Error Multibeam bathymetry sonar system consists of GPS, compass, ship motion attitude sensors and other components. The total error of Multibeam system measurement together constitute by the sensor error, called total propagation errors. According to beam forming principles, multibeam soundings plane coordinates (x, y) and vertical sounding value (z) are calculated by the following formula (1): z = r cos p cos（θ +R） x=x0 + r 1 − cos 2 p cos 2（θ +R）cos α
(1)
y =y0 + r 1 − cos 2 p cos 2（θ +R）sin α Where, r is slope distance of multi-beam sonar measure, θ is beam angle, p is pitch angle of the beam, R is beam roll angle, x0 , y0 are original coordinates of GPS positioning, and α is heading of the survey line. Sonar ranging error, beam angle error, GPS positioning error, heading α , and the standard deviation of p , R , can get by detecting and manufacturers. Then, we use formula (1) to calculate the total error propagation of the plane coordinates (HxTPE、HyTPE) and the total error propagation of the vertical sounding(DzTPE). And the results express by 95% confidence intervals, which is equivalent to 1.96 times of the standard deviation. Based on the total propagation error calculation, the filter setted in accordance with IHO standard to filter multibeam data automatically. The uncertainty control of soundings requires the following equation (2):
DzTPEC≤ a 2 +（b × d）2
(2)
Where, a is the permissible value of IHO standard error (a=0.25m), b is the error coefficient (b=0.0075), d is the depth value. And the plane coordinates error should be less than 2 m. If the total propagation error exceeds the limitation of IHO, the date will be rejected. Total propagation error filter program is based on the vertical sounding error judgement, supplemented by plane coordinates. When the sounding error is available, the plane coordinate error is determined. Only if both of them meet the request, the soundings would be accepted. And as long as the sounding error exceeds the limitation, the soundings will be removed to reduce the number of calculations. Digital Terrain Model (DTM) based on Total Propagated Error Computation(TPEC) The workflow can be summarized as follows: Firstly, compute the total propagated error. Next, according to the IHO standard, eliminate noises automatically. Further, generate a plurality of depth and associated uncertainty estimation of grid nodes. Finally, construct “the best” DTM based on the principles of density and neighborhood. The Soundings’ Choice of DTM
FIG. 1 UNCERTAINTY CONTROL OF SOUNDING POINTS
By TPE calculation, the soundings choice is determined by the combination of uncertainty and distance control of
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Studies in Surveying and Mapping Science (SSMS) Volume 3, 2015
soundings. The uncertainty control of soundings, as defined in equation (2), requires the error less than the limitation of IHO. In fig. 1, according to IHO special order, sounding point “A” attends the computation of the left grid node, not the right. So the soundings meet the IHO request. Distance control of soundings, as defined in equation (3), requires the distance between sounding point and nodes less than 5% of depth. In genenal, depth around the node varies continuously or has little change. In Fig. 2, sounding point “A” attends the computation of the left grid node, not the right, so soundings and nodes have good correlation. In addition, the distance control of sounding points is different from the regular grid of conventional algorithm. The DTM grid will change with the variation of water depth, as grid spacing is small in shallow water area, big in deep-water area. It guarantees that the model has a good resolution. L≤0.05d
(3)
FIG. 2 DISTANCE CONTROL OF SOUNDING POINTS
Estimation of Depth and Related Uncertainty In DTM computation, uncertainty is inversely proportional to the propagation distance. See the model by the following formula(4): Z1 Z=
1 1 1 1 + Z2 + Zi + ⋅⋅⋅ + Z n DZ TPE DZ TPE DZ TPE DZ TPE 1 1 1 1 + + + ⋅⋅⋅ + DZ TPE DZ TPE DZ TPE DZ TPE 1
2
1
DZ TPE =
2
i
n
i
n
DZ1 TPE + DZ 2 TPE + DZi TPE + ⋅⋅⋅ + DZ n TPE
(4)
n
Where, Z is depth estimate value of grid nodes, DZ TPE is uncertainty estimate value of grid nodes, Z i is real depth value, DZ TPE is the total propagation error of Z i . i
4σ
FIG. 3 DEPTH AND RELATED UNCERTAINTY ESTIMATION OF GRID NODES
If we put Z1 and DZ TPE as node initial value, then Z i and DZ TPE participate in the calculation, finally get Z 1
i
and DZ TPE . When depth data is discrete or has larger gross error, and difference between the estimated value of
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the previous time and the next time is more than four times of the arithmetic mean of the error. Then, we stop the program and recompute it based on the current depth and total propagation error. The model uses the current sounding point to calculate the next soundings, so there may be more than one depth and error estimation on some nodes, as seen in Fig 3. Best Choice of Estimation When there are more than one depth and error estimations on a node, choose the best estimation according to the principles of density and neighborhood. In general, the more sounding points there are, the bigger density it is. Correspondingly, the data can reflect the terrain correctly. So the principle of the density value choice is choosing based on the number of the sounding points. In Fig. 4a, the number of sounding points having estimations: 5, 7, 9, so we choose ‘9’. The principle of neighborhood produces the best estimation based on the correlation of depth. If a node has more than one estimation, we select the estimated value close to the adjacent water depth. In Fig. 4b, the estimations on the node is 120.5,128.5,135.7, we select 135.7 as the estimated value. 120.5
