On Tanaka's Prolongation Procedure for Filtered Structures of Constant Type

We present Tanaka's prolongation procedure for filtered structures on manifolds discovered in [Tanaka N., J. Math. Kyoto. Univ. 10 (1970), 1–82] in a spirit of Singer–Sternberg's description of the prolongation of usual $G$-structures [Singer I. M., Sternberg S., J. Analyse Math. 15 (1965), 1–114; Sternberg S., Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964]. This approach gives a transparent point of view on the Tanaka constructions avoiding many technicalities of the original Tanaka paper.