-n$ vector bundle $\pi_0:E_0\rightarrow M$ with a moving Parseval frame $(g_i)_{i=0}^k$ so that $(f_i\oplus g_i)_{i=0}^k$ is a moving orthonormal basis for the vector bundle $\pi_0\oplus\pi_0:E_0\oplus E_0\rightarrow M$.  If $