128.5 Density principle
Neighborhood principle
135.0 135.7 a
b
FIG. 4 OPTIMIZED ESTIMATION SELECTION OF GRID NODES
Data processing and analysis Data Source To evaluate the efficiency and quality of the TPEC algorithm, TPEC algorithm and conventional method are used respectively to process the same MBES data of Lau Basin. The conventional method uses man-machine editor to reject gross error and construct DTM by beam inverse weighting algorithm. TPEC algorithm removes gross error automatically by filter based on IHO special order, and builds DTM by the combined estimation of the depth and related uncertainty. Results The results of data processing are shown in table 1, the number of gross error rejected by TPEC is 2 times of the number of gross error rejected by man-machine editor. While the number of nodes constructed by TPEC algorithm is nearly 2 times of the conventional method, the data processing speed of TPEC algorithm is 5 times of the manmachine editor. TPEC algorithm greatly improves the efficiency of data processing. By Using TPEC algorithm to generate DTM, the grid spacing of DTM can change with water depth varying, results in a better resolution. In Fig. 5, there are obvious valleys paralleling to the spreading center on the east side of the spreading valley in TPEC model, while not obvious in general model. And there are multiple small conical seamounts in TPEC model, while there is no seamount in general model. In a word, TPEC algorithm is superior both in efficiency and uncertainty control. TABLE 1 COMPARISON OF TPEC ALGORITHM WITH GENERAL ALGORITHM
Method
Points (number)
Gross error (number)
Grid distance (m)
Nodes (number)
Processing time(h)
TPEC
302242
25127
60-150
28600
1.9
Man-machine editor
302242
12818
150
15000
10.5
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Discussion and Conclusions Currently, multibeam automatic filtering algorithm in processing gross errors has some defects. For example, the simplest method is to set the maximum and minimum depth threshold, but it only fit flat topography. In trend surface model, we can easily mark obvious gross errors, but it’s hard to identify small gross errors. Median filter model can filter abnormal data well, but it also will lead to the loss of the terrain details. The biggest problem is that the existing filtering algorithms are mostly based on statistical characteristics of the data, or we filter data based on regional topography trend without considering the size of the error in the data itself. In this paper, we get the following understanding through the research and application of TPEC algorithm. i) According to the IHO standard, TPEC algorithm eliminates noises automatically based on the total propagated error computation. And it overcomes the defects that man-machine editor is easily affected by the subjective judgment. The data processing speed of TPEC algorithm is 5 times of the man-machine editor. So TPEC algorithm is a considerable choice for processing MBES data. ii) By using TPEC algorithm to generate DTM, the grid spacing of DTM can change with water depth varying, thus the model can offer a good resolution without losing the terrain detail in general algorithm. iii) TPEC algorithm generates depth and related uncertainty estimation at the same time. And also chooses the best estimation according to the principles of density and neighborhood. So the model has a better robustness, and is suitable for the research of complex seabed terrain environment. What’t more, it provides a possible technological method to the study of terrain features in submarine hydrothermal area.
Seamounts like circle cone
Valley paralleling to the spreading center
FIG. 5 COMPARISON OF TPEC MODEL WITH GENERAL MODEL ACKNOWLEDGEMENTS
This study was supported by Public Science and Technology Research Funds Projects of Ocean (201105001) ,the Fundamental Project of Science and Technology (2013FY112900), the National Natural Sciences Foundation of China(4157060145), State Oceanic Administration Youth Science Fund (2010319) and Scientific Research Fund of Second Institute of Oceanography (Grant No. JT1403). REFERENCES
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Calder BR,Mayer LA. Automatic processing of high-rate,high-density multibeam echosounder data,Geochem-GeophysGeosyst,2002,4(6):24-48. First author: Li Shoujun(1977- ), Male, PHD, majors in submarine topography, tectonic geomorphology and GIS. E-mail: 0911guang@163.com Corresponding author: Wu Ziyin(1972surveying and data processing.
), Male, PHD, Professor, majors in submarine topography
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