# Use of a Weighted ICP Algorithm to Precisely Determine USV Movement Parameters
## 1 Introduction  
Heading (HDG), speed over ground (SOG) and rate of turn (ROT) are basic movement parameters which characterize the way a ship's hull moves in relation to the Earth's surface. They are crucial in the decision-making process, particularly when navigating in congested areas, including harbors and rivers. Currently, these parameters are most frequently determined on a ship using a gyrocompass and a log, i.e., navigational instruments whose measuring accuracy, according to the International Maritime Organization (IMO) requirements, is not required to be very high: \"Errors in the indicated speed, when the ship is operating free from shallow water effect and from the effects of wind, current and tide, should not exceed 2% of the speed of the ship, or 0.2 knots, whichever is greater\" [1], \"The follow-up error for different rates of turn should be: less than \(\pm\)0.5\({}^{\circ}\) at rates up to 10\({}^{\circ}\)/s; and less than \(\pm\)1.5\({}^{\circ}\) between a rate of 10\({}^{\circ}\)/s and 20\({}^{\circ}\)/s\" [2], although it determines the precision and the ability to control the ship's movement which, consequently, may affect the navigational safety level. It is therefore reasonable to carry out scientific research aimed at searching for new measuring and data processing methods in order to minimize measuring errors in a ship's movement parameters. For many years, maritime navigation has placed increasing emphasis on the development of methods to determine position and navigational parameters that could offer an alternative to the GNSS system [3]. In the age of the development of unmanned surface vehicles (USVs) whose main tasks increasingly involve independent (autonomous) maneuvering in restricted areas, it is necessary to develop new methods to obtain precise (accurate) navigational movement parameters (in particular the HDG, SOC, course over ground (COG), and ROT) [4; 5]. Basing the USV decision-making processexclusively on the parameters of movement and positions obtained from satellite systems is unjustified, particularly in port basins in which infrastructure facilities and other ships may suppress and reflect the system signals [6; 7; 8]. Another reason why one should not rely exclusively on such solutions is the new techniques of satellite signal jamming and spoofing [9]. A good way to avoid the satellite system inconveniences may be the development of locally operating systems whose actuator is located on a carrier ship, making their operation more difficult to interfere with. A system with a local range of operation needs no special, external infrastructure to generate correct data. Recently, the clear development of devices such as Light Detection and Ranging (LIDAR) [10] has been noted, with increased capacities in terms of the range, accuracy of generated data and the purchase price. Certain devices have a range above 500 m and high accuracy in angle and distance measurements, which enables more widespread use of such devices in sea-going ship navigation. It should also be noted that the measuring capacity of such sensors is not limited by the radar's dead zone at close ranges. On the other hand, such a phenomenon is typical of pulse radars which are commonly used on almost every vessel [11]. This article presents a method for the precise determination of the SOG and COG parameters through processing, using a modified iterative closest point (ICP) algorithm [12; 13; 14; 15] of a horizontal 2D layer of cloud points obtained from LIDAR measurements. The main process is based on the simultaneous localization and mapping (SLAM) method. In simple terms, this is a method allowing a map of an unknown environment to be built, which, after processing, is used for navigating in a particular area. This technique was isolated as a separated area of interest in 1996. The SLAM evolution was described in [16]. SLAM is rarely used in determining the position of surface vessels. Only a few applications of the method in the context of its use on an open sea surface are known [17].