1.10 Оценка точности
а) Вычисление СКО единицы веса
,
где n
– число
измеренных величин
k – число необходимых величин
µ=5.967
б) Вычисление обратной весовой матрицы уравненного вектора измеренных величин
Qβ= QA·Q т.к. Q = E
Qβ - QA
QA = (E – QAT(AQAT)-1A
QA = (E-AT(AAT)-1A
0.452 |
-0.292 |
-0.160 |
0.114 |
-0.128 |
0.014 |
-0.008 |
-0.078 |
0.085 |
0.160 |
0.086 |
-0.246 |
-0.292 |
0.464 |
-0.171 |
-0.091 |
0.125 |
-0.033 |
-0.021 |
0.095 |
-0.075 |
0.171 |
-0.243 |
0.072 |
-0.160 |
-0.171 |
0.331 |
-0.023 |
0.004 |
0.019 |
0.028 |
-0.018 |
-0.011 |
-0.331 |
0.157 |
0.174 |
0.114 |
-0.091 |
-0.023 |
0.263 |
-0.061 |
-0.202 |
0.246 |
0.004 |
-0.249 |
0.023 |
0.034 |
-0.057 |
-0.128 |
0.125 |
0.004 |
-0.061 |
0.320 |
-0.258 |
0.033 |
-0.248 |
0.215 |
-0.004 |
-0.053 |
0.057 |
0.014 |
-0.033 |
0.019 |
-0.202 |
-0.258 |
0.460 |
-0.278 |
0.244 |
0.034 |
-0.019 |
0.019 |
0.000 |
-0.008 |
-0.021 |
0.028 |
0.246 |
0.033 |
-0.278 |
0.276 |
-0.037 |
-0.238 |
-0.028 |
0.016 |
0.012 |
-0.078 |
0.095 |
-0.018 |
0.004 |
-0.248 |
0.244 |
-0.037 |
0.298 |
-0.260 |
0.018 |
-0.046 |
0.028 |
0.085 |
-0.075 |
-0.011 |
-0.249 |
0.215 |
0.034 |
-0.238 |
-0.260 |
0.499 |
0.011 |
0.030 |
-0.040 |
0.160 |
0.171 |
-0.331 |
0.023 |
-0.004 |
-0.019 |
-0.028 |
0.018 |
0.011 |
0.331 |
-0.157 |
-0.174 |
0.086 |
-0.243 |
0.157 |
0.034 |
-0.053 |
0.019 |
0.016 |
-0.046 |
0.030 |
-0.157 |
0.145 |
0.012 |
-0.246 |
0.072 |
0.174 |
-0.057 |
0.057 |
0.000 |
0.012 |
0.028 |
-0.040 |
-0.174 |
0.012 |
0.161 |
в) вычисление ковариационной матрицы уравненного вектора измеренных величин или СКО уравненного вектора измеренных величин
где
-
диагональные элементы матрицы Qβ
4.0128 |
4.0627 |
3.433 |
3.063 |
3.3741 |
4.0493 |
3.1339 |
3.2566 |
4.2143 |
3.433 |
2.27 |
2.3978 |
г) Вычисление обратной весовой матрицы функций измеренных величин (дирекционных углов и длин сторон)
Q α,s=FQβFT; где F – матрица частных производных.
