Week 9: Techniques II

Question 1

To undergo an intersection and determine coordinates for a point, we require a minimum of

Answer 1

2 bearings

Question 2

Considerations of an intersection

Answer 2

1. Strength of geometry
2. Redundancy
   - more intersecting rays
   - measure distances

Question 3

Intersection applications

Answer 3

1. Determine coordinates of an inaccessible point, e.g a church spire, harbour beacon, airport runway lights
2. Detail fixing for points delineating a topographical feature e.g a building corner or tree
3. Cadastral survey road calculations or boundary intersections

Question 4

In an intersection, accuracy and precision will depend on what four factors

Answer 4

1. The instrument used
2. The geometry
3. Combined with other measurements to strengthen fix
4. The uncertainty of known points

Question 5

How does the instrument used impact accuracy and precision

Answer 5

1. Least count or resolution e.g a 5” T/S
2. The number of measurements (how many sets)

Question 6

How does the geometry impact accuracy and precision

Answer 6

A 90 degree intersection is best

Question 7

How does combining with other measurements to strengthen fix impact accuracy and precision

Answer 7

1. Include distances
2. Free station

Question 8

How does the uncertainty of known points impact accuracy and precision

Answer 8

You cannot compute accurate coordinates if the known points have inaccurate coordinates

Question 9

Both observations and calculations need to be checked for the reliability of an intersection. 3 intersecting rays gives a check and will show

Answer 9

That an error exists, but not where the error is

Question 10

4 intersecting rays will show

Answer 10

Which observation is wrong, so long as there is only one blunder

Question 11

Redundancy in intersections is critical for determining

Answer 11

Measurement/position precision
E.g an intersection of only 2 rays at 90 degrees apart is not reflected in the shape/size of an error ellipse. The error ellipse will look fine, but the intersection is unchecked

Question 12

Calculation process for a two bearing intersection

Answer 12

1. Compute join bearing and distance
2. Compute bearing
3. Compute angle and distance
4. Compute coordinate of intersection point

Question 13

Calculation process for a two-distance intersection

Answer 13

1. Compute join bearing and distance
2. Using the cosine rule, calculate angle a
3. Compute bearing
4. Compute coordinate of intersection point

Question 14

Two soft ways to handle redundancy in intersections

Answer 14

1. Compute a semi-graphical solution (using all observations) and also using an error figure
   - Rays (observed lines) were weighted according to distance from point p, and a best fit solution arrived.
2. Can compute multiple coorsinates for point P using different combinations of intersecting rays. Compute mean coordinate
   - solution is adhoc and will be biased towards the observed lines used more often
   - not optimal

Question 15

Best method of handling redundancy

Answer 15

Using the least squares estimation (LSE)

Question 16

A least squares estimation involves

Answer 16

1. All observations being used (m and observation weighting)
2. Unique solution and provides an estimate of coordinate precision (standard deviations, error ellipse)
3. Today there are various software packages available (12D)

Question 17

A position fix, irrespective of method, is dependent on

Answer 17

Measurement geometry and measurement precision

Question 18

For any position error ellipse, shape is dependent on

Answer 18

Measurement geometry

Question 19

For any position error ellipse, size is dependent on

Answer 19

Measurement precision

Question 20

Note the provided information for a resection calculation to three points

Answer 20

1. Coordinates of three points A, B and C
2. Observed directions (unoriented) from a point P (coordinates unknown) - alternatively angles a and g

Question 21

A resection calculation is required when

Answer 21

Angle observations have been made to an unknown point

Question 22

The problem with conducting a resection

Answer 22

Angle observations lack orientation

Question 23

In a resection, a strong position fix is obtained if

Answer 23

The angles are large - > 60 degrees is ideal

Question 24

In a resection, directions (i.e unorientated) are observed from an unknown point to a minimum of

Answer 24

Three points with known coordinates

Question 25

In a resection, 3 rays will give a unique solution, but

Answer 25

There is no redundancy and hence no check - if you have booked/observed one direction incorrectly, the calculated solution will be wrong

Question 26

In a resection, 4 rays will give

Answer 26

4 solutions, ABC, ABD, BCD, CDA

Question 27

In a resection, 5 rays is better still, and gives how many arbitrary possible solutions

Answer 27

10

Question 28

Two resection uses

Answer 28

1. A resection saves visiting distant survey marks which have beacons e.g trigs 2. Distance measurements require a prism ... but now we have reflectorless

Question 29

Three ways resections can be strengthened

Answer 29

1. Observe one or more forward rays - from one of the points with known coordinates 2. Measure one or more distances - to one of the points with known coordinates 3. A free station involves observing directions and measuring distances to a minimum of two points with known coordinates

Question 30

A 2D resection involves

Answer 30

Horizontal distances

Question 31

A 3D resection involves

Answer 31

Horizontal distances, Slope distances and zenith angles

Question 32

Free stations are convenient for requirements of

Answer 32

Safety, i.e where there is heavy traffic on a road or survey marks in the road

Question 33

Three scenarios of a resection

Answer 33

1. P between three fixed points 2. Middle point further 3. Middle point closer

Question 34

In a resection, the danger circle is when

Answer 34

The position solution is indeterminate because A, B, C and P all lie on the circumference of a circle

Question 35

The danger circle is only possible when

Answer 35

The middle point is the furthest

Question 36

Why is the danger circle bad

Answer 36

1. The three points A, B, C, lie on the same circle 2. Therefore, the three circles are coincident (or almost coincident) 3. Hence, the tangent lines are parallel 4. Mathematically, the solution becomes weak and unstable as points approach the danger circle

Question 37

Checks for a three ray (unique) solution resection

Answer 37

Take out joins from the coordinates you compute and check that a constant OC applied to all observations equals the three join bearings

Question 38

Checks for when there are more than three rays in a resection

Answer 38

Review the results of the least squares solution - The size of residuals on angles will give some measure of how good the resection has been, and - the error ellipse should ideally be small and circular

Question 39

Uses of calculations in resections

Answer 39

1. Can use 12D 2. Review script 3. Consider layout of coordinates 4. Consider layout of dataset 5. Results as detailed in script - LS estimate of 3D positions (ENH) - Residuals - error ellipse

Question 40

How can hybrid surveys be advantageous

Answer 40

1. GNSS used for control and TA for peg ties and detail work - GNSS requires sky visibility - TS requires orientations and intervisibility 2. Combining GNSS an TS provide robust checks

Question 41

Choices of methods available for positioing and heighting surveys

Answer 41

1. Hybrid surveys 2. EDM measurements in a GNSS local transformation 3. GNSS and inertial to overcome GNSS constraints such as shadowing that can make traversing more cost effective (need motion measurement or determination

Question 42

GNSS equipment often has a higher capital cost, therefore

Answer 42

Has to be kept busy to justify return on investment

Question 43

It may make sense to use what in conjunction with GNSS

Answer 43

Less expensive equipment such as a total station

Question 44

Combine GNSS(ppints) and distance measurements (EDM or taped distances) in a network adjustment using

Answer 44

SNAP, or other adjustment tools