=Paper=
{{Paper
|id=Vol-3137/paper14
|storemode=property
|title=Formation of a Method for Estimating the Error of Determining the Coordinates of the Source of a Sound Anomaly
|pdfUrl=https://ceur-ws.org/Vol-3137/paper14.pdf
|volume=Vol-3137
|authors=Alexandr Trunov,Zhan Byelozyorov,Serhii Maltsev,Maksym Skoroid
|dblpUrl=https://dblp.org/rec/conf/cmis/TrunovBMS22
}}
==Formation of a Method for Estimating the Error of Determining the Coordinates of the Source of a Sound Anomaly==
https://ceur-ws.org/Vol-3137/paper14.pdf
Formation of a Method for Estimating the Error of Determining
the Coordinates of the Source of a Sound Anomaly
Aleksandr Trunov 1, Zhan O. Byelozyorov 1, Serhii I. Maltsev1, Maksym Skoroid1
1
Petro Mohyla Black Sea National University, Mykolaiv, Ukraine, 68 Desantnikov, 10, Mykolaiv 54000,
Ukraine.
Abstract
The methods of determining the coordinates of the source of a sound anomaly are
considered. Improving the quality of the equipment of the computerized systems of
microphones for registration of intensity of noise was done by the method of Monte-Carlo
simulation. The computing for different components and parameters of the system and
evaluation of error for comparison of the efficiency of four algorithms was done. As a result,
consideration set a task conduct simulation of random processes that form a random
component of error into computer systems of microphones and movable unmanned aerial or
ground vehicles as a source of a dynamic error. To experimental study the propagation of the
front of SA wave, the nature of its attenuation, and physical modeling of the random position
of the point of the source SA, it was proposed to use a rotary platform on thrust bearings
driven by a stepper motor. The model of rotation control of platform in Matlab by using
especially a hybrid two-phase stepper motor model is considered. The comparative analysis of
estimates of the maximum possible error of algorithms for symmetric and asymmetric
echograms was provided. On the bases of analyzing the algorithms for recognizing and
determining the momentum of input time of complex echograms was done The
recommendation for conditions and advantages for algorithm application was formulated.
Keywords 1
Sound Anomaly, coordinates, random simulation, estimating error, static, dynamic
1. Introduction
The strategy of offensive and defensive actions demonstrates the success of the use of unmanned
aerial vehicles and anti-tank systems. These results show that the paradigm of success is dominated by
the number of personnel and tanks with artillery successfully changing the paradigm of automation
and implementation of computer-integrated technologies, which aims to maximize the preservation of
personnel [1-3]. However, its further development and practical application require the development
of small-sized means of determining the coordinates of the sound anomaly (SA) [4-5] and ensuring
the assessment of the maximum possible error [6-9]. This task is becoming especially important and
relevant for devices installed on mobile devices such as unmanned aerial vehicles (UAVs) or ground
unmanned vehicles (GUVs) or ground unmanned combat vehicles (GUCVs) [1-3]. In addition to
these, the possible use of small-scale means of determining the coordinates for further improvement
of monitoring systems for civilian use [4-5] requires the development of methods for estimating the
maximum possible error and the formation of measures to reduce it.
2. Analysis of recent publications
The work [1] reveals the advantages of using UAVs for compatible video and audio
CMIS-2022: The Fifth International Workshop on Computer Modeling and Intelligent Systems, Zaporizhzhia, Ukraine, May 12, 2022
EMAIL: trunovalexandr@gmail.com (A. Trunov); zhan.byelozyorov.@gmail.com (Z. Byelozyorov); mserg92@gmail.com (S. Maltsev);
hahido71@gmail.com (M. Skoroid)
ORCID: 0000-0002-8524-7840 (A. Trunov); 0000-0002-3216-8153 (Z. Byelozyorov); 0000-0001-9094-5259 (S. Maltsev);
0000-0003-1641-9124 (M. Skoroid)
© 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
reconnaissance, which complement each other in information and allows you to enter this information
in the electronic fire card of the department. However, despite the advantages of such implementation
of computer-integrated technologies, the complication of effective use of metrological measurement
scheme used in this article is the lack of binding of coordinates of the carrier and device for
determining the coordinates of the source SA to one basic coordinate system. In addition, it is
unreasonably assumed that the error of the coordinates of the center of gravity of the UAV, as
determined by GPS, is zero, and its relative orientation does not contribute to the magnitude on the
error. In work [2] the necessity is highlighted and the reality of NBR application is demonstrated.
