U ovome radu objašnjen je problem određivanja položaja na temelju vektorskih mjerenja senzora. S obzirom na problematiku korištenih senzora pri određivanju položaja, kao estimator položaja izabran je multiplikativni prošireni Kalmanov filter zbog svojih prednosti. Prednosti ovog filtera su računska jednostavnost s obzirom kako su jednadžbe filtera razvijene na temelju kvaternionske parametrizacije položaja. Dodatna prednost ovog filtera je i ta, da filter ne estimira dinamiku stanja tijela, nego samo stanje pogrešaka položaja koje se dodaju na nominalno stanje sustava, a to dodatno ubrzava iteraciju algoritma. Rezultat ovog rada je uspješna implementacija MEKF algoritma u Matlabu, što je i potvrđeno kroz pokuse i mjerenja s obzirom na referentne skupove mjerenja. Rad daje i objašnjenje problema prilikom korištenja izabranog referentnog skupa mjerenja.

This thesis explains attitude determination problem based on sensor measurements in vector space. It gives a short overview of deterministic methods used to solve this problem and then progresses with the state space stochastic methods, mainly using the Multiplicative Extended Kalman Filter. The MEKF was chosen due to its advantages, which include, lower computational requirements since state equations are developed using quaternion parametrization of attitude, hence there is no trigonometric operations used in the state transition equation. One additional advantage of this filter is its complementary or indirect nature, i.e. we are not estimating the full-state of the system, just the error-states which brings additional simplifications and robustness when using MEKF for attitude estimation. The result of this work is a successful implementation of the MEKF algorithm in a discrete form, using Matlab, this form is suitable for calculation on digital computers or embedded systems. Implementation is evaluated through comparison of attitude estimates with highly accurate reference measurements. Unfortunately, due to a mistake in the experiments when the reference measurements were gathered, it wasn’t possible to correctly evaluate accuracy of the estimated yaw angle.