As the first step in the development of a mobile mechatronic system, the design of the platform itself was made using the CAD tool SolidWorks. The design was performed under the assumption of known/fixed dimensions of system parts and all components. Furthermore, the kinematic model of the platform and the kinematics of the omnidirectional wheel drive are described. The principle of operation of individual sensors is additionally described in order to implement sensor fusion with a discrete Kalman filter (DKF). Expressions for the realization of a discrete linear Kalman filter and a discrete extended Kalman filter (D-EKF) are derived due to the need for fusion of a magnetometer and gyroscope, and later for the estimation of the position and orientation of a mobile mechatronic system. As an additional input besides measuring the angle obtained by fusing a magnetometer and gyroscope in D-EKF, an accelerometer measurements are also used. Therefore, the system needs to be expanded with four more conditions in order to be able to express the measurement equation, relatively the output equation. The state estimation simulation was performed in the MATLAB/ Simulink programming environment. The obtained position estimation and orientation responses show high accuracy and good implementation of D-EKF.