However, during the operation of the GUAV there will also be a problem of determining the
coordinates and its spatial orientation. In [3] there is also the problem of estimating the error and its
impact on the result of reliable data entry into the electronic card of the fire department. Thus, the
development of acoustic means of detecting a shot from a small weapon, their classification and
formation of design requirements are presented in [4]. However, these issues of choosing a
metrological scheme and determining the error were not raised and resolved. The development of
devices for wireless monitoring and recording the coordinates of the shot as one of the examples of
SA [5] opens up new opportunities for further improvement of equipment. Thus, [6] forms a method
for estimating the error of measuring the angle directly to the target by a distributed system of sound
artillery reconnaissance. However, the error of determining the coordinates of SA is ignored. The
methodical error of direction-finding target by sound artillery reconnaissance system [7] is not taking
into account the motion of computer system of microphones.
Peculiarities of the application of the sound metric complex in the deployment at short distances
with simulation as a combat application, which determines the priority tasks of data reliability and
accuracy of the coordinates of the source SA [8]. The proposed method of the evaluation value is
applied for Polish aviation in the SBAS APV landing procedure [8]. The experience and results of its
implementation into Position Dilution of Precision are demonstrated and compared for the two air
tests in Dęblin and Chełm [8].
Analysis of the reasons and factors for the formation of error in the processes of sound
reconnaissance or other types of SA shows that further expansion of the scope of application with the
use of mobile vehicles will only increase the maximum possible error [9]. The article shows
preliminary results of EGNOS Safety of Life service performance in Dęblin in comparison to the
results obtained in Olsztyn [9]. The main parameters characterizing a navigational system i.e.
accuracy, integrity, continuity, and availability were analyzed in detail [9]. The experience can have
to consider as a basis to assess the possibility of implementing the EGNOS APV approach and
landing procedures in Dęblin and Olsztyn [9].
The useful contribution to the formation of causes and quantification of error is presented in [10]
for a multilevel learning approach based on B-splines for the localization of sound sources. In [11] the
algorithm and the process of automatic determination of microphone coordinates are presented. The
quality of the created hardware, which shows the tendency to miniaturize and integrate single-chip
single-board computers, leads to the spread of examples of use in the rehabilitation of the military,
working in high-noise areas [12]. The second success is the use in flexible robotic systems [13]. A
special role was played by successes in the development of elements of the CS in the robotic systems
of navigation units and positioning of production elements of flexible systems [14].
Enhancement of methods and modernization of means of study opportunities to improve the
accuracy and reliability especially in-flight due to geometric calibration of the spacecraft imaging
complex using known and unknown landmarks are demonstrated in works [15]. The constructing
dynamic scenarios in the work of navigation geographic information systems based on the principles
of sound location is also improved based on the development of CS elements [15] and requires
comprehensive accounting and modeling of all components that form the error of the device as a
whole.
Thus, the search for the causes of methodological and random errors in mobile monitoring systems
by UAV, GUV and GUCV has emerged as an unsolved problem, due to growing needs for accuracy
assessment and application requirements.
Thus, the availability of innovative hardware [5], which has been created recently, will contribute
to the formulation and solution of the problem of developing a perfect metrological scheme and
method of correctly estimating the maximum possible error.
