单一符合导线测量控制网平差程序
梁彩艳
(西北石油局工程服务大队,新疆乌鲁木齐830011)
摘要:由于全站仪(光电仪) 的不断普及,导线布网已在测量控制网中广泛应用。为了简化计算,提高平差精度,节约
平差经费,结合实际工作中的一个实例,运用PC —E500 计算器编制了单一符合导线高斯平差程序。
关键词:单一;符合导线;平差程序
1 差原理及程序框图(见图1)
2 实例
在单一符合导线(如图2) 中,已知各起始数据,观测了各折
角方向值,测量了各边长(见表1) ,观测方向中误差δr = ±5″,边长丈量中误差δsi = ±0. 5 simm ,求各导线点的坐标平差值和最弱点4 号点的点位精度(可假设单位权中误差δ0 = ±5″,则观测角权为0. 5 ,观测边权Psi = 100/ Si) 。
图2 单一符合导线示意图
表1 测量数据一览表
点号
已知坐标(m)
X Y
编号
已知坐标
方位角
B 3020. 348 - 9049. 801 αAB 226°44′59″
C 3702. 437 - 10133. 399 αC
D 57°59′31″
编号观测角度编号
观测边长
(m)
1 230°32′37″ 1 204. 952
2 180°00′42″ 2 200. 130
3 170°39′22″ 3 345. 153
4 236°48′37″ 4 278. 059
5 192°14′25″ 5 451. 692
6 260°59′01″
3 平差程序
10 :REM SUB 10 - 190 QIU DAO XIAN DIAN GAI LUE
ZUO BIAO
20 :REM SHU ZU”A”WEI FANG WEI J IAO ,”B”WEI
GUAN CE ZUO J IAO ,”S”WEI BIAN CHANG,”P”WEI
QUAN ,”V”WEI GAI ZHENG SHU ,”MX、MY、M”WEI
DAI QIU DIAN ZHONG WU CHA ,”X、Y”WEI ZUO
BIAO
30 : INPUT”GUAN CE J IAO GE SHU :N = ”;N
40 :DIM A (N) ,B (N) ,S (N) ,X(2 3 N) , Y(2 3 N) , P (2 3
N) ,V(2 3 N) ,MX(N) ,MY(N) ,M(N)
45 :FOR I = 1 TO N
50 :READ B( I) ,S( I)
60 :B( I) = DEG (B( I) )
70 :NEXT I
80 : INPUT”QI SHI FANG WEI J IAO :A0 = ”;A(0)
90 :A(0) = DEG (A(0) )
100 :FOR I = 1 TO N
110 :A( I) = A( I - 1) + B( I) + 180
120 : IF A( I) > 360 THEN A( I) = A( I) - 360
130 :NEXT I
140 : INPUT”QI SHI DIAN ZUO BIAO : X0 = ”; X(1) ,”Y0 = ”; Y(1)
总第93 期
2004 年第2 期
西部探矿工程
WEST - CHINA EXPLORATION ENGINEERING
series No. 93
Feb. 2004
145 : PRINT ”DAO XIAN DIAN GAI LUE ZUO BIAO ZHI :”
150 :FOR I = 2 TO N
160 :X( I) = X( I - 1) + S( I - 1) 3 COS(A( I - 1) ) : Y( I) = Y( I
- 1) + S( I - 1) 3 SIN(A( I - 1) )
170 :PRINT ”X(”; I ;”) = ”;X( I) ,”Y( ;”I ;”) = ”; Y( I) 180 :NEXT I
185 :LOCATE 12
190 :PRINT ”# # # # # ”
200 :REM SUB 200 - 370 QIU TIAO J IAN FANG CHENG
XI SHU ”A1 ,BI ,C1”SHU ZU J I QUAN HAN SHU XI
SHU ”FX ,FY”SHU ZU
210 :DIM A1 (2 3 N - 1) ,B1 (2 3 N - 1) ,C1 (2 3 N - 1) ,FX(2 3 N - 1) ,FY(2 3 N - 1)
220 :FOR I = 1 TO N
230 :READ A1( I)
240 :NEXT I
250 :FOR I = 1 TO 2 3 N - 1
260 :B1 ( I) = ( - Y(N) + Y( I) ) / 206. 26
270 :C1 ( I) = (X(N) - X( I) ) / 206. 26
280 : IF N < I THEN B1( I) = COS(A( I - N) :C1 ( I) = SIN (A ( I - N) )
290 :NEXT I
300 : INPUT ”ZUI RUO DIAN HAO :FN = ”;FN
310 :FOR I = 1 TO 2 3 N - 1
