## 2 Factors Influencing Ultrasonic Signals  
There are two basic principles of realizing an ultrasonic sensor for measuring the level in liquids [1; 25], namely at the edge of the vessel, where the distance from the surface is measured, or at the bottom of the vessel, where the measurement is made directly in the liquid. The bottom-of-vessel measurement method is more technically challenging due to the presence of the sensor directly in the liquid but is more precise. The propagation of the ultrasonic signal in liquid is faster (approximately 1500 m/s in water) compared to the speed of propagation of ultrasound in the air (approximately 330 m/s).  
Liquids with higher density have a lower damping coefficient, which affects the magnitude of the measured signal, as described in [6]. The temperature and pressure of the liquid have a significant effect on the accuracy of the ultrasonic measurement [21; 22], and they are the parameters we investigated and whose interdependence we analyzed. The aim of the proposed analysis is to standardize the received envelope of the ultrasound signal so that the measurement is as independent as possible of the temperature and pressure of the liquid, as experimentally verified in the works of [21; 26]. Statistical correlation and regression analysis are also used in other fields, for example in the analysis of motor bearings [27], the working conditions of photovoltaic panels [28], or in predictions [29].  
The principle of ultrasonic measurement itself is to measure the time it takes for an ultrasonic pulse to travel from the transmitter to the surface and back to the receiver. Based on this time, the height of the liquid level is then calculated. This is called the Time of Flight (ToF). This principle is commonly used by scientists [30; 31; 32; 33; 34]. Support Vector Machine (SVM)can be also used for signal processing [35]. However, this solution is more challenging in terms of implementation and evaluation of results. [PERSON] et al. [36], in their publication, compared different methods for ToF echo signal processing based on Defect Peaks Tracking Model (DPTM) and were able to reduce the auto-diagnostics error to 0.25%.  
The most important property that affects the behavior of waves is the principle of superposition--the resulting state is the weighted average of all partial states. The deviation at any place (and time) is given by the sum of the deviations of all occurring waves at that place (and time). The result is interference phenomena, for example, in [37].  
Mechanical waves can be divided according to several criteria. When a wave propagates gradually from its source, it is referred to as a progressive wave. A special case is standing waves, where the composition of the wave is a gradual combination of forward and reflected waves. Then there are places where the middle one does not oscillate at all (nodes) and places where it oscillates with maximum amplitude (oscillations) [38].  
Another important wave character is the direction types of motion of the oscillating particles. If they oscillate perpendicular to the direction of wave propagation, we call them transverse waves. If the waves oscillate in the direction of movement, they are longitudinal waves [37; 38].  
The last important factor is the coherence of the waves--coherent waves are characterized by a perfect course (still the same frequency, speed, phase, amplitude, and direction)--their deviation and phase are not affected by any random influences. In this case, we know the parameters of the wave anywhere, we can determine them anywhere. By contrast, incoherent waves retain their regular character for only a short time. From the parameters of a wave in a certain place, we can determine its behavior only near this place. In practice, completely coherent waves do not occur. However, at short distances, they approximate the real case well [37].