CC BY
11
УДК 528.11
Obidova D. trainee teacher SamSACU
https://orcid. org/0009-0002-6337-773X
Khamdamova D. trainee teacher SamSACU
THE PROCEDURE FOR PERFORMING CORRELATE EQUALIZATION OF A TRIANGULATION GRID USING MICROSOFT
EXCEL
Annotation. One of the main tools in the Microsoft Office 2010 package is a spreadsheet program Microsoft Excel, which is part of the software of modern computers. Microsoft Excel is designed for the preparation and mathematical processing of spreadsheets under the control of the Windows operating system.
We aim to perform the process of equalization of the triangulation node by the correlate method using Microsoft Excel.
Key words: Excel, triangulation, measure, mathematical processing, Windows operation system, result, correlate method.
One of the main tools in the Microsoft Office 2010 package is a spreadsheet program Microsoft Excel, which is part of the software of modern computers. Microsoft Excel is designed for the preparation and mathematical processing of spreadsheets under the control of the Windows operating system.
We aim to perform the process of equalization of the triangulation node by the correlate method using Microsoft Excel.
Figure 1 shows a schematic of the measurement of angles in the triangulation type and Table 1 shows the results of the measured angles. V.D.Bolshakov, Yu.I.Markuze, D.O. Juraev, B. S. Kuz'min learn this methods.
Measurement Scheme:
E
Figure 1
Measured Angle Values Table 1
Bur-chaklar Bur-chaklar Olchangan qiymatlar xt Tenglama
1 A0B 580 15' 45",8 ti
2 B0C 380 10' 10",8 t2
3 COD 61001' 11",0 i3
4 AOC 96025' 53",1 ti + t2
5 BOD 99011' 21",3 + h
6 AOD 1570 27' 04",6 t1 + t2 + t3
As parameters, we take the first four of the ten measured angles. We define them by their equalized value tx, t2, t3, t4 (Table 1).
As an approximate value of the desired unknowns, we take the results of their measurements, namely:
if - 58° 15'45, "8
38°10 10, "8 61°0l'll, "0
Then we express the equal value of all ten measured quantities by the equal value of the four required unknowns to construct the dependence of the correlate equations.
Xi = Xi ~ Vi = fi(t1, , , ^4 )
(1) according to the formula
1 ) xt = 4) x4
h + t2
2)x2 =t2 5)xs = t2+t3 (2)
3)*3 = t3 6) x6 = t± + t2 +t3
To perform the process of correlate equalization of the triangulation network using Microsoft Excel is necessary to perform the following procedure:
1. In the Microsoft Excel program, we enter the measured values in the order shown in Figure 2, the selected desired unknowns (parameters), the approximate value of the detected parameters and the dependence of the constructed correlate equations [2].
3 H *> - f -I- matritsa [Pe>
Д Главная Вставка Разметка страницы Формулы Данные Рецензирование 1
4, .
- " (1 * ■'
Буфер обмена i G6
<2» . £ ■ Ш Ж Ш iW if g . sp . % ООО г, I Выравнивание_rI_Число
fx I O'lchangan burchak
O'lchangan burchak Burchak nom! Tenglama
38 00:01 AOB a
42 00:01 BOC b
44:00:01 COD с
33 00:01 DOE d
80 00:22 ДОС a+b
86:00:12 BOD b+c
76 59:52 СОЕ c+d
123 ЕЭ 43 AOD a+b+c
119 00:18 ВОЕ b+c+d
156 59 49 AOE a+b+c+d
Figure 2.
2. We convert the measured values in degrees, minutes, seconds to radians in Microsoft Excel using geodetic instruments (theodolite tool). To do this, we enter the information in column 2 of Table 1 in the order shown in Figure 2 in Microsoft Excel - left-click on the arrow (format cell: number) in the corner of the item "Number" of the "Main" section of the program window (Figure 3 a) and an additional working window as shown in Figure 3b is formed[2].
a)
b)
Figure 3.
