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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 |
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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:
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 Statistics 1 | Mandatory |
Prerequisite relations (Requires logging in to POP)
Correspondence of content
| Course | Corresponds course | Description |
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More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |
| 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 % |