2.3.4. Reduction

The methodology v1 test area was divided into strips with no overlay between them. The scheme for this division (methodology v1.1) is shown in Figure 4a and that for methodology v1.2, in which strips are selected with overlay, is shown in Figure 4b.

**Figure 4.** Scheme of test area division into strips (**a**) with and (**b**) without overlay.

After the measurement was completed, we obtained a set of observations (Figure 5).

**Figure 5.** Whole test area (694,185 points).

The statistical characteristics of the datasets obtained by methodology v1 are shown in Table 1. Each dataset represented an individual strip, pi characterized by number of points in the dataset, and the minimum and maximum height of points. Additionally, information about range and standard deviation of height was included. They allowed us to initially assess the fragments of measured areas.


**Table 1.** Statistical characteristics for datasets in methodology v1. (Where: H—height, R—range, STD—standard deviation).

In methodology v2, the original dataset was optimized using the OptD method. As in the previous case, the test area was divided into strips with and without overlay, and the variants are shown in Figures 6 and 7.

Figures 6 and 7 show the difference between methodology v2.1 and v2.2. In the case of v. 2.1, there are more points where the strips contact each other than in the middle of the strips. However, in the case of v2.2 more points are in the entire overlay area.

The appearance of the whole dataset after reduction conducted using the same optimization criterion (*c* = 2%) is shown in Figure 8. The time required for the reduction of the whole set to 2% of the original set was about 20 s, which is acceptable for comparative navigation.

**Figure 6.** Scheme of the test area division into strips without overlay (methodology v2.1).

**Figure 7.** Scheme of test area division into strips with overlay (methodology v2.2).

**Figure 8.** Optimized test area (13,976 points).

In the case of reducing the whole data set presented in Figure 8, we observed that the points remained in characteristic places of the studied area.

The statistical characteristics of the datasets obtained by methodology v2 are shown in Table 2.


**Table 2.** Statistical characteristics for datasets in methodology v2. (Where: H—height, R—range, STD—standard deviation).

The average data acquisition time in strips of 20 m at a measuring unit speed of 4 knots was about 20 s. The reduction within strips without overlay took 4–7 s, whereas for strips with overlay it took 6–9 s. The data processing time was much faster than for that of obtaining one strip.

#### **3. Results**

Each dataset representing strips pi and poi was used for DTM generation. The DTMs generated for strips p1, p2, and p3 are shown in Figures 9–11, respectively. Next to DTMs, corresponding to them isoline maps are attached. They show, how the fragment of measured bottom of the lake look alike, when methodologies v1.1 and v2.1 were applied.

**Figure 9.** Isolines1v1.1 and digital terrain model (DTM)1v1.1, and isolines1v2.1 and DTM1v2.1 generated for strip 1 (p1) by methodologies v1.1 and v2.1, respectively.

**Figure 10.** Isolines2v1.1 and DTM2v1.1, and isolines2v2.1 and DTM2v2.1 generated for strip 2 (p2) by methodologies v1.1 and v2.1, respectively.

The generated DTMs and isolines maps were more readable in the case of v2.1. Fewer data has made the isoline image easier to read. Visibility of places with great depths was definitely better. Therefore, it was easier to assess the nature of the bottom from the DTMs generated by methodology v2.1. The statistical characteristics of the DTMs are presented in Table 3. As can be seen, DTMs from both methodologies v1.1 and v2.1 do not show significant statistical differences. In height, observed differences usually were about 2–3cm. For DTM4 and DTM6 they equaled −6 cm and 5 cm, respectively. This may indicated, on existence of some items on the bottom of the lake, that reduction allowed us to notice. The standard deviations calculated for DTMs generated from original dataset was

usually smaller, about 1 cm in comparison to standard deviations corresponding to DTMs obtained from reduced datasets.

**Figure 11.** Isolines3v1.1 and DTM3v1.1, and isolines3v2.1 and DTM3v2.1 generated for strip 3 (p3) by methodologies v1.1 and v2.1, respectively.


**Table 3.** Statistical characteristics forDTMmv1.1 andDTMmv2.1. (Where: H—height, STD—standard deviation).

The total generation time for DTMv1.1 was 159 s, whereas that for DTMv2.1 was 126 s.