Then we click on the "Number" item in the additional working window "Format cells" in Figure 3b, select the command "(all formats)" from the menu "Numeric formats:" and from the menu "Type" we select the "[ch]: mm: ss icon and activate the mode "Number" by pressing the button LJ.
3. After activating the "Number" mode, multiplying the measured 1800 values (expressed in degrees, minutes, seconds) entered in Microsoft Excel, n = 3,141592.......our values become radian[10], (Figure 4)
Figure 4.
4. Then we construct the correlate equation of corrections
This here: a =
Г д x,Л
, й-2
iд x Л
Kdt2 J
; aik =
fд x,Л
\dtk J0
v5ii y
l i = f i (10,....., iV - x i = xi - x i (4)
In the example of the 4th correction equation we show how to construct. The 4th equation is due to: dx4
«41 = (-T—)o = +i;
a42
a43
dt± dx4
dt2 0
dx-ij.
dto 0
+ 1
Free limit:
i4 = (t1° + tj) -x4 = 58°15'47,8'r + 38o10J12J8''-96°25 25,1'= 3,5' We write the equation of all corrections in the same way.
Tl
4)^4
T3
3,5 = +1,0 0,5 = -0,5 3,0 = +1,5
We enter the above steps in the Microsoft Excel spreadsheet (Figure 5).
®| A 1 ■ matrrtsa [Режим о □ вместимости] - Microsoft Excel [Сбой активации продукта) □ ЕР ЕЗ
Файл | Главная Вставка Разметка страницы Формулы Данные Рецензирование Вид '¿Î 1 j?
*
-У) •
- 10 Шрифт
A" I *
m . %
Удалить • IP Формат• Ячейки
; %r Êk
Сортировка Найти и и фильтр • выделить -Редактирование_I
£
1С
н
5
6 O'Ichangan burchak Burchak nom! Tenglama 1 a
7 33:00:01 АО В a 2 b
S 42:00:01 вое b 3 с
9 44:00:01 COD с 4 d
10 33:00:01 DOE d 5 a+b-0.00.20
11 80:00:22 АОС a+b 6 b+c-0.00.10
12 86:00:12 BOD b+c 7 c+d+0:00 10
13 76:59:52 СОЕ c+d 8 a+b+c+0 00:20
14 123 59 43 AOD a+b+c 9 b+c+d-0 00 15
15 119 00 18 ВОЕ b+c+d 10 a+b+c+d+0 00 15
16 156'59'49 AOE a 1: С 1 i
17
18 0 39 46 0'43'58 1 23 44 1 23 44 0:00:00 0:00 20
19 0:43 58 0 46 03 1 30 01 1 30 01 0:00:00 0:00:10
20 0 46 03 0 34 32 1 20 36 1 20 35 0:00:00 0 00:10
21 0 39 46 0 43 53 0 46 03 2:09:47 2 09:47 0 00:00 0:00:20
22 0 43 58 0 46 03 0 34 32 2 04 33 2 04:34 0:00:00 0:00:15
23 0 39 46 0:43 58 0 46 03 0 34 32 2 44:20 2 4419 0:00:00
24
м < ► w Лист! Лист2 ЛетстЗ , i J Il <
о
-17 -7 2 15 -12 10
Среднее: 1,520958609 Количество 92
Figure 5 [9].
5. After that, we compile the table of coefficients of the correction equation (1) according to the formula (5) in accordance with Table 1 and enter it
into the spreadsheet of Microsoft Excel and calculate it using the program (Figure 6-7).
Figure 6[9].
Figure 7 [9].
Since it is the sum of the numbers on the columns, the sum of all the values of Si is equal to the sum of the values above the double line. 6. Solving normal equations:
The system of equations consisting of four unknowns is as follows:
Solving a system consisting of this normal equation is done in Microsoft Excel using the Kramer method as shown in Figure 8[2].
