误差理论与测量平差基础习题集5(参考答案)

= 28

1

1111(?)?P3 3.5.60 (1)1/Px =Qx =1 (2)1/PY =QY =4P1P24L2111?9L43P1P3

(3)1/PZ =QZ =3.5.61

PA?62C2?3

3.5.62

1????????2?????f12??2ff?f2?12???PF?P??P??P??22

?????1??2???P??=P1P2式中:

?2?nPn

??????1?1??2?2???P2P??=P1

?????1??2??? ?P?=P1P222?n?nPn

??n2Pn

?69??914?? 3.5..63 QYY =??69??96??139??913??139??96?????? 3.5.64 Qyy= Qyz = Qzx =??2124??3135??7383??3135??2124??8394?????? Qyw= QZW = QWW=??2?.??.QLL=?66?.?.??.3.5.65

.?2-1...??-12...??..2-1.?..-12.??....2? ....?2-1......??-12......????..2-1....???..-12....?QLL=?66?....2-1..???....-12..???......2-1???......-12???? 3.5.66 3.5.67 (1) (2)

-1QXX=(BTB)

-1TQ??=B(BTB)BLL

QVX=0 V与X互不相关

QVVL?=0?互不相关 V与L???3.6.71 (1)S=6 000.027(m) (2)0=1.11(mm)

(3) (5)

?全???=2.72(mm) (4)平=1.92(mm) ?L?2=1.57(mm)

3.6.72 (1) (2) (3) (4)(5)

?0?=1.27(mm)

???1???=1.33(mm) 2=2.06(mm) 3=0.90(mm) ?L?1=0.94(mm)

?L?2

=1.46(mm)

?L?3

=0.64(mm)

?全?=2.62(mm)

?L?全=1.85(mm)

3.7.75 σ全 =0.004 2(m)

3.7.76 DZZ =KDLLKT + KεεTKT DZY = KDLLKT + KεεTFT 3.8.77 令P点坐标X、Y的协方差阵为

2?x?xy?????2??????yz? y? ??LD???31LL本题分两步解算:第一步先求平差角向量L的协方差阵,令=

??L?1?L2?2-1-1?1??2DLL-12-1(秒)??=??T3??L?3??-1-12??,可求得

第二步求平差后P点坐标X、Y的协方差阵,其中有:

?YAP??12???XcotL?]D??XcotL???x??2[?YAP?XAPcotL2AP3LL?AP2?????XcotL??AP3? ?

???XAP?12???XcotL?]D??YcotL???y??2[?YAP?XAPcotL2AP3LL?AP2?????YcotL??AP3??

???XAP?12???YcotL?]D??YcotL???y??2[??XAP?YAPcotL2AP3LL?AP2?????YcotL??AP3? ? </

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