320 :FX( I) = ( - Y(FN) + Y( I) ) / 206. 26
330 :FY( I) = (X(FN) - X( I) ) / 206. 26
340 : IF FN < I THEN FX( I) = 0 :FY( I) = 0
350 : IF N < I THEN FX( I) = COS(A ( I - N) ) : FY( I) = SIN (A( I - N) )
360 : IF I > N + FN - 1 THEN FX( I) = 0 :FY( I) = 0
370 :NEXT I
414 : INPUT ”FU HE FANG WEI J IAO :A2 = ”;A2 ,”FU HE DIAN ZUO BIAO :X2 = ”;X2 ,”Y2 = ”; Y2
415 :WA = - DEG(A2) + A(N) :WX = - X2 + X(N) :WY =
- Y2 + Y(N)
416 :WA = DMS(WA) : IF WA > 360 THEN WA = WA - 360
419 :WA = WA 3 10000 :WX = WX3 1000 :WY= WY3 1000
420 :REM SUB 420 - 740 J IE SUAN FA FANG CHENG
425 :REM SUB 430 - 470 J I SUAN GUAN CE J IAO、BIAN
DE QUAN
430 : INPUT ”J IA SHE DAN WEI QUAN ZHONG WU
CHA :D0 = ”;D0
440 :FOR I = 1 TO 2 3 N - 1
450 :P( I) = 0. 5
460 : IF I > N THEN P( I) = (D0 3 D0) / (0. 25 3 S( I - N) ) 470 :NEXT I
500 :REM ”E”WEI DAI QUAN QIU HE FU HAO
520 : EAA = 0 : EAB = 0 : EAC = 0 : EAFX = 0 : EAFY= 0
530 : EBB = 0 : EBC = 0 : EBFX = 0 : EBFY= 0
540 : ECC = 0 : ECFX = 0 : ECFY= 0 : EFFX = 0 : EFFY= 0
550 :FOR I = 1 TO 2 3 N - 1
560 :EAA = A1 ( I) 3 A1 ( I) / P ( I) + EAA : EAB = A1 ( I) 3 B1
( I) / P( I) + EAB
570 :EAC = A1 ( I) 3 B1 ( I) / P( I) + EAC: EAFX = A1 ( I) 3 FX
( I) / P( I) + EAFX: EAFY = A1 ( I) 3 FY( I) / P ( I) + EAFY
580 :EBB = B1 ( I) 3 B1 ( I) / P ( I) + EBB : EBC = B1 ( I) 3 C1
( I) / P( I) + EBC
590 :EBFX = B1 ( I) 3 FX( I) / P ( I) + EBFX: EBFY= B1 ( I) 3 FY( I) / P( I) + EBFY
600 :ECC = C1 ( I) 3 C1 ( I) / P ( I) + ECC: ECFX = C1 ( I) 3 FX
( I) / P( I) + ECFX: ECFY= C1( I) 3 FY( I) / P( I) + ECFY
610 :EFFX = FX( I) 3 FX( I) / P( I) + EFFX: EFFY= FY( I) 3 FY( I) / P( I) + EFFY
620 :NEXT I
630 :EBB1 = EBB - EAB 3 EAB/ EAA : EBC1 = EBC - EAB 3
EAC/ EAA : EWX1 = WX - EAB 3 WA/ EAA
640 :EBFX1 = EBFX - EAB 3 EAFX/ EAA : EBFY1 = EBFYEAB
3 EAFY/ EAA
650 :ECC2 = ECC - EAC3 EAC/ EAA - EBC1 3 EBC1/ EBB1
660 :EWY2 = WY- EAC 3 WA/ EAA - EBC1 3 EWX1/ EBB1
670 :ECFX2 = ECFX - EAC 3 EAFX/ EAA - EBC1 3 EBFX1/
EBB1
680 :ECFY2 = ECFY- EAC3 EAFY/ EAA - EBC1 3 EBFY1/
EBB1
690 : KC = - EWY2/ ECC2
700 : KB = - EBC1 3 KC/ EBB1 - EWX1/ EBB1
710 : KA = - EAB 3 KB/ EAA - EAC 3 KC/ EAA - WA/ EAA
720 : EPVV = WA 3 WA/ EAA + EWX1 3 EWX1/ EBB1 +
EWY2 3 EWY2/ ECC2
730 : EFFX3 = EFFX - EAFX 3 EAFX/ EAA - EBFX1 3
EBFX1/ EBB1 - ECFX2 3 ECFX2/ ECC2
740 : EFFY3 = EFFY - EAFY 3 EAFY/ EAA - EBFY1 3
EBFY1/ EBB1 - ECFY2 3 ECFY2/ ECC2
750 :REM SUB 750 - 910 QIU GUAN CE BIAN、J IAODE
GAI ZHENG SHU ,DAO XIAN DIAN ZUO BIAO PING
CHA ZHI J I ZUI RUO DIAN J ING DU PING DING
748 :PRINT ”V (1～6) WEI GUAN CE J IAO GAI ZHENG
SHU , V ( 7 ～ 11 ) WEI BIAN CHANG GAI ZHENG
SHU :”
750 :FOR I = 1 TO 2 3 N - 1
760 :V( I) = (A1 ( I) 3 KA + B1 ( I) 3 KB + C1 ( I) 3 KC) / P( I) 770 : IF I < = N THEN B ( I) = B ( I) + DEG(V ( I) / 10000) ELSE S( I - N) = S( I - N) + V( I) / 1000
780 :PRINT ”V(”; I ;”) = ”;V( I) ,
790 :NEXT I
795 :LOCATE 12
798 :PRINT ”# # # # # ”
68 西部探矿工程
Feb. 2004
No. 2
800 :FOR I = 1 TO N
810 :A( I) = A( I - 1) + B( I) + 180
820 : IF A( I) > 360 THEN A( I) = A( I) - 360
830 :NEXT I
835 :PRINT ”DAO XIAN DIAN PING CHA ZHI :”
840 :FOR I = 2 TO N
850 :X( I) = X( I - 1) + S( I - 1) 3 COS(A( I - 1) )
860 : Y( I) = Y( I - 1) + S( I - 1) 3 SIN(A( I - 1) )
870 :PRINT ”X(”; I ;”) = ”;X( I) ,”Y( ;”I ;”) = ”; Y( I) 880 :STOP
890 :NEXT I
894 :LOCATE 12
896 :PRINT ”# # # # # ”
900 :M0 = SQR( EPVV/ 3) :MX( FN) = M0 3 SQR( EFFX3) :
MY( FN) = M0 3 SQR ( EFFY3) :M ( FN) = SQR (MX
(FN) 3 MX(FN) + MY(FN) 3 MY(FN)
910 : PRINT ”J I SUAN DAN WEI QUAN ZHONG WU
CHA :M0 = ”;M0 ,”ZUI RUO DIAN WU CHA :M( ”;
FN ;”) = ”;M(FN) ;”mm”
911 :LOCATE 12
912 :PRINT ”# # # # # ”
914 :LOCATE 15
916 :PRINT ”END !”
918 :REM 920 HANG FANG ZHI GUAN CE ZUO J IAO、
BIAN CHANG ZHI ,930 HANG FANG ZHI FANG WEI
J IAO TIAO J IAN XI SHU
920 : : DATA 230. 3237 , 204. 952 , 180. 0042 , 200. 130 , 170. 3922 , 345. 153 , 236. 4837 , 278. 059 , 192. 1425 , 451. 692 ,260. 5901 ,0
930 :DATA 1 ,1 ,1 ,1 ,1 ,1 ,0 ,0 ,0 ,0 ,0 ,0
940 : END
4 运行结果
RUN
GUAN CE J IAO GE SHU :N = 6
QI SHI FANG WEI J IAO :A0 = 226. 4459
QI SHI DIAN ZUO BIAO :X0 = 3020. 348
Y0 = - 9049. 801
DAO XIAN DIAN GAI LUE ZUO BIAO ZHI :
X(2) = 3046. 36649 Y(2) = - 9253. 09478
X(3) = 3071. 81326 Y(3) = - 9451. 60039
X(4) = 3059. 53346 Y(4) = - 9796. 53488
X(5) = 3286. 66789 Y(5) = - 9956. 93052
X(6) = 3702. 48850 Y(6) = - 10133. 33597
# # # # #
ZUI RUO DIAN HAO :FN = 4
FU HE FANG WEI J IAO :A2 = 57. 5931
FU HE DIAN ZUO BIAO :X2 = 3702. 437
Y2 = - 10133. 399