## 1 Introduction  
At the beginning of their adventures at sea, people only went out during the day for safety reasons. With the invention of the compass, sailors began to use the stars and draw maps. The growing demands of sailors, travelers, and researchers were the impetus for developing depth measurement methods and techniques that have evolved over the centuries from very simple techniques to the complex and technologically advanced. For hundreds of years, the only possible way to measure the depth of seas and oceans was a calibrated hemp rope terminating in a weight lowered from the side of the vessel. Until World War II, most depth measurements were made with the use of a lead line. That method was not only inaccurate but also very time-consuming. World War I and II saw the rapid development of echosounders and simple sonar. Since then, the need for updated nautical charts has increased. This was dictated by the increase in traffic in the coastal zone, the growing popularity of recreational shipping, and the continually developing world maritime trade. The necessity to update the charts forced the state hydrographic services to conduct systematic marine surveys using single-beam echosounders (SBESs) within territorial waters. Hydrographic vertical echosounders became increasingly available, which positively impacted the safety of navigation and the accuracy of nautical charts [1; 2]. Scientists were interested not only in the depths directly under the ship's hull but also those at some lateral distance from it. New military and defense challenges and cognitive needs have prompted scientists and engineers to start work on new technological solutions in sea bottom research. These efforts led to the development of a new technology, multi-beam echosounders (MBESs), which were initially a secret project of the US Navy in the 1950s [3; 4; 5]. The last three decades have seen a dynamic advancement in survey technologies. Multi-beam echosounders providing full seabed coverage have become very popular. Their attractiveness is associated with an increased quality and quantity of data as well as much greater coverage. Measurements obtained via this method are used in many scientific fields, including seabed imaging and classification [6; 7; 8; 9; 10], learning about the processes occurring in bottom sediments [11; 12; 13], identifying geotechnical hazards and gas leakages from the seabed [14], and exploration of the marine habitat [15; 16; 17; 18]. MBES is widely used in the operations of laying of trans-oceanic telephone cables, exploration and drilling for the oil extraction industry, locating underwater mineral deposits, and learning about Earths geological processes [19; 20; 21; 22]. These swath systems are also successfully used in the study of underwater cultural heritage [23; 24]. The primary and most common application of modern multi-beam echosounders is the multi-point and multi-directional measurement of depth values for the purpose of navigation safety and marine cartography [25; 26]. The ability to record the depth simultaneously via several hundred points on the sea bottom together with their associated positions is undoubtedly an advantage of this device, which has been noticed by scientists of various specialties [27; 28; 29; 30; 31; 32]. The authors emphasize not only the wide coverage of MBES bathymetric measurements but also the susceptibility of the external beams of the multi-beam systems to various factors that reduce depth measurement accuracy. Hydrographic surveys executed with the use of MBES are carried out, among others, to ensure safety of navigation through developing nautical charts and marine publications and updating digital databases of underwater objects [33]. Each survey requires detailed planning and thorough preparation, especially since the costs, due to the equipment used, are incomparably higher than for land measurements [34; 35].