In this thesis, several deterministic and stochastic attitude filtering solutions on the special orthogonal group SO(3) are proposed. Firstly, the attitude estimation problem is approached on the basis of nonlinear deterministic filters on SO (3) with guaranteed transient and steady-state measures. The second solution to the attitude estimation problem considers nonlinear stochastic filters on SO (3) with superior convergence properties with two filters being developed in the sense of Ito, and one in the sense of Stratonovich. This thesis also presents several deterministic and stochastic pose filtering solutions developed on the special Euclidean group SE(3). The first solution includes two nonlinear deterministic pose filters on SE (3) with predefined transient as well as steady-state performance, while the second one involves a nonlinear stochastic filter on SE (3) in the sense of Stratonovich. The proposed nonlinear deterministic filters on SO(3) and SE(3) guarantee that attitude and pose error are trapped to initially start within a known large set and converge systematically and asymptotically to the equilibrium point from almost any initial condition, respectively. The proposed stochastic filters ensure that errors of the estimates and attitude or errors of the estimates and pose are semi-globally uniformly ultimately bounded in mean square, and they converge to a small neighborhood of the origin from almost any initial condition. The output performance of the proposed filters is examined and simulated considering high level of uncertainties in the measurements and large error in initialization. The above-mentioned consideration makes the proposed filters a good fit for measurements obtained from low-cost inertial measurement units or low-cost inertial vision systems.