surveying-chapter7

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Surveying handout

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  • 1

    Triangulation Trilateration

    1.

    2.

    3.

  • 2

    1.

    2.

    3.

    1. A,B C,D,E,F

  • 3

    1.

    r124(2)=4

    ABFBCFCEFCDE

    180r

    r84(2)=0

  • 4

    2.

    AB

    CDEF

  • 5

    2.

    r164(2)=8

    (1) ABCBCFCFACFDCDEDEF

    180

    (2) ABBCCFFAAB

    AB

    62=8=r

    18sin6sin4sin2sin

    7sin5sin3sin1sin

    116sin14sin12sin10sin

    15sin13sin11sin9sin

  • 6

    2.

    r104(2)=2

    (1) ABCABFCF

    (2) CFDCFEDE

    2=r

  • 7

    3.

    AB

    CDEF

  • 8

    3.

    r154(2)=7

    (1) 5AFBBFCCFDDEFEFA

    180

    (2) 111+12+13+14+15=360

    (3) AFBFCFDFEFAF

    511=7=r

    110sin8sin6sin4sin2sin

    9sin7sin5sin3sin1sin

  • 9

    3.

    r94(2)=1

    ABFBFCCFDDFEAE

    1=r

  • 10

    1. RedundancyConstraint

    2.

    3

    1+2+3+4=180(1)

    3+4+5+6=180(2)

    5+6+7+8=180(3)

    1+2+7+8=180(4)

    1+2+3+4+5+6+7+8=360(5)

    (4)=(1)-(2)+(3)

    (5)=(1)+(3)

    3(1)(2)(3)

  • 11

    3.

    r=7-4=3

    (1)

    1+2+3+4=180

    3+4+5+6=180

    (2)

    765180sin6sin4sin2sin7sin5sin3sin1sin

  • 12

    r=148=6

    (1)

    1+2+10=180

    3+4+11=180

    5+6+12=180

    7+8+13=180

    (2)

    10+11+12+13+14=360

    (3)

    914180sin8sin6sin4sin2sin9sin7sin5sin3sin1sin

  • 13

    r=98=1

    ABCABF

    CF

    4. 0

    Least Squares AdjustmentLSA

  • 14

    5. LSA

    LSA

    LSAr0

    6. Dells Method

    Dells MethodLSA

  • 15

    7. /

    8. /LSA

    9. /

    10.

    (1)

    (2)

    11.

  • 16

    /

    AB

    CC

    ( ) ( )

    AB

    = ( )

    ( )

    AC

    BC ACd BCd

    AC BC

    ACd

    BCd

  • 17

    Distance Angle

    AB

    AC

    ABAB

    0180

    90

    ACd

    sinsin

    ABAC sin/sin ABAC

    sin/cos

    AB

    AC

    2sin

    cossin

    AB

    AC

    2

    1

    2

    2

    2

    22

    sin

    cossinsin/cos

    ABABAC

    ACAC

  • 18

    = = =

    k=1

    k>>1

    r(=1)

    AC

    kdd

    180

    180

    2

    1

    2

    r

    1803

    1

  • 19

    (1) C

    (2)

    (3) AB

    AC AC

    AC

  • 20

    AB

    C

    C

    C

    11 dd

    22 dd

    1d AC 2d BC

    1d

    2d

  • 21

    cos=

    cos2 312

    3

    2

    1

    2

    2 ddddd

    222321312

    1cos ddd

    dd

    31222321 2/ ddddd

    222

    2

    21

    2

    2

    2

    2 1/

    1

    1

    2

    2

    2

    2

    2

    1

    2

    21 dd dd

    3

    2

    1

    2

    2

    2

    1

    3

    31 222

    1

    dd

    d

    d

    d

    dd

    31

    2

    2 dd

    d

    d

  • 22

    case1.

    =100.000m 100.000m 199.990m

    = =0.010m 0.000m

    case2.

    =100.000m 100.000m 0.010m

    = =0.010m 0.000m

    case3.

    =100.000m 100.000m 141.421m

    = =0.010m 0.000m 1d

    1d

    1d

    1d

    1d

    1d

    2d

    2d

    2d

    2d

    2d

    2d

    3d

    3d

    3d

    3d

    3d

    3d

  • 23

    X Y (m) (m)

    Case1 00-24-18.5 0.010 0.707

    Case2 81-01-42.5 141.421 0.012

    Case3 00-00-20.6 0.010 0.010

  • 24

    case1.

    Rad=00-24-28

    9995.010099.1992/10010099.199 222

    3

    2

    2

    2

    3

    2

    1

    2

    2

    2

    1

    3

    31

    1099925.4

    99.1991002

    100

    1002

    99.199

    99.1992

    1

    222

    1

    dd

    d

    d

    d

    dd

    3

    31

    2

    2

    1000025.599.199100

    100

    dd

    d

    d

    10232322 10995.491000025.51025.999.401.0 5210222 1099962.499995.01/10995.491/

    2107071.0

  • 25

    case1.

    m

    m

    cos1 dX cos1

    d

    X

    sin1

    d

    X

    221222 sincos1

    ddX

    422422 1001.01010001.099995.0 010.0X

    sin1 dY sin1

    d

    Y

    sin1d

    Y

    221222 cossin1

    ddY

    49991.010 99962.4 99995.010001.010 52224

    7070.0Y

  • 26

    case2.

    Rad=81-01-42.5

    -5222 1050.011002/1000.01100

    100

    0.011002

    100

    1002

    0.01

    0.012

    1

    222

    12

    2

    2

    3

    2

    1

    2

    2

    2

    1

    3

    31

    dd

    d

    d

    d

    dd

    1000.01100

    100

    31

    2

    2

    dd

    d

    d

    210010001.0 2222

    2.0000Rad10251/21/ -10222 1.414

  • 27

    case2.

    m

    m

    cos1 dX cos1

    d

    X

    sin1

    d

    X

    221222 sincos1

    ddX

    200002.0000110010105 222-25- 141.421X

    sin1 dY sin1

    d

    Y

    sin1d

    Y

    221222 cossin1

    ddY

    4-25-22 101.5 2.0000 105 10001.01 012.0Y

  • 28

    case3.

    Rad=00-00-20.6

    2

    121000012/1002100100 2

    22

    0

    20011002

    100

    1002

    2001

    20012

    1

    222

    12

    2

    2

    3

    2

    1

    2

    2

    2

    1

    3

    31

    dd

    d

    d

    d

    dd

    2100

    1

    2100100

    100

    31

    2

    2

    dd

    d

    d

    82

    222 102

    1

    2100

    1001.0

    Rad102

    11/10

    2

    11/ 8

    2

    8222

    -410

  • 29

    case3.

    m

    m

    cos1 dX cos1

    d

    X

    sin1

    d

    X

    221222 sincos1

    ddX

    48-2

    2

    2

    10102

    110001.0

    2

    1

    010.0X

    sin1 dY sin1

    d

    Y

    sin1d

    Y

    221222 cossin1

    ddY

    4-8-2

    2

    2

    1010 2

    110001.0

    2

    1

    010.0Y

  • 30

    1. C

    2.

    3.

    4.

  • 31

    1.

    2.

    3.

    4.

    5.

    6.

    7.

  • 32

    1. 1. 2.

    1. 2.

    2. 1. 2.

    1. EDM

    3. 1. 2.

    1. 2. GPS

    4.

    1. 1. GPS

    5. 1. GPS()