3. Purpose and objectives of the study
The aim of the work is to improve the quality of the equipment of the CS of microphones of
registration of SA, by simulation, accounting for components that form the error of its evaluation and
the introduction of algorithms that reduce it.
To achieve this goal, the following tasks were set:
- Set a task and conduct simulation of random processes that form a random component of error;
- Carry out a comparative analysis of estimates of the maximum possible error of algorithms for
symmetric and asymmetric echograms;
- To analyze the algorithms for recognizing and determining the time of complex echograms.
4. Statement of the problem of modeling and research of the influence of
the algorithm on the value of the random component of the maximum
possible error.
The echogram recordings that formed sound simulators were used as a source of data material [5].
The methods of error estimation theory, probability theory, normal distribution, Monte - Carlo,
recurrent approximation and simulation in Matlab methods were used to solve the research problems.
4.1 Statement of the problem of simulation modeling of random processes
that form a random component of error.
The CS consisting from four microphones was considered, each of which is located at the vertices
of an equilateral pyramid with an equilateral triangle at the base [5]. A connected Cartesian coordinate
system is chosen. Its starting point O is taken so that it coincides with the point of intersection of the
three bisectors of the triangle base AKD. In some cases, it was assumed that the fourth microphone is
turned off, then the pyramid degenerates into a triangle. The scheme of arrangement of microphones
as point and stationary receivers is presented in fig. 1.
Figure 1: Scheme of four microphones location as point receivers
Next, we assume that SA are point and stationary sources. Let us denote by the letter C the point
where the source SA is located. When the source is shifted to the point C’, the rays CB and C’B form
an angle CBC’, which changes randomly, which is described by the normal law of Gaussian density.
Under these conditions, as indicated, the range of change of the angle CBC’ will be a limited interval
[-5 / 6π, 5 / 6π]. In the simulation, the intermediate value of the angle CBC’ was calculated from this
range by the expression:
CBC 2 k i , (1)
where k i - is a random number evenly distributed in the interval [0, 1].
The angle ABC' is calculated by eq. (1) as a random variable and forms the elements of the
sample:
ABC 180 CBC 30 150 CBC . (2)
The distance from the wave front to the microphone will also be a random variable and will be equal
to:
AL r 2 2ra cos ABC a 2 r . (3)
In [5-9] it was assumed that the front of the acoustic wave during propagation did not change the
amplitude, and hence the intensity of the wave. This assumption led to the formation of an error in
determining the coordinate SA. t was mainly supposed in recent works that the amplitude of the
intensity of the wave is inversely proportional to the square of the distance between the sound source
and receiver. As a result of this assumption, the intensity of the wave recorded by the first microphone
will change its values when fixed by subsequent microphones depending on the distance to the source
of SA. As a result of such attenuation, the amplitude of intensity of the wave will change by:
1 1
i I max 2. (4)
r AL r
2
For scientifically based choice of equipment for experimentally studying the propagation of the SA
wave, the nature of its attenuation and modeling the random position of the point of origin of the
source SA, it was proposed to use a rotary platform on thrust bearings driven by a stepper motor to
position determine by eq. (1)-(4). The Matlab's model of stepper motor control is implemented using
specially a hybrid two-phase model.
The input data as a specified parameter was changed in the dialog box in accordance
experiment program as selected from the specific data. Each of the motor phases can be powered by
two PWM converters on H-bridge MOS transistors. The auxiliary DC source is generated by a DC
voltage drop in range from 12 to 28 V. Two not connected controllers independently measure and
control currents by comparators. The MOSFET drives signal also are referenced by these controllers.
The current pulsation is controlled by the hysteresis band of the comparators. In the formation of
frequency-modulated output signals, their variable is selected depending on the parameters of the
engine and generated by the simulation algorithm.
