GATE Geomatics Engineering Common Syllabus

Common syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Common in GATE Geomatics Engineering, not a summary of it.

1. 1

   Engineering Mathematics

   7 topics

   • Surveying measurements
     • Accuracy
     • Precision
     • Most probable value
   • Errors and their adjustments
   • Regression analysis
   • Correlation coefficient
   • Least square adjustment
   • Statistical significant value
   • Chi square test
2. 2

   Remote Sensing

   6 topics

   • Basic concept
   • Electromagnetic spectrum
   • Spectral signature
   • Resolutions
     • Spectral
     • Spatial
     • Temporal
     • Radiometric
   • Platforms and Sensors
   • Remote Sensing Data Products
     • PAN
     • Multispectral
     • Microwave
     • Thermal
     • Hyperspectral
     • Visual and digital interpretation methods
3. 3

   GNSS

   5 topics

   • Principle used
   • Components of GNSS
   • Data collection methods
   • DGPS
   • Errors in observations and corrections
4. 4

   GIS

   7 topics

   • Introduction
   • Data Sources
   • Data Models and Data Structures
   • Algorithms
   • DBMS
   • Creation of Databases (spatial and non-spatial)
   • Spatial analysis
     • Interpolation
     • Buffer
     • Overlay
     • Terrain Modeling
     • Network analysis

Common flashcards for GATE Geomatics Engineering

22 of 50 cards from the Common deck — real questions with worked answers.

1. What is the fundamental purpose of taking surveying measurements, and why are they never exact?

   Surveying measurements quantify distances, angles, and elevations to determine relative positions of points. They are never exact because every measurement is affected by instrumental imperfections, human limitations, and environmental conditions, so each contains some error.

2. Define 'accuracy' in the context of surveying measurements.

   Accuracy is the degree of closeness (conformity) of a measured value to its true value. High accuracy means small total error (small deviation from the truth).

3. Define 'precision' in surveying.

   Precision is the degree of closeness or repeatability among a set of repeated measurements of the same quantity. It reflects the refinement/consistency of the measurements, independent of the true value.

4. Compare accuracy and precision: can a measurement set be precise but not accurate?

   Yes. Precision = repeatability (small spread); accuracy = closeness to truth. A set can be tightly clustered (precise) yet systematically offset from the true value (inaccurate). High accuracy requires both small random spread and absence of systematic error.

5. What is the 'most probable value' (MPV) of a quantity measured repeatedly with equal weight?

   The most probable value is the value with the greatest likelihood of being closest to the true value. For equally weighted direct observations it is the arithmetic mean: $$\text{MPV} = \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

6. How is the most probable value computed for weighted observations?

   It is the weighted mean: $$\text{MPV} = \frac{\sum w_i x_i}{\sum w_i}$$ where $w_i$ is the weight assigned to observation $x_i$.

7. Define 'residual' (deviation) in measurement adjustment.

   A residual is the difference between an individual observation and the most probable value: $v_i = x_i - \bar{x}$. It is an estimate of the error and the sum of residuals about the mean is zero, $\sum v_i = 0$.

8. What are the three main classes of errors in surveying?

   (1) Gross errors (mistakes/blunders) due to carelessness; (2) Systematic (cumulative) errors that follow a physical law and have consistent sign/magnitude; (3) Random (accidental) errors that remain after blunders and systematic errors are removed.

9. How do systematic errors differ from random errors in behaviour and treatment?

   Systematic errors are predictable, follow a definite law, accumulate, and have a consistent sign — they can be computed and corrected/eliminated. Random errors are unpredictable in sign and magnitude, follow the normal distribution, tend to cancel, and are treated statistically (cannot be removed, only minimized).

10. Why are only random errors handled by the theory of errors / least squares?

    Because blunders are detected and removed and systematic errors are eliminated by calibration/correction beforehand. The remaining residual random errors obey the normal (Gaussian) probability law, which underlies least-squares adjustment.

11. State the laws (axioms) of accidental (random) errors.

    (1) Small errors occur more frequently than large errors; (2) Positive and negative errors of the same magnitude are equally likely; (3) Very large (extreme) errors do not occur (they are blunders). This produces the symmetric bell-shaped normal distribution.

12. What is the standard deviation $\sigma$ of a set of measurements, and what does it represent?

    It is a measure of dispersion (precision) about the mean: $$\sigma = \sqrt{\frac{\sum v_i^{2}}{n-1}}$$ where $v_i$ are residuals and $n$ the number of observations. Smaller $\sigma$ indicates higher precision.

13. What is the standard error (standard deviation) of the mean?

    $$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$$ It expresses the precision of the most probable value (mean); it decreases as the number of observations $n$ increases.

14. Define the 'probable error' of a single observation and the constant used.

    The probable error is the magnitude of error such that there is a 50% chance the true error is smaller. For a single observation: $$E_s = 0.6745\,\sigma = 0.6745\sqrt{\frac{\sum v^{2}}{n-1}}$$

15. How are weights related to the standard error of observations?

    Weight is inversely proportional to the square of the standard error (variance): $$w_i \propto \frac{1}{\sigma_i^{2}}$$ A more precise observation (smaller $\sigma$) receives a larger weight.

16. State the principle of least squares used in measurement adjustment.

    The most probable values of observed quantities are those that make the sum of the weighted squares of the residuals a minimum: $$\sum w_i v_i^{2} = \text{minimum}$$ For equal weights, $\sum v_i^{2}$ is minimized.

17. What is the objective of least square adjustment in a redundant survey network?

    To find a unique, statistically optimal set of corrected (adjusted) values that satisfies all geometric conditions when there are more observations than unknowns (redundancy), by minimizing $\sum w v^{2}$. It yields the most probable values and their precision estimates.

18. In least squares, what is meant by 'degrees of freedom' (redundancy)?

    Degrees of freedom = number of observations minus number of unknowns ($r = n - u$). It is the number of redundant measurements available to check and adjust the network; redundancy enables error detection and statistical adjustment.

19. Define regression analysis and what it determines.

    Regression analysis is a statistical method that establishes a functional (mathematical) relationship between a dependent variable and one or more independent variables, allowing prediction of the dependent variable. It fits a best line/curve (often by least squares) through the data.

20. Write the equation of a simple linear regression line of $y$ on $x$ and identify the terms.

    $$y = a + bx$$ where $b$ is the regression coefficient (slope) and $a$ is the intercept. They are found by least squares: $b = \frac{\sum(x-\bar{x})(y-\bar{y})}{\sum(x-\bar{x})^{2}}$ and $a = \bar{y} - b\bar{x}$.

21. What does the regression coefficient $b$ of $y$ on $x$ physically represent?

    It is the slope — the average change in the dependent variable $y$ per unit change in the independent variable $x$: $$b_{yx} = \frac{\text{Cov}(x,y)}{\sigma_x^{2}} = r\frac{\sigma_y}{\sigma_x}$$

22. Define the correlation coefficient $r$ and give its formula.

    The (Pearson) correlation coefficient measures the strength and direction of the linear relationship between two variables: $$r = \frac{\sum (x-\bar{x})(y-\bar{y})}{\sqrt{\sum (x-\bar{x})^{2}\,\sum (y-\bar{y})^{2}}} = \frac{\text{Cov}(x,y)}{\sigma_x \sigma_y}$$

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Planning Common for GATE Geomatics Engineering

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