Towards Estimating Bias in Stereo Visual Odometry

Stereo visual odometry (VO) is a common technique for estimating a camera´s motion, features are tracked across frames and the pose change is subsequently inferred. This position estimation method can play a particularly important role in environments in which the global positioning system (GPS) is not available (e.g., Mars rovers). Recently, some authors have noticed a bias in VO position estimates that grows with distance travelled, this can cause the resulting position estimate to become highly inaccurate. The goals of this paper are (i) to investigate the nature of this bias in VO, (ii) to propose methods of estimating it, and (iii) to provide a correction that can potentially be used online. We identify two effects at play in stereo VO bias: first, the inherent bias in the maximum-likelihood estimation framework, and second, the disparity threshold used to discard far-away and erroneous stereo observations. In order to estimate the bias, we investigate three methods: Monte Carlo sampling, the sigma-point method (with modification), and an existing analytical method in the literature. Based on simulations, we show that our new sigma point method achieves similar accuracy to Monte Carlo, but at a fraction of the computational cost. Finally, we develop a bias correction algorithm by adapting the idea of the bootstrap in statistics, and demonstrate that our bias correction algorithm is capable of reducing approximately 95% of bias in VO problems without incorporating other sensors into the setup.