1'Й1
H Главная вставка Разметка страницы Формулы Данны D30 ' fx matritsani islilash
— А В С D Е F
33 34 J5 36 4 3 2 1 3 В 4 2 2 4 6 3 1_2_3_4 125
38 39 40 41 J2 -15 3 2 1 10 6 4 2 -20 4 6 3 -10 2 3 4 -1000
44 45 4-15 2 1
46 47 48 3 10 4 2 2 -20 6 3 1 -10_3_4 1375
50 51 52 53 54 4 3 -15 1 3 6 10 2 2 4 -20 3 1_2 -10_4 -1000
56 57 58 59 4 3 2 -15 3 В 4 10 2_4_6 -20
60 61 1 2 3 -10 0
62 -8
н < ► к Лист1 Лисг2 ЛистЗ О
Готово
Figure 8.
7. Calculation of corrections to the measured results: Vi for the measured angle value is found from the spreadsheet in Figure 6 according to the formula and the construction of this table is completed (Figure 9)[9], Equality (1) and (4) are also checked._
Ш d *) - matritsa [Режим совместимости] - Microsoft Excel (Сбой активации продукта) ^Я <=, £3
U Главная | Вставка Разметка страницы Формулы Данные Рецензирование Вид * € ) а # 23
В ' -1 л - Вставить - J Arial С/ -|и> • А" л" — _ Цг - ■ Общий - ш m m в*™ Вставить Удалить И Формат - £ а- а & ift
Ж А' Ч - ш - л - д - = « a- g % 000 Условное Форматироват форматирование' как таблицу' ячеек* Сортировка Найти и и фильтр * выделить *
Буфер обмена ri Шрифт . выравнивание La Число a стали Ячейки Редактирование
Кб А 1 V
Е F 0 н J К I L M N о Р Q
3 4 5 —I
6 Olchangan burchak Burchak nomi Tenglama 1 а -8
7 38 00:01 AO В a 2 b 11 -
8 42 00:01 вое b 3 с -8
9 44 00:01 COD с 4 d 0
10 33 00:01 DOE d 5 a+b-0 00:20 -17
11 80.00:22 ДОС a+b 6 Ь+с-0 00 10 -7
12 86:00:12 BOD b+c 7 c+d+0 00:10 2
13 76'59:52 СОЕ c+d 8 a+b+c+0 00 20 15
14 123 59 43 AOD a+b+c 9 b+c+d-0:00:15 -12
15 11900 18 ВОЕ b+c+d 10 a+b+c+d+0 00:15 10
16 17 IS 156'59'49 AOE a+b+c+d
0 39 46 043.58 1:23:44 1.23:44 0:00:00 000:20
19 0 43 58 0:46 03 1:30:01 1 30:01 0 00:00 0 00:10
20 0 46 03 0 34 32 1:20:36 1'20:35 0 00:00 0 00:10
21 0 39 46 0.43.58 0:46:03 2.09:47 2 09:47 0 00:00 0:00:20
22 0 43 58 0:46 03 0:34:32 2 04:33 2 04:34 0 00:00 0:00:15
23 0 39 46 0 43 58 0:46:03 0:34:32 244:20 2'44:19 0:00:00 0:00:15 т
и ► м Лист! Лист2 ЛистЗ 4. H< I
Готово I Среднее; 2,05 Количество: 30 Сумма: 41 ||и|0 Щ 100%
Figure 9.
9. Calculation the equivalent value of the unknowns (parameters). Hence, in this example, the measured quantities are selected as
parameters, and it is appropriate to perform the considered calculations together with the calculations of the next stage.
10. Calculating the equivalent value of the measured quantities.
The correction is the equalized value of the angles in Figure 10 using Vi.
11. Final check of equation[9].
It consists of recalculating the equalized value of the angle according to the dependence of equations (2).
The test calculations are given in Figure 10.
Figure 10.
12. Accuracy assessment.
1. The mean square error of the directly measured results and the mean square of the "error of error"
m —
mm =
¡[V2]
n - k
(7)
m
sl2(n - k)
(8)
To use the above formula in Microsoft Excel, we need to do the work in the order shown below. To do this, we need to enter formulas (7) and (8) into Microsoft Excel. In formula (7) we enter the numbers under the root in the spreadsheet of the program (Figure 11).