The single-phase excitation scheme, the formation of a rectangular voltage drop pulse with
the specified parameters of amplitude and time length according to the values specified in the dialog
box makes such a scheme convenient and easy to conduct experimental simulations based on Monte
Carlo simulation. The motion and rotation position of the stepper motor rotor is controlled by STEP
and DIR input modulated DC voltage from the output Signal Builder unit. In accordance with values
from the range, 0 to 2 A and 0 to 500 steps/s in correspondence value are chosen in dialog mask will
be selected current amplitude and step speed. In the fig. 2 are shown an example STEP and DIR input
and on fig. 3 is shown the oscillogram of shaft rotation. This oscillogram demonstrates the possibility
to modulate the area of growth, of the constancy and of the fall.
Figure 2: Appearance of signals for stepper motor control
The cover of the oscillogram fig.2 as time function is shown how a set of values 0 and 1 in
STEP and DIR output from the Signal Builder effected on the character of the output signal: 1.0 a
positive value initiates the rotation of the motor; a zero value stops the rotation. The DIR generally
controls the direction of rotation. A positive value (1.0) imposes a positive direction, and a zero value
initiates the opposite rotation. The operation of the stepper motor drive is illustrated by the main
characteristics of the signals: voltage drop, current, torque, angular position, speed, and time
decrement. Each of these characteristics a function of time displayed on the Scope unit.
For simulation was performed fixed decrement of time 1 μs. As was determined by the
analysis of the results of the experiments this value is quite good enough because provides acceptable
accuracy for PWM. To distinguish higher PWM accuracy is required, a decreased decrement of time,
but for this case, the simulation will be so slower. The one type of realized signal applied to the
engine are shown in Fig. 2. The process of rotation of the rotor by a stepper motor in Matlab is
displayed as an oscillogram: the angle defined in degrees as a function of time. An example showing
the reaction to random numbers of the angle of rotation of the platform is presented in Fig. 3. The
engine from the initial position begins to rotate the rotor clockwise to a time of 0.105 ms, then fixed
its position for 0.05 ms, and 0.155 ms changes the direction of rotation counterclockwise to 0.205 ms,
and then fixed again..
Figure 3: Oscillogram of shaft rotation
Such fragments of the presented movements correspond to a random set of numbers generated by
simulation. Thus, the simulation of the rotational movements of the platform confirms the suitability
of the system, which is proposed for physical modelingThus, the error resulting from the hypothesis
of intensity constancy, causes an error in determining the time according to the echogram:
i
t (5)
i i a
However, if the CS of the microphones is located on the UAV, the coordinates of which are
determined by the GPS with an error, then due to the movement there are additional components that
should be considered together with the static error.
Consider the case of monitoring and control UAV when the physical field wave intensity is scalar
and inhomogeneous. In this case, the error of its measurement is determined in the first approximation
by field fluctuations and sensor properties:
r rg 3 i
i gradi vi tnp FCT l lg vi tnp iCT , (6)
2 2 2 l max max
where r – generalized coordinate, l – coordinate in the direction of greatest intensity increase, l g –
maximum size of the measuring part of the microphone in this direction, vi – UAV speed, t np - signal
conversion time, іCT – static sensor intensity error.
The last expression shows that the error of determining the intensity field using sensors located on
the UAV depends not only on the static error іCT , the value sensor, but also on the time constant,
the error of the speed sensors, and hence the acceleration. The latest shows that inflated requirements
for static error of sensors are not always justified. In addition, it is possible to reduce this component
of the error by reducing the size of the sensor as an averaging zone. Despite the increase in error, the
advantage of this system is that due to its installation on an inexpensive UAV, it is relatively
inexpensive and maneuverable and durable. The latter allows you to read data at different heights.
This fact allows us to obtain information bypassing the natural terrain and other obstacles, such as
trees, buildings, etc., while the UAVs themselves can be at a safe distance and height and even in the
rear, both outside the affected area and over enemy positions.
