一 秩亏自由网平差
N=B'*B
N =
4 -1 -1 -1 3 -1 -1 -1 3 -1 -1 0 -1 0 0 0 0 -1 >> NN=N*N
NN =
20 -5 -6 -5 12 -5 -1 -1 -1 0 0 0 2 0 0 1 0 0 -5 -5 -4 1 0
0
-1
0
0
1
1
1
-6 -5 12 2 1 -4
-5 -4 2 6 1 0
-5 1 1 1 2 0
1 1 -4 >> NM=pinv(NN) NM =
0.1019 0.0386 0.0386 0.1523 -0.0721 -0.0053 0.0824 0.1284 0.1471 -0.1246 -0.2978 -0.13 >> NNM=N*NM 0 0
-0.0721 -0.0053 0.1731 -0.0995 -0.2978 0.3016
2
0.0824 0.1284 -0.0995 0.3363 -0.3877 0.1471 -0.2978 1.0255 -0.6902 -0.2978
-0.13
0.3016
-0.3877
-0.6902
1.2634
-0.1246 -0.0600 -0.0600
NNM =
0.2118 0.0035 -0.0590 0.0243 0.0451 -0.2257
0.0035 0.2951 -0.0174 0.0660 -0.1632 -0.1840
-0.0590 -0.0174 0.0243 0.0660 0.0451 -0.1632 -0.2257 -0.1840 >> X=NNM*B'*L X =
0.32
0.1042
2.2292
-0.2708
0.2951 -0.1215 -0.2257 -0.1215 0.4618 -0.1424 -0.2257 -0.1424 0.8785 0.1285 -0.2882 -0.3924 x= N-m * Bt * l)
0.1285
-0.2882
-0.3924
0.9618
(即:
-2.58
0.2292
>> V=B*X-0.001*L
V =
0.6240
2.9970
1.8750
-1.9980
-2.1210
-0.2520
0.3750
二 拟稳平差
>> B2=[B(1:7,4:6)
]
B2=
1 0 0
1 0 0
-1 0 1
0 0 -1
0 1 -1
-1 1 0
0 1 0
]B1=[B(1:7,1:3)
B1 =
-1 0 0
0 -1 0
0 0 0
0 0 1
0 0 0
0 0 -1 0 >> N=B'*B
N =
4 -1 -1 3 -1 -1 -1 -1 -1 0 0 0 0
0
-1 -1 -1 -1 3 0 0 2 0 0 -1 0 -1 0
0 0
0 -1
0 0
1 0
0 1
>>
N22=[N(4:6,4:6)]
N22 =
4 -1 -1
-1 3 -1
-1 -1 3
>> N21=[N(4:6,1:3)]
N21 =
-1 -1 0
-1 0 0
0 0 -1
>> N11=[N(1:3,1:3)]
N11 =
2 0 0
0 1 0
0 0 1
>> N12=[N(1:3,4:6)]
N12 =
-1 -1 0
-1 0 0
0 0 -1
>> N111=pinv(N11) (N11的逆矩阵)
>> M1=N21*N11*N12 (为)
)
>> M=N22-M1 (为)
)
>> K1=B2'-N21*N111*B1' ( K1即为αT )
>> MM=M*M
>> MMM=pinv(MM)
>> MMMM=M*MMM (MMMM 即为M m -
>> K2=MMMM*K1 (K2即为α-)
>> KP=B1'-N12*K2 (kp 即为
)
>> K3=N111*KP (K3即为β)
>> X1=K3*L
结果为:
V =
-0.6260
-0.3780
0.5000
2.0020
-2.8710
-2.3770
-3.0000
三 转换
H1=I-ST'*ST*PX/3
H1 =
1.0000 0 0 1.0000 0 0 0 0 0 0 0 0 1.0000 0 0
-0.3333 -0.3333 -0.3333 0.6667 -0.3333 -0.3333 -0.3333 -0.3333 -0.3333 0.6667 -0.3333
-0.3333
-0.3333
-0.3333
-0.3333
0 0 0 -0.3333 -0.3333 0.6667
>> XN=H1*X
XN =
1.2500
1.0000
3.1250
0.6250
-1.7500
1.1250
>> V=B*XN-0.001*L
V =
0.6240
2.9970
1.8750
-1.9980
-2.1210
-0.2520
0.3750
残差v的结果与拟稳平差的结果一致
四 假设一点a的高程,利用经典平差,进行平差计算。
>> N=A*Q*A'
N =
3 2
2 3
>> K=inv(N)*W
K =
2.0000
0
>> V=Q*A'*K
V =
0
0
2.0000
0
2.0000
-2.0000
0
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