The performance of model-based motion control for free-flying robots relies on accurate estimation of their parameters. In this work, a method of rigid body inertial parameter estimation which relies on a variational approach is presented. Instead of discretizing the continuous equations of motion, discrete dual quaternion equations based on variational mechanics are used to formulate a linear parameter estimation problem. This method depends only on the pose of the rigid body obtained from standard localization algorithms. Recursive semi-definite programming is used to estimate the inertial parameters (mass, rotational inertia and center of mass offset) online. Linear Matrix Inequality constraints based on the pseudo-inertia matrix ensure that the estimates obtained are fully physically consistent. Simulation results demonstrate that this method is robust to disturbances and the produced estimates are at least one order of magnitude more accurate when compared to discretization using finite differences.