PERFORMANCE ANALYSIS OF TOTAL LEAST-SQUARES METHODS IN 3-DIMENSIONAL MOTION ESTIMATION

An algorithm is presented to obtain the total least squares (TLS) estimates of the motion parameters of an object from range/stereo data or perspective views in a closed form. TLS estimates are suitable when data in both time frames are corrupted by noise, an appropriate model for motion analysis in practice. We analyze the robustness of different linear least squares methods for the estimation of motion parameters against the sensor noise and possible mismatches in establishing object feature point correspondence. As the errors in point correspondence increase, the performance of an ordinary least squares (LS) estimator was found to deteriorate much faster than that of the TLS estimator. The Cramer-Rao lower bound (CRLB) of the error covariance matrix is derived for the TLS model under the assumption of uncorrelated additive Gaussian noise. The CRLB for the TLS model is shown to be always higher than that for the LS model. Simulation experiments are performed to demonstrate that the proposed solution closely approximates the CRLB for the TLS model.