Autonomous navigation of an agent strongly relies on the capability of tracking multiple moving objects. The first part of the thesis presents a method for multiple moving objects tracking on the unit sphere based on the von Mises distribution, and probability hypothesis density filter based on random finite sets. The state of objects in the agent's surrounding are typically determined with their position and orientation which evolve on a non-Euclidean geometry. The thesis further proposes several methods for estimating motion evolving on the special Euclidean group based on the extended Kalman filter on Lie groups. As an alternative to the extended Kalman filter on Lie groups, the thesis also proposes the estimation method relying on an information form for states evolving on matrix Lie groups. The thesis proposes two methods suitable for multiple objects tracking applications when states evolve on matrix Lie groups. The first one relies on joint integrated probabilistic data association filter, while the second one employs the probability hypothesis density filter on matrix Lie groups. Contributions: 1. Method for multiple moving objects tracking on the unit sphere based on the von Mises distribution and the random finite sets. 2. Method for moving object tracking in the space of the special Euclidean group based on the extended Kalman filter on Lie groups. 3. Extended information Kalman filter for state estimation on matrix Lie groups. 4. Method for multiple moving objects tracking on Lie Groups based on the concentrated Gaussian distribution and the random finite sets.