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The paper proposes derivative-free nonlinear Kalman Filtering and state estimation-based control for MIMO nonlinear dynamical systems, such as unmanned ground vehicles. The considered nonlinear filtering scheme which is based on differential flatness theory can be applied to the autonomous vehicle model without the need for calculation of Jacobian matrices, and in general extends the class of MIMO nonlinear systems for which derivative-free Kalman Filtering can be performed. Nonlinear systems such as unmanned ground vehicles, satisfying the differential flatness property, can be written in the Brunovsky (canonical) form via a transformation of their state variables and control inputs. After transforming the nonlinear system to the canonical form it is straightforward to apply the standard Kalman Filter recursion. The performance of the proposed derivative-free nonlinear filtering scheme is tested through simulation experiments on the problem of state estimation-based control for autonomous navigation of unmanned ground vehicles.