Articulatory representations are expected to bring better speech recognition results. This requires to estimate the parameters of a speech production model from the speech sound, problem known as acoustico-articulatory inversion. Known methods to solve this problem usually introduce a heavy computational cost. Alternately, it is known that Linear Prediction analysis offers an analogy with acoustic filtering. This analogy had been exploited to develop a less expensive analytic method applicable to the estimation of tube shapes discretized in equal-length sections. We have extended the method to the DRM case, where the tube is made of unequal-length sections. The proposed DRM inversion scheme is thus simpler and faster. Furthermore, it shows good performance in terms of low residual modeling error. It also enhances speech recognition results when used to compute Log Area Ratios.