4.2. Comparative analysis of estimates of the maximum possible error of
algorithms for symmetric and asymmetric echograms
The formation of the algorithm for determining the time of the phases of echograms according
to the sound time series, which are registered by different microphones, is the main source of errors
[5-9] as a static component. In this regard, it was determined to develop a key element of the general
algorithm of the module program [5]. The task of the module is to establish conditions that ensure the
uniqueness and uniformity of fixation of the identical moment of time in different echograms of one
SA. Consideration of SA, in the form of a long-term function of intensity change, leads to the
hypothesis of phase invariance of any of its points during propagation. Based on the above, it was
assumed that such an echogram point was found, and there is an unambiguous relationship to
determine it. Based on one of the conclusions of [5] on the calibration procedure, as a tool to expand
the functions and capabilities of the monitoring CS, a four-point schedule using the method of
recurrent approximation (MPA) was used. According to the expression of the analytical series of
MPA [5], the approximate value of the time of entry of the acoustic wave is calculated. In the case
where the discrepancy between two consecutive moments of time does not satisfy the required
accuracy, the approximation is repeated until the required convergence is reached.
Thus, the introduction of the intensity of the SA as a continuous function that is integrated with
the square, the norm of which allows several ways to determine the characteristic phase according to
the calibration of multipliers λωi, as one that uniquely determines the time of registration. Analysis of
the results of comparing the amplitude of the wave and the norm, the center of gravity or the relative
location of the point of length as an unambiguous criterion on which to base the algorithm for fixing
SA is set as one of the most important tasks to minimize error.
To establish practical recommendations for the choice of the algorithm for fixing the time of
entry of the same phase of the wave into the microphone, simulation modeling was used, in particular
the Monte-Carlo method. When placing the microphones at the vertices of an equilateral triangle at a
distance of 0.6 m and a distance of 100 m from the event, the magnitude of the error was analyzed. A
simple SA, represented by the triangular law of intensity distribution, with symmetric and asymmetric
law of change of intensity in time and their composition, was considered. The distributions and
intensity parameters of several examples are given for symmetric dependence in table 1 for
asymmetric in table 2, and for the composition in table 3.
Table 1
Dependences of intensity distribution on time for symmetric SA
№ Relative time, Relative intensity
calculated from the
beginning of SA, t, s Example 1 Example 2 Example 3 Example
4
1 0 0 0 0 0
2 0,1 0,2 0,2 0,4 0,5
3 0,2 0,4 0,6 0,8 0,7
4 0,3 0,6 0,8 0,9 0,8
5 0,4 0,8 0,9 1 0,9
6 0,5 1 1 1 1
7 0,6 0,8 0,9 1 0,9
8 0,7 0,6 0,8 0,9 0,8
9 0,8 0,4 0,6 0,8 0,7
10 0,9 0,2 0,2 0,4 0,5
11 1 0 0 0 0
Table 2
Dependences of intensity distribution on time for asymmetric SA
№ Relative time, Relative intensity
calculated from the
beginning of SA, t, s Example 1 Example 2 Example 3 Example
4
1 0 0 0 0 0
2 0,1 0,3 0,6 0,8 0,35
3 0,2 0,6 0,9 0,9 0,7
4 0,3 0,8 1 1 1
5 0,4 1 0,9 0,8 0,9
6 0,5 0,9 1 0,9 0, 8
7 0,6 0,6 0,9 0,7 0,5
8 0,7 0,4 0,8 0,5 0,4
9 0,8 0,3 0,6 0,4 0,3
10 0,9 0,2 0,2 0,2 0,1
11 1 0 0 0 0
Table 3
Dependences of intensity distribution on time for the composition SA
№ Relative time, Relative intensity
calculated from the
beginning of SA, t, s Example 1 Example 2 Example 3 Examp
le 4
1 0 0 0 0 0
2 0,1 0,3 0,6 0,8 0,2
3 0,2 0,6 0,9 0,9 0,7
4 0,3 0,8 1 1 1
5 0,4 1 0,7 0,8 0,7
6 0,5 0,8 1 0,9 0, 8
7 0,6 0,6 0,7 0,7 0,5
8 0,7 0,7 0,6 0,5 0,7
9 0,8 0,4 0,5 0,4 0,5
10 0,9 0,2 0,3 0,2 0,1
11 1 0 0 0 0
The results of calculations showing the effect of influences of distance from microphon to the
source of the SA on the error are presented in table 4.