The DTMs generated for strips p1, p2, and p3 are presented Figures 11–14.

**Figure 12.** Isolines1v1.2 and DTM1v1.2, and isolines1v2.2 and DTM1v2.2 generated for strip 1 (po1) by methodologies v1.2 and v2.2, respectively.

**Figure 13.** Isolines2v1.2 and DTM2v1.2, and isolines2v2.2 and DTM2v2.2 generated for strip 2 (po2) by methodologies v1.2 and v2.2, respectively.

Analyzing Figures 12–14, it can be stated, as in the case of v2.1, that methodology v2.2 gave better results in terms of visibility and effectiveness of generated isolines maps and DTMs. In the figures showing the results of processing with the new v2.2 methodology, it was easier to read shallow and deep places. Methodology v1.2 figures were hard to read, and the isolines map were difficult to analyze.

The statistical characteristics of the DTMs are presented in Table 4.

**Figure 14.** Isolines3v1.2 and DTM3v1.2, and isolines3v2.2 and DTM3v2.2 generated for strip 3 (po3) by methodologies v1.2 and v2.2, respectively.


**Table 4.** Statistical characteristics forDTMmv1.2 andDTMmv2.2. (Where: H—height, STD—standard deviation).

The generation time for DTMv1.2 was 260 s, whereas that for DTMv2.2 was 201 s. Analyzing the statistical characteristics of DTMs obtained in methodologies v1.2 and v2.2, the trend can be observed. DTMs generated on the basis of the reduced dataset were about 1 cm higher than corresponding DTMs obtained from original measurement data.

DTM 100% and DTM 2% were also generated (Figures 15 and 16).

**Figure 16.** Isolines2% and DTM2%.

In Figures 15 and 16, the conclusion about a more readable isoline map was repeated. Figure Isolines2% (Figure 16) shows areas of depth in the test area better than Isolines100% in Figure 15.

The statistical characteristics of the isolines2%, DTM2%, isolines100% and DTM100% are presented in Table 5.


**Table 5.** Statistical characteristics for DTM100% and DTM2%. (Where: H—height, STD—standard deviation).

The total development time of the whole set was 508 s, consisting of 240 s acquisition time of the whole set and 268 s DTM100% generation time. The total development time of the reduced set was 410 s, consisting of 240 s acquisition time of the whole set, 20 s reduction of the set to 2% of the original set, and 150 s DTM2% generation time.

To assess how the DTM strips fit together, the height differences at the corresponding nodes between adjacent strips were calculated. The results for methodologies v1 and v2 are shown in Tables 6 and 7, respectively.


**Table 6.** Height differences between strips in methodology v1. (Where: H—height, STD—standard deviation).

Both methodologies gave similar results; the differences between almost all the statistical characteristics were close to zero. However, the difference for ΔH min. was larger (from −0.25 to 0.14 m) because some points representing an object with various values of H may be near the area where adjacent strips are coincident. Therefore, the content of the set processed by the OptD method was different. Nonetheless, data reduction by the OptD method made the main features in the modeled areas clearer (Figures 9–14).


**Table 7.** Height differences between strips in methodology v2. (Where: H—height, STD—standard deviation).

The statistical characteristics of the height differences for methodologies v1 and v2 are shown in Tables 8 and 9, respectively.

**Table 8.** Statistical characteristics for height differences between strips (methodology v1). (Where: H—height, STD—standard deviation).


Table 10 shows the differences between statistical characteristics for height differences between methodologies v1 and v2.

The differences in statistical characteristics for height differences between using strips with and without overlay for methodology v2 are shown in Table 11. The majority of values were from −0.01 to 0.08 m, indicating that there were no significant differences between the approaches. However, the processing time for strips with overlay was longer than for strips without overlay. Therefore, the methodology based on data reduction and the variant that uses strips without overlays are suitable for depth area calculation.


**Table 9.** Statistical characteristics for height differences between strips (methodology v2). (H—height, STD—standard deviation).

**Table 10.** Differences between statistical characteristics for height differences between methodologies. (Where: H—height, STD—standard deviation).


