Course Catalog 2012-2013
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Basic Pori International Postgraduate Open University

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Course Catalog 2012-2013

MAT-45807 Mathematics for Positioning, 4 cr

Additional information

The course MAT-45807 is for masters students whose major subject is mathematics and for all PhD students. The course MAT-45806 is for masters students whose major is other than mathematics. The two courses have common lectures and exercises but different homework problems and different exams.
Suitable for postgraduate studies

Person responsible

Henri Pesonen, Robert Piche, Simo Ali-Löytty

Lessons

Study type P1 P2 P3 P4 Summer Implementations Lecture times and places
Lectures
Excercises


 
 2 h/week
 2 h/week


 


 


 
MAT-45807 2012-01  

Requirements

Exam and weekly exercises. The student needs to obtain at least one third of the exercise points before taking the exam.
Completion parts must belong to the same implementation

Principles and baselines related to teaching and learning

The course consists of lectures, homework problems and weekly teacher-supervised exercises where students work on problems using their own computers and present their solutions.

Learning outcomes

Upon completing the required coursework, the student understands the principles of mathematical tools such as quaternions, optimisation algorithms and Bayesian estimation, well enough to adapt and apply them for novel technology solutions in positioning, navigation, and other application areas.

Content

Content Core content Complementary knowledge Specialist knowledge
1. Conversion between three representations of rotation in space: direction cosine matrix, axis and angle of rotation, quaternions; applying a sequence of rotations; tracking coordinates (heading and elevation)  Rotation of point vs rotation of frame; representations' singularities and uniqueness; Euler angles  The closest orthogonal matrix; the closest unit quaternion; the algebra SO(3) 
2. Multivariate normal distribution: mean, covariance, affine mapping, marginal distribution, conditional conditional distribution;  95% ellipsoid, Chebyshev inequality; uncorrelation and independence   
3. Static positioning: measurement function and its linearization, Bayesian estimation for linear model, approximate posterior using linearization or cubature; MAP estimate using Gauss-Newton method.  GPS pseudorange; triangulation measurements; weighted least squares; Matlab/Octave implementation   
4. Filtering: Kalman filter, Extended Kalman Filter (EKF), Cubature Kalman Filter (UKF)  Matlab implementation; steady-state Kalman filter; batch filter   

Evaluation criteria for the course

The final grade is based on the combined points from exercises and final exam. The exam will be "open book" style, meaning you can bring your calculator and any written material you wish. Student must earn at least one third of the exercise points before writing the exam.

Assessment scale:

Numerical evaluation scale (1-5) will be used on the course

Partial passing:

Completion parts must belong to the same implementation

Study material

Type Name Author ISBN URL Edition, availability, ... Examination material Language
Book   Bayesian Estimation of Model Parameters   Robert Piche       The URL is to a draft version of a chapter from the book Mathematical Modeling with Multidisciplinary Applications edited by Xin-She Yang and published by Wiley      English  
Book   Quaternions and Rotation Sequences   Jack B. Kuipers            English  

Prerequisites

Course Mandatory/Advisable Description
MAT-31096 Matrix Algebra 1 Mandatory    
MAT-33311 Tilastomatematiikka 1 Mandatory    

Prerequisite relations (Requires logging in to POP)



Correspondence of content

Course Corresponds course  Description 
MAT-45807 Mathematics for Positioning, 4 cr MAT-45806 Mathematics for positioning, 3 cr  
MAT-45807 Mathematics for Positioning, 4 cr MAT-60606 Mathematics for Positioning, 4 cr  

More precise information per implementation

Implementation Description Methods of instruction Implementation
MAT-45807 2012-01 This course is for masters students whose major subject is mathematics and for all PhD students. The course MAT-45806 is for masters students whose major subject is other than mathematics. The two courses have common lectures and exercises but different homework problems and different exams.   Lectures
Excercises
Practical works
   
Contact teaching: 0 %
Distance learning: 0 %
Self-directed learning: 0 %  

Last modified07.03.2012