Table 4
Analysis of the influence of intensities and parameters of SA on the magnitude of the error
Example Distance to Maximum Absolute time Relative
SA SA, intensity error error Δt,s coordinate
r, m error,%
1 25 7,41E-05 1,74121E-05 0,0689
1 50 9,43E-06 1,0943E-05 0,0538
1 75 2,81E-06 1,02811E-05 0,0532
1 100 1,19E-06 1,01189E-05 0,0531
2 25 7,41E-05 1,37061E-05 0,0789
2 50 9,43E-06 1,04715E-05 0,054
2 75 2,81E-06 1,01405E-05 0,0532
2 100 1,19E-06 1,00595E-05 0,0531
3 25 7,41E-05 1,37061E-05 0,1719
3 50 9,43E-06 1,04715E-05 0,0343
3 75 2,81E-06 1,01405E-05 0,0273
3 100 1,19E-06 1,00595E-05 0,0267
4 25 7,41E-05 2,48242E-05 0,0327
4 50 9,43E-06 1,1886E-05 0,0215
4 75 2,81E-06 1,05621E-05 0,0213
4 100 1,19E-06 1,02379E-05 0,0212
As evidenced by the analysis of the calculation results (see table 4) for symmetric SA (examples of
table 1), the distance to SA has a significant effect on the magnitude of the error. Thus, when
recording the intensity, it is assumed that the maximum value of the intensity of the wave coming to
each of the microphones was assumed to be constant. The latter assumption also makes a significant
contribution to the magnitude of the overall methodological error, as the intensity decreases as the
wave propagates from the first microphone to the next. It is known that almost all [5] algorithms do
not take this fact into account. In addition, the time used by the system is synchronized with the time
of reading information from the microphones, and therefore, as a second factor, introduces a time
error equal to half the sample time of reading. Thus, in the simulation, simulating the changes in
intensity, the value of the maximum possible error of the maximum intensity, the absolute error of the
time and the relative error of the coordinate SA are estimated. The results of the analysis show that for
the selected four examples of symmetric distributions of intensity SA, the same regular changes in the
dependence of the maximum possible error are observed. Increasing the distance between the
microphones increases the amount of error, but it should be noted that this impairs the mobile quality
of the system. Data demonstrating the grounds for such conclusions are presented in table 5 for
example 4 of the symmetric variant of echograms. Thus, with increasing distance between the
microphones, significantly increases the maximum possible error and, as a consequence, the relative
error of determining the coordinates.
Table 5
Analysis of the influence of the distance between the microphones on the error? algorithm 5
№ The distance Distance Maximum Absolute Relative
between mic- to SA, r, m intensity error time error Δt, s coordinate
rophones a, m error, %
1 0,2 25 2,53E-05 1,10118E-05 0,0145362
2 0,6 25 1,29648E-05 7,41E-05 0,0206952
3 1,0 25 0,000121 1,48284E-05 0,0287785
4 1,4 25 0,000165 1,66079E-05 0,0372271
To select the algorithm for determining the time, the simulation and comparison of processes by
the criterion of the magnitude of the relative error, the number of operations and the time required to
fully calculate the time of entry of the wave into the microphone. In [5-9] the authors established that
the determining factor of the three criteria is the accuracy of coordinate determination. Its value is
determined by the error of fixing the time of entry of the wave to each of the microphones. In this
regard, four algorithms were considered.
Algorithm 1.
The calculated time is the arithmetic mean time between the moment of time at which the value of
0.5 of the maximum intensity in the jump phase is reached and the time at which the intensity
decreases to 0.5 of the maximum intensity.
Algorithm 2.
