Human movements measured by a motion capture system are often represented by the motions of a multi-rigid link model of the body, which allows mechanodynamic analysis of the movements. In such cases, the position and posture of the model at time t, denoted as J(t) parameterized by unknown constant body parameters, should be determined so that they are consistent with the spatial position x(t) of a set of reflective markers attached to the body and satisfy the rigid link assumption of the model. Challenges in constructing a map from x(t) to J(t) are associated with the so-called “skin motion error”, which is the motion artifact of the markers induced by the fact that each body segment modeled by a single rigid link is in reality a multi-link system and not rigid. The skin motion error generates inconsistency between x(t) and J(t) and lowers the accuracy of the estimation. Here, we propose a novel computational algorithm for constructing the map for a small number of markers with skin motion errors, in which J(t) is estimated iteratively so that the updated J(t) is more consistent with the marker positions and the rigid link assumption, and is less affected by the skin motion error. In particular, we determine the optimal J(t) over a range of t as a fixed point of the map that is formulated as a discrete nonlinear dynamical system. Although this study is preliminary and limited to a planar double rigid link system for simplicity, mathematical analysis suggests that the performance of posture estimation may be improved using our algorithm by determining the appropriate locations at which the markers should be attached.