**1. Introduction**

Unmanned underwater vehicles, also known as underwater robots, have developed rapidly over the past few years. These systems supersede previously used methods of the underwater exploration of Earth, such as, e.g., hydrographic measuring units with human crew. The trend in unmanned systems development is toward the execution of underwater tasks, including hydrographical surveys, near the bottom by underwater robots, such as remotely operated vehicles remotely controlled by an operator and autonomous underwater vehicles (AUVs) operated without operator

input. Underwater positioning methods are not keeping pace with the fast development of AUVs and measurement tools. The main global navigational satellite system (GNSS) positioning method for submersible vehicles is limited to situations where the submersible vehicle can raise an antenna above the surface of the water. However, some AUVs need the more independent method of comparative (terrain) navigation via digital terrain models (DTMs) [1–7].

New methods of spatial data measurement using interferometric multibeam echosounders (MBES), high-frequency side scan sonar, and integrated MBES with sonars require new data processing methods. These new methods may also be suitable for creating autonomous navigation systems for unmanned underwater platforms based on the development of comparative navigation, which uses redundant positioning sources based on navigational radar and electronic navigational charts.

Comparative (terrain reference) navigation is an alternative method for position determination where the GNNS signal is unsuitable or unavailable. This type of navigation is based on searching for matches between a reference image prepared for a specific area (reference map) and a recorded image of a specific, small area, recorded in real time and used to generate a fragment of an area to compare with the reference map.

In comparative navigation, the ship's or vehicle's position is plotted by comparing a dynamically registered image with a pattern image. The pattern images can be bathymetric electronic navigational charts (bENCs), digital radar charts, sonar images, aerial images, or images from other sensors, such as magnetometers or gravimeters, suitably prepared for comparison with radar, sonar, aerial, or other images, respectively. The most frequently registered images at the sea are radar images, whereas the pattern is a numeric radar chart generated from topographic and hydrometeorological data or previous radar observations.

Many scientists globally are working on comparative (terrain reference) navigation [8–10]. Most studies have analyzed the shape of the bottom of bodies of water obtained from the depth of the basin. For example, in [11,12] the authors presented an autonomous underwater vehicle optimal path planning method for seabed terrain matching navigation to avoid these areas. In [13] authors present an application for the practical use of priors and predictions for large-scale ocean sampling. The proposed method takes advantage of the reliable, short-term predictions of an ocean model, and the utility of priors used in terrain-based navigation over areas of significant bathymetric relief to bound uncertainty error in dead-reckoning navigation. Another author [14,15] proposes a comprehensive evaluation method for terrain navigation information and constructs an underwater navigation information analysis model, which is associated with topographic features. Similar problems are presented in [16–18]. In [17], a tightly-coupled navigation is presented to successfully estimate critical sensor errors by incorporating raw sensor data directly into an augmented navigation system. Furthermore, three-dimensional distance errors are calculated, providing measurement updates through the particle filter for absolute and bounded position error. All these solutions are time consuming because they use a big data sets. MBES big data processing [19–30] has also been investigated. In [19], authors propose algorithm CUBE (combined uncertainty and bathymetry estimator). A model monitoring scheme CUBE ensures that inconsistent data are maintained as separate but internally consistent with the depth hypotheses. The other method is presented in [29]. The main purpose of the presented reduction algorithm is that, the position of point and depth value at this point will not be an interpolated. In the article, the author focused on the importance of neighborhood parameters during clustering of bathymetric data using neural networks (self-organizing maps).

Big data problems are closely related to the idea of single-beam echosounders measurements [31] and Light Detection and Ranging (LiDAR) [32–38].

The method of comparative underwater navigation presented in the work compares depth area images registered in semi-real time with depth areas in bENCs. The construction of bENCs for comparative navigation has been described previously [39].

A ship's position can be plotted by comparative methods using one of three basic methods [40].


In addition to ANN, the literature also provides other solutions that can be used in comparative navigation. One possible solution is the application of a system based on an algorithm of multi-sensor navigational data fusion using a Kalman filter [40]. The said solution is intended to be implemented in a navigational decision support system on board a sea-going vessel. The other possible solution is comprehensive testing and analysis of a particle filter framework for real-time terrain navigation on an autonomous underwater vehicle [41].

Deterministic methods include comparative navigation, which is mainly performed using distance and proximity functions, as well as correlation and logical conjunction methods [42].

The idea of using ANN for position plotting is particularly intriguing. The teaching sequence of the ANN consists of registered images correlated with their positions. Teaching is performed in advance and can take as long as necessary. During the use of the trained network, the dynamic registered images are passed to the network input, and the network interpolates the position based on recognized images closest to the analyzed image. A merit of this method is that the network is trained with real images, including their disturbances and distortions, which are similar to those that are used in practice. The main problem with this method is that it requires previous registration of numerous real images in various hydrometeorological conditions, and the processing and compressing of images. After compressing the analyzed image, a teaching sequence for the neural network designed to plot the vehicle's position is constructed. The task of the network is to construct a mapping function associating the analyzed picture with the position.

Regardless of the method of comparative navigation, the basic problem is registration, filtering, and reduction of measurement data.

The standard methodology of the development of MBES big data, in general, consists of following stages: (1) Obtaining a whole 3D multibeam sonar data set, (2) pre-processing (including, among others the filtration process, noise removal and data reduction), (3) main processing (including, among others, DTM construction and development of bathymetric maps), (4) visualization, (5) analysis.

In this work, we present a new approach of acquiring and simultaneously processing a set of bathymetric observations. This is a different approach than presented in the literature on the subject [19,27,29]. The approach includes fragmentary data acquisition, and fast reduction (the optimum dataset method—OptD [35]) within acquired measuring strips in almost real time, and generation of DTMs. The OptD method was modified for this purpose. This modification relies on introducing in the OptD method a loop (FOR instruction) for fragmentary data processing. All these processes in our approach were performed in a first stage under acquisition of data, during measurement, whole data set was not obtained, but a fragment of the data set. The approach was considered where measuring strips were obtained without overlay and where measuring strips had overlay between each other. The proposed approach was compared with the method that uses full sets of bathymetric data. The results showed that our approach quickly obtained, reduced, and generated DTMs in almost real time for comparative navigation.

The originality of this paper was a new approach for 3D multibeam data processing. Reduction and 3D model generation in almost real time is an important research subject in the context of comparative navigation. The navigators need to have, in short time, the results of measurement for opportunity to compare generated isolines map (or DTMs) with existing maps (or DTMs). In this way, the navigators can detect differences in depth, and recognize obstacles at the bottom of the water reservoir.
