We give a unified method for the general equivalence problem of extrinsic geometry, on basis our formulation geometry as that an osculating map $\varphi\colon (M,\mathfrak f) \to L/L^0 \subset \operatorname{Flag}(V,\phi)$ from filtered manifold $(M,\mathfrak f)$ to homogeneous space $L/L^0$ in flag variety $\operatorname{Flag}(V,\phi)$, where $L$ is finite-dimensional Lie group and $L^0$ its cl...