Using reference objects to estimate the point spread function?
As you probably know, there is a developed literature on deblurring. Regarding the evaluation of the PSF, you may find these useful:


Understanding and evaluating blind deconvolution algorithms
Modeling the Performance of Image Restoration From Motion Blur


If the known object $X_0$ is going to be shot head on in subsequent frames $Y_i$, you can find the blur kernel $K$ by maximizing some image similarity metric $I$ for basic (say, procrustes) transformations $T$ of $X_0$:

$K_i = \underset{K, T}{\arg \max} \; I \left( K \ast T X_0 ; Y_i \right)$

In a more sophisticated formulation, you could enforce temporal smoothness priors on the $K_i$'s and $T$'s. I would also suggest using the last frame's optimal estimates as initial values for the next frame.

If $X_0$ appears at an angle in $Y_i$ (since it is moving, after all) I conjecture that you will have a hard time finding a good match (that is, $X_0$ will not be of much use). Obviously, there is some information to be leveraged, even when shot at an angle, but I suspect the effort will not be worth it. This leads me to wonder what sort of a scenario you would be able to use this technique in. You know what they say: there's one way to find out.