**Table 11.** Differences in statistical characteristics for height differences between strips with and without overlay. (Methodology v2). (where: H—height, STD—standard deviation).


#### **4. Discussion**

The new approach of methodology for processing MBES big data proposed by the authors was based on fragmentary 3D multibeam sonar data processing conducted in almost real time. All stages of standard methodology were performed not after acquisition of the whole dataset but in time, the fragments of data were acquired. While the one fragment of data was processed (execution of all stages: Reduction, DTM generation, isolines generation, analysis) the next fragment was obtained.

The most important step during the processing was reduction, because a reduced number of data allowed faster 3D bottom model generation, which can be compared with other types of data within terrain reference navigation.

Various tests can be found in the literature to speed up the calculation time of big data, e.g., parallel programming can be used with compute unified device architecture (CUDA). Using CUDA in processing of big datasets was tested, among others, by [47–49]. Within these works, tests on the possibility of using CUDA to generate a digital elevation model were performed. To speed up calculations there was also possibility to use artificial neural networks for modeling sea bottom shape, as these also continually implemented a surface approximation process [50,51]. These methods processed the entire dataset upon completion of the measurement. The use of these methods in almost real time was difficult, so in the new development methodology, we proposed using the OptD method.

The time needed to reduce the 3D multibeam sonar dataset based on OptD method with optimization criterion of 2% in strips was 4–7 s, whereas for strips with overlay it took 6–9 s. Such time can be considered as insignificant compared to the entire time needed for processing the whole data set. Moreover, the benefit of the reduction was a shorter time needed to generate the model. The times were as follows:


Thus, the longest time was needed to generate a DTM100%. In all other cases, the time was shorter. The shortest time was needed for DTMv2.1 generation (the version with strips without overlay and with processing based on OptD method). The processing time depended on performed computer equipment and software. It is important, however, that the reduction algorithms, whose task is to speed up the development time, were uncomplicated and easy to implement.

The proposed solution also enables ongoing control during measurement. Acquired data were observed and initially analyzed in almost real time, therefore, if there was need, measurement can be repeated, completed or omitted in the selected area. Therefore, the presented approach can save time, labor, space on disks, etc.

#### **5. Conclusions**

For comparative navigation, data from MBES was processed by a new methodology which consisted of the OptD method to reduce the number of observations and generate DTMs representing measured fragments of the bottom of the area in almost real time. The data was then used to perform depth area calculations. The methodologies were based on fragmentary processing of observations organized in strips with or without overlay. Our analysis showed that using strips without overlay and with reduction by the OptD method (methodology 2.1) was an efficient, fast way to obtain data appropriate for 3D model generation that can be compared with a reference chart, such as bENCs. A major advantage of our method is that only points containing relevant information about depth differences are used for DTM construction and unimportant points belonging to flat areas are omitted. The resulting depth model of the bottom forms the first layer of a multi-layered model of the reference image bottom, which in many methods there is the only one layer. For comparative navigation based on the depth model above the flat bottom, the system cannot determine the position and additional information is required. For example, subsequent layers could be a bottom object layer and a layer containing information about the type of bottom. The layer containing characteristic points and bottom objects will use the same reduced points as the depth layer, allowing the analysis of data in semi-real time.

The general conclusions can be formulated as follows:


**Author Contributions:** Conceptualization, A.S. and A.S.-Z.; methodology, W.B.-B.; bibliography review, A.S. ˙ and W.B.-B.; acquisition, analysis, and interpretation of data, A.S., W.M. and M.W.; writing—original draft preparation, A.S., A.S.-Z. and W.B.-B.; writing—review and editing, A.S., W.M. and M.W. ˙

**Funding:** This study was funded by the European Regional Development Fund under the 2014–2020 Operational Programme Smart Growth as part of the project "Developing of autonomous/remote operated surface platform dedicated hydrographic measurements on restricted reservoirs" implemented as part of the National Centre for Research and Development competition, INNOSBZ.

**Acknowledgments:** National Centre for Research and Development No. POIR.01.02.00-00-0074/16.

**Conflicts of Interest:** The author(s) declare(s) that they have no conflicts of interest regarding the publication of this paper.
