Course Catalog 2010-2011
Basic

Basic Pori International Postgraduate Open University

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Course Catalog 2010-2011

MAT-45807 Mathematics for Positioning, 4 cr

Person responsible

Henri Pesonen, Robert Piche, Simo Ali-Löytty

Lessons

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



 
 2 h/week
 2 h/week
 24 h/per



 



 



 
MAT-45807 2010-01  

Requirements

Exam, approved week exercises (at least 34%) and at least half of returnable exercises need to be passed before the exam.
Completion parts must belong to the same implementation

Principles and baselines related to teaching and learning

The course consists of lectures, returnable exercises and week exercises. Solving week exercises at home gives bonus points (0-6 points) for exam.

Learning outcomes

Upon completing the required coursework, the student is able to analyze mathematically and apply different position methods. He/she can also apply linear algebra and the probability theory to real world problem. After the course the student has the necessary skills to use basic closed form static positioning methods, nonlinear Kalman filters, Gaussian mixture filters and particle filters. Moreover, the student is able to apply these methods to new position application.

Content

Content Core content Complementary knowledge Specialist knowledge
1. Review of linear algebra and probability theory: Schur decomposition, square root of matrix, overdetermined system of equations, non-singular and singular multivariable Gaussian (normal) distribution and expectation of random variable.  Independence of random variables; conditional probability density function; conditional expectation; expectation of affine transformation; Generation of the sample from the Gaussian distribution; Uniform distribution  rank theorem; null space; orthogonal matrix; properties of idempotent matrix; definiteness of a matrix; Gaussian mixture (sum) distribution; visualization of probability density function of the Gaussian distribution; chi-square distribution 
2. Static positioning: measurement equations, iterative least squares method (Gauss-Newton method), maximum likelihood method and Bayesian method.  Weighted Gauss-Newton method; sensitivity analysis; closed form positioning formulas; Bayesian error analysis; Confidence intervals; Chebyshev inequality.  Bancroft method; Dilution of Precision (DOP)-numbers: GDOP, PDOP, HDOP, VDOP and TDOP; n-dimensionla Chebyshev inequality; coordinate systems.  
3. Filtering: different variations of Kalman filter, general Bayesian filter. Optimal estimators: posterior mean, maximum a posteriori (MAP) and Best Linear Unbiased Estimator (BLUE); Nonlinear Kalman filters: Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF); particle filters: Sequential Importance Sampling (SIS), Sampling Importance Resampling (SIR)  Derivation of Kalman filter; constant velocity model; Monte Carlo integration; number of effective samples; systematic resampling; filters MatLab implementations  Stochastic process; white noise; Gaussian mixture filter; law of large number; different proposal distributions 

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 pocket calculator and any written material you wish. Student have to get at least two bonus points and half of returnable exercises need to be passed before the final 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
Summary of lectures   Mathematics for Positioning   Simo Ali-Löytty et al.       download from course home page      English  

Prerequisites

Course Mandatory/Advisable Description
MAT-20501 Todennäköisyyslaskenta Mandatory    
MAT-33311 Tilastomatematiikka 1 Mandatory    
MAT-34000 Tilastomatematiikka 2 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  

Additional information

This course MAT-45807 is applying to the students whose main subject is mathematics. Course MAT-45806 is applying to the students whose main subject is not mathematics. Courses MAT-45806 and MAT-45807 have common lectures.
Suitable for postgraduate studies

More precise information per implementation

Implementation Description Methods of instruction Implementation
MAT-45807 2010-01   Lectures
Excercises
Practical works
   
Contact teaching: 0 %
Distance learning: 0 %
Self-directed learning: 0 %  

Last modified10.12.2010