® B ■
Figure 11
Then we go to the command line "FORMULAS" from the command line of the program and click on the command "ROOT" from the menu
"Mathematical" in the submenu "Library of functions" and type 1060 / (10-4) in
the window "Number " and click on the button ---], and the result will
appear on the screen (Figure 12).
Figure 12.
After doing the above, we determine the values according to formula (8), again enter cell I-21 of the spreadsheet, create the formula = I20 * (J20-K20) and press Enter (Figure 13)[9].
Figure 13.
Then we go to cell I-22, click "=", enter the command "FORMULAS" from the command line and click on the command "BASIC" from the submenu "Library of functions" from the menu "Mathematical" and the additional
"Arguments function" In the "Number" window of the window, type the 1-21
cell icon and t OK 1 press the button, and the result is displayed on the screen (Figure 14).
Figure 14.
Then we go to cell I-24, create the formula "= L23 / I22" and get the final result (Figure 15).
Figure 15.
In short, Microsoft Excel spreadsheet is a ready-made program that not only solves economic and financial problems, but also helps to solve complex calculations in the field of geodesy.
Thus, Microsoft Excel has the ability to solve existing problems in the discipline of "Theory of mathematical processing of geodetic measurements (correlate equalization of the triangulation network and the assessment of accuracy) and is a very useful program for solving complex problems in the field of geodesy.
References:
1. V.D.Bolshakov, Yu.I.Markuze. Practicum on the theory of mathematical processing of geodetic old measurements. / Moskva. NEDRA 1984.
2. D.O. Juraev. A collection of lectures on "Theory of mathematical processing of geodetic measurements." / Tashkent. TABI, 1999. 123 pages
3. Mardonovich, P. I., Davronzoda, O. D., & Oglu, K. M. M. Update of agricultural electronic digital maps. international journal of innovations in engineering research and technology, 7(4), 1-3.
4. Мирзаев, А. А., Обидова, Д. Д., & Михеев, Д. О. (2020). Метрологический контроль электронных тахеометров на эталонном геодезическом базисе. журнал агро процессинг, (special issue).
5. Bobokalonov, M. K., & Khamdamova, D. (2022). Using arcgis software to create a land reclamation map. Barqarorlik va yetakchi tadqiqotlar onlayn ilmiy jurnali, 2(11), 385-388.
6. Муллоджанова, Г. М. (2020). Мавзули хариталарни яратишда маълумотлар базасини шакллантириш. журнал Агро процессинг, (special issue).
7. Разработка технологии съёмки и исследований состояний памятников архитектуры современными геодезическими методами Издательство "фан" академии наук республики узбекистан. 15.03.2021. 168/10.8п.л.. рекомендована к печати решением ученого совета самаркандского государственного архитектурно - строительного института имени мирзо улугбека
8. Muhandislik Geodeziyasi "Innovatsion rivojlanish nashriyot-matbaa uyi". toshkent - 2021-y. 188/12 b.t. (grif raqami 137-019, 06.04.2016 y.)
9. Bobokalonov, T. M. K. (2022). The procedure for performing parametric equalization of a triangulation grid using Microsoft Excel. The Peerian Journal, 11, 19-30.
10. Haydarovich, B. M., Yarkulov, Z. R., & Mashrab, P. (2023). Main Characteristics of Geoinformation Technologies and Modern Gis. Web of Synergy: International Interdisciplinary Research Journal, 2(2), 194-200.
11. Haydarovich, B. M., Lazizbek, I., Rakhmanovich, Y. Z., & Mashrab, P. (2023). Theoretical and Practical Issues of Water Cadastre Management. Web of Synergy: International Interdisciplinary Research Journal, 2(2), 293-298.
12. www.ziyonet.uz
13. Usmanovich, S. T., Rashitovich, S. S., & Adkhamovich, B. U. (2022). It is Currently Modern in the Field of Geodesy Application of Levels. EUROPEAN JOURNAL OF INNOVATION IN NONFORMAL EDUCATION, 2(4), 193-197
14. Сафаров, Т. У., Саманкулов, Ш. Р., Худайкулов, Ш. Ш., & Бердикулов, У. А. Методика Юстировки Много Фацетных Гелиостатов.
