# GMPE340 Kalman Filter and Sensor Fusion

Credits (ECTS):5

Campus / Online:Taught campus Ås

Teaching language:Engelsk, norsk

Course frequency:Annually

Teaching and exam period:This course has teaching/evaluation in autumn parallel.

Autonomous vehicles provides the technology towards a more sustainable transportation. The performance of modern transportation systems has been greatly improved by the rapid development of connected and autonomous vehicles, of which high precision and reliable positioning is a key technology. This is one application that relies on the use of sensor fusion with the Kalman filter as the main workhorse providing reliable estimates of the system states (e.g. position, velocity and orientation).

This course introduces the use of stochastic processes and applied Kalman filtering with focus on positioning, navigation and timing applications (PNT).

The first part includes the essential notions of probability, an introduction to random signals and response to linear systems, state-space modelling and Monte Carlo simulations.

The second part contains the main theme of the course, which is applied Kalman filtering. This part starts with the basic filter derivation using the minimum mean square error approach. This is followed by various approaches to the base theory such as: the information filter, suboptimal analysis, conditional density viewpoint, Bayesian estimation, relationship to least squares adjustment (LSQ) and other estimators, smoothing and methods to deal with non-linearities.

### Learning outcome

Students are to understand the basic filter derivation applied to dynamic systems. This is followed by various approaches to the basic theory such as: bayesian estimation, information filter, particle filter, least squares (LSQ) and other estimators. Further students are to understand methods for dealing with non-linearities.
• Lectures, colloquium, student presentations, exercises.
• Teaching support will be given primarily in connection with that part of the structured teaching that is set aside for exercise guidance. It will also be possible to communicate directly with the subject teacher by appointment during office hours.
• Calculus and linear algebra. Differential equations. Parameter estimation.
• Final written exam
• The external and internal examiner jointly prepare the exam questions and the correction manual. The external examiner reviews the internal examiner's examination results by correcting a random sample of candidates exams as a calibration according to the Department's guidelines for examination markings.
• Exercises. Compulsory, submitted work must be passed in order for the candidate to gain access to the exam.
• The course is recommended for students in Geomatics and Robotics.
• Lectures and discussion groups: 26 hours. Exercises: 52 hours.