Error growth in position estimation from noisy relative pose measurements

We examine how the estimation error grows with time when a mobile robot estimates its location from relative pose measurements without global position or orientation sensors. We show that in both 2-D or 3-D space, both the bias and variance of the position estimation error grows at most linearly with time (or distance traversed) asymptotically. The bias is crucially