The calculated time is the time of the center of gravity of the echogram at ten points, and its
countdown is from the point in time at which the value of 0, 5 maximum intensity is reached.
Algorithm 3.
The calculated time is the time of the arithmetic mean between the time of the jump phase from 0,
2 values of maximum intensity and level to 0.2 of its decrease in maximum intensity.
Algorithm 4.
The estimated time is according to the recurrent algorithm according to MPA [5] for which the
estimated time is as the time of equivalent areas, according to the recurrent relation.
First of all, their work was studied and the influence of factors on the error for each of the four
algorithms was studied. The properties of these algorithms were studied. The general conclusion of
this analysis is that the generalized first and third algorithms are the simplest and most effective for
symmetric intensity distributions. The use of a given value of the constant from 0.2 to 0.5 in the
formal essence of the algorithm does not change. However, it leads to unified values of zero and one.
In addition, the choice of a constant value of 0.2 significantly reduces the total calculation time, which
is critical for specific applications. Algorithm 4 is efficient in terms of action and accuracy, but
requires the organization of complex calculations. The accuracy of algorithm 4 is justified for
complex non-symmetric intensity distributions, and for symmetric simple SA it is advisable to use
algorithm 1.
4.3. Analysis of algorithms for recognizing and determining the time of
complex echograms
On the basis of the conducted analysis the generalized algorithm of definition of time of
occurrence of a sound wave of difficult structure ON as follows was formulated.
Algorithm 5. The calculated time is the arithmetic mean time between the time of the jump time
from 0.2 to the value of the maximum intensity and the first subsequent maximum. To analyze the
advantages and disadvantages of Algorithm 4, we analyze the effect of the distance between the
microphones on the amount of error when using Algorithm 4.
Table 6
Analysis of the influence of distance between the microphones on the error value using algorithm 4
№ The Distan Maximu Absolute Relative Total
distance ce to SA, m error error of time error of the calculation
between r, m intensity Δt, c coordinates of time
microphones , Δі its decline, %, Δtміn, s
a, m
1 0,2 25 2,53E-05 1,253E-05 0,000143128 0,20002265
2 0,6 25 7,41E-05 1,741E-05 0,000182726 0,20004716
3 1,0 25 0,000121 2,207E-05 0,023603 0,20007036
4 1,4 25 0,000165 2,652E-05 0,029351 0,20009259
To confirm this conclusion, we present the calculations by algorithm 4 (see Table 6). Thus, the
calculations of the variant of table 5 show a significant reduction in error due to the choice of
algorithm 5. However, the calculation of time costs shows that in the case when the origin is unknown
and to be determined, the simple algorithm 5 prevails because it has a millisecond time.
Thus, when the accuracy of determining the value of the coordinate by algorithm 5 is sufficient,
and the time of determining the coordinate is critical, the advantage over algorithm 4 is algorithm 5.
In addition, it should be noted that for MES, military, with an error of centimeters, time is decisive,
and for other purposes there is an accuracy of coordinates of a source SA.
5. Conclusions
1. The task of simulation modeling and estimation of the magnitude of the components of the
maximum possible error that occurs when determining the coordinates of SA is set and carried out.
Comparative analysis of the simulation results shows that the distance to the source SA and the
relative position and distance between the microphones of the CS significantly affects the amount of
static error. Thus, when increasing the relative distance from 41.66 to 82.33, the error decreases from
0.0689% to 0.0538%, and then almost unchanged for the case of symmetric echograms.
2. The choice of the algorithm does not significantly affect the estimation of the static maximum
possible error in determining the coordinates SA for symmetric echograms, however for asymmetric
echograms the choice of the algorithm significantly recognizes its value.
3. The algorithm for determining the moment of time of the identical phase of the occurrence of
the wave front is determined by the required accuracy or the required calculation time. For critical
accuracy, more preferable is the MPA algorithm 4, and at critical time, acquires algorithm 5.
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