Geomatic Computation

Year: III Semester: VI

Course Objectives:

a. To provide a basic concept of the propagation of error.
b. To provide theoretical and practical knowledge on survey computation.

Course Content:

1. Most Probable Value (8 hrs)

1.1 Rounding of figures: Digit-based, Unit-based
1.2 Estimation, Interpolation, Extrapolation
1.3 Error, Types of Error
1.4 Central Tendency: Mean, Median, Mode, and their properties
1.5 Least square adjustment
1.6 Most probable value
1.7 Laws of Weight
1.8 Normal Equations

2. Level Adjustments (8 hrs)

2.1 Errors in levelling and adjustment
2.2 Obstacles in Levelling
2.3 Effect of Refraction and Curvature
2.4 Trigonometric Levelling

• Base Accessible
• Base Inaccessible and instruments in the same vertical
• Base Inaccessible and instruments in different verticals

3. Traverse Adjustment (10 hrs)

3.1 Measurement of distance and angle
3.2 Station adjustment and figure adjustment
3.3 Angle adjustment (Equal proportion and proportional to distance)
3.4 Height adjustment (Equal proportion and proportional to distance)
3.5 Least square adjustment

4. Triangulation Adjustment (10 hrs)

4.1 Introduction
4.2 Single chain and multiple chain
4.3 Strength of figure
4.4 Condition equations
4.5 Adjustment of geodetic triangle
4.6 Adjustment of braced quadrilateral
4.7 Adjustment of polygons with a centre station

5. Photogrammetric Adjustment (8 hrs)

5.1 Introduction
5.2 Geometry of photographs
5.3 Errors in photographs
5.4 Bundle block adjustment

• Inner, relative, and absolute Geometry
• Interior and exterior orientation
• Rectification and selection of transformation types
  5.5 Height measurement
  5.6 Coordinate transformation

Exercise: (30 hrs)

1. Related calculations of chapters 2-5.

Recommended Reading and Reference Books:

1. H.F. Rainsford, Survey Adjustment and Least Squares, London, UK.
2. A.L. Allan, J.R. Holloway, and J.H. Maynes, Practical Field Survey and Computation, London, UK.
3. P.R. Wolf, Adjustment Computation (Practical Least Squares for Surveyors), Land Mark Enterprises, 1980.
4. E.M. Mikhail & G. Gracie, Analysis and Adjustment of Surveying Measurements, Van Nostrand-Reinhold, Co. New York, NY, 1981.
5. B. Austin Barry, Errors in Practical Measurement in Science, Engineering, and Technology, Landmark Enterprises, Ranch Corvado, CA, 1992.

Examination Scheme

Model Questions

Very short questions [4×2 = 8]

1. Define unit-based rounding.
2. What are the errors in levelling?
3. What do you understand by figure adjustment?
4. List the errors corrected by stereo orientation.

Short Questions [8×4 = 32]

5. Explain how you can form a normal equation to find the values of variables.
6. List the laws of weight and explain with an example.
7. How can you measure the height of an inaccessible object where instruments are kept in the same vertical and at a similar height?
8. Explain the method of angle adjustment with equal proportion in a traverse loop.
9. Derive the condition equation for a polygon with a centre station.
10. How can you check the error in exterior orientation and adjust it?
11. Explain the indirect method of coordinate transformation.
12. Explain when you select a single chain triangulation network and why.

Long Questions [10×2 = 20]

13. Derive a relation to show that the sum of squares of deviations from the mean is minimum.
14. Derive a relation to find the height of an object whose base is inaccessible and the instruments are kept in different verticals.
    OR
    Derive the required relations to adjust the interior angles of a braced quadrilateral formed in a triangulation chain by the method of least squares.