Computational Techniques in Geomatics

Syllabus

1. Introduction (8 hours)
   1. Fundamentals of computational techniques
   2. Programming languages: Python, R and MATLAB for geomatics (Basic data structures, algorithms and programming concepts)
   3. Geospatial software and tools
   4. Geospatial data processing and management
2. Matrix Operations in Geomatics Engineering Problems (8 hours)
   1. Solution of linear equations
   2. Gauss method, Gauss-Jordan method
   3. Eigenvalues and eigenvectors
   4. Differentiation of matrices and quadratic forms
3. Coordinate System and Transformations (12 hours)
   1. Coordinate system
   2. Two-dimensional (2-D) and three-dimensional (3-D) transformations: Conformal, affine, projective transformation
   3. 2-D coordinate transformation by general least squares: Adjustment in cartesian geodetic system; Adjustment in curvilinear geodetic system; Adjustment in local system
   4. 3-D coordinate transformation by general least squares
4. Blunder Detection in Horizontal Networks (8 hours)
   1. Blunders: Priori method for blunder detection; Posteriori blunder detection
   2. Outliers detection: Data snooping and tau criterion
   3. Reliability of adjusted control network
   4. Statistical blunder detection
5. Dynamic Mode Filtering and Prediction (12 hours)
   1. Prediction, filtering and smoothing
   2. Static mode filter: Real-time moving averages and sequential least adjustment
   3. Kalman filtering process
   4. Kalman filter and the least squares method: Relationship (Linear, linearized and extended Kalman filter); System model and process noise model; Real-time trajectory estimation and GNSS/INS integration
6. Network Design (12 hours)
   1. Pre-analysis of survey observations: Survey tolerance limits; Pre-analysis models; Trigonometric leveling problems
   2. Network design model: 2-D and 3-D
   3. Simulation of network: 2-D, 3-D; Monte-Carlo and agent based modelling
   4. Computer optimization: Cholesky decomposition; Storage optimization; Spareness and optimization of the normal matrix

Tutorials

1. Geospatial analysis: Principal component analysis (PCA)
2. Remote sensing: Processing and analyzing satellite images
3. Network analysis: Analyzing and optimizing transportation and utility networks
4. Monte Carlo method and applications
5. Agent-based model and applications
6. Spatiotemporal big data analytics and applications
7. Spatial smoothing and spatial interpolation

Practicals

1. Matrix operations in geomatics problems: Solution of linear equations; Gauss method, Gauss-Jordan method; Eigen values and eigenvectors; Differentiation of matrices and quadratic forms
2. 2-D and 3-D coordinate transformations
3. 2-D and 3-D datum transformations
4. Blunder detection and computer optimization (Cholesky decomposition)
5. Algorithm development and application labs on Kalman Filtering