Course content

Examples of sensor fusion. Random variables and probability distributions. Concepts in estimation: ML, MAP, MMSE estimator, total probability theorem, Bayes and orthogonality principle. The multivariate Gaussian and the product identity. The Kalman filter. Stochastic processes driven by white noise. The extended Kalman filter. Gaussian mixtures. Hybrid systems and the IMM algorithm. Data association in single and multiple target tracking. The PDAF and the JPDA. Methods for detection and track initiation. Smoothing. Loosely coupled inertial navigation systems (INS). Error models for INS. Variations of the multiplicative extended Kalman filter for attitude estimation. The standard model for feature-based simultaneous localization and mapping (SLAM) and its EKF solution. Data association for SLAM. Graphical models, the information filter and smoothing. Graphical SLAM methods. Practical implementation of methods for multi-target tracking, INS and SLAM.

Learning outcome

Knowledge: Knowledge about core applications in sensor fusion. Knowledge about key results in probability and estimation. Knowledge about linear and nonlinear filtering techniques. Knowledge about methods for target tracking in clutter. Knowledge about modeling and implementation of INS. Knowledge about feature-based SLAM methods. Skills: Be able to use different estimation principles in a variety of estimation problems. Manipulate multivariate Gaussians. Design and implement Kalman filters for Gaussian linear filtering problems. Analyze the stochastic properties of Gaussian-linear filtering. Implement nonlinear extensions of the Kalman filter for non-linear filtering problems. Implement single-target and multi-target tracking methods. Implement methods for feature-based SLAM. General competence: Be able to apply the fundamental estimation principles in cooperation with other disciplines. Consciousness about the role of sensor fusion in automation. Consciousness about the strengths and weaknesses of different sensor fusion methods.

Learning methods and activities

The course is given as a mixture of lectures, written assignments and computer assignments. The computer assignments will involve implementation of sensor fusion methods on real data. A minimum of 3 written assignments and 2 computer assignments must be approved to enter the final exam.

Compulsory assignments

• Compulsory assignments

Recommended previous knowledge

TTT4275 Estimation, detection and classification is strongly recommended.

Required previous knowledge

At least one of the following (or equivalent from other universities): TTK4115 Linear system theory, TTT4275 Estimation, detection and classification, TMA4268 statistical learning or TMA4267 Linear statistical models.

Course materials

The course uses a compendium written for the course. The updated compendium will be available before semester start.