|
αII-1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
αI-1 |
0 |
-1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
αI-2 |
0 |
-1 |
0 |
0 |
0 |
-1 |
0 |
0 |
0 |
0 |
0 |
0 |
|
αIII-1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
|
αIII-2 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
|
α1-2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-1 |
0 |
0 |
1 |
0 |
|
SII-1 |
-0.002 |
0.015 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
SI-1 |
-0.003 |
0 |
0.010 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
F= |
SI-2 |
-0.002 |
0 |
0.008 |
0.002 |
0.012 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
SIII-1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0.022 |
0 |
0.007 |
|
SIII-2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-0.014 |
-0.029 |
0.029 |
0 |
0.010 |
|
S1-2 |
0 |
0 |
0 |
0 |
0 |
0 |
0.026 |
0 |
-0.011 |
0.011 |
0 |
0.004 |
Q =
0.331 |
0.171 |
0.152 |
0.157 |
0.185 |
0.175 |
-0.002 |
0.004 |
0.003 |
-0.006 |
-0.007 |
-0.002 |
0.171 |
0.464 |
0.430 |
0.243 |
0.264 |
0.339 |
-0.008 |
0.001 |
-0.001 |
-0.004 |
-0.007 |
-0.003 |
0.152 |
0.430 |
0.858 |
0.224 |
0.523 |
0.564 |
-0.007 |
0.001 |
0.003 |
-0.004 |
-0.002 |
0.005 |
0.157 |
0.243 |
0.224 |
0.145 |
0.161 |
0.190 |
-0.004 |
0.001 |
0.000 |
-0.003 |
-0.005 |
-0.002 |
0.185 |
0.264 |
0.523 |
0.161 |
0.453 |
0.244 |
-0.004 |
0.002 |
0.002 |
-0.004 |
0.002 |
0.008 |
0.175 |
0.339 |
0.564 |
0.190 |
0.244 |
0.534 |
-0.006 |
0.001 |
0.003 |
-0.004 |
-0.009 |
-0.004 |
-0.002 |
-0.008 |
-0.007 |
-0.004 |
-0.004 |
-0.006 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.004 |
0.001 |
0.001 |
0.001 |
0.002 |
0.001 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.003 |
-0.001 |
0.003 |
0.000 |
0.002 |
0.003 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
-0.006 |
-0.004 |
-0.004 |
-0.003 |
-0.004 |
-0.004 |
0.000 |
0.000 |
0.000 |
0.000108 |
0.000 |
0.000 |
-0.007 |
-0.007 |
-0.002 |
-0.005 |
0.002 |
-0.009 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000441 |
0.000 |
-0.002 |
-0.003 |
0.005 |
-0.002 |
0.008 |
-0.004 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000417 |
д) Вычисление СКО дирекционных углов и длин сторон
αII-1 |
3.433 |
αI-1 |
4.063 |
αI-2 |
5.526 |
αIII-1 |
2.270 |
αIII-2 |
4.015 |
α1-2 |
4.360 |
SII-1 |
0.069 |
SI-1 |
0.042 |
SI-2 |
0.052 |
SIII-1 |
0.062 |
SIII-2 |
0.125 |
S1-2 |
0.122 |
е) Вычисление обратной весовой матрицы вектора координат определяемых пунктов Q x,y=FQα,s FT
|
αII-1 |
αI-1 |
αI-2 |
αIII-1 |
αIII-2 |
α1-2 |
SII-1 |
SI-1 |
SI-2 |
SIII-1 |
SIII-2 |
S1-2 |
|
0 |
0.010213113 |
0 |
0 |
0 |
0 |
0 |
-0.811 |
0 |
0 |
0 |
0 |
|
0 |
0.014141805 |
0 |
0 |
0 |
0 |
0 |
0.5855 |
0 |
0 |
0 |
0 |
F= |
0 |
0 |
0.012242157 |
0 |
0 |
0 |
0 |
0 |
-0.35903 |
0 |
0 |
0 |
|
0 |
0 |
0.00470925 |
0 |
0 |
0 |
0 |
0 |
0.933327 |
0 |
0 |
0 |
|
|
0.0000661 |
0.0000385 |
0.0000607 |
-0.0000190 |
||||
|
|
0.0000385 |
0.0001245 |
0.0000743 |
0.0000450 |
||||
Q x,y=FQα,s FT |
0.0000245 |
0.0000607 |
0.0000743 |
0.0001143 |
|||||
|
|
-0.0000190 |
0.0000450 |
0.0000504 |
0.0001097 |
||||
ж) Вычисление СКО положения пунктов
0.049 |
0.067 |
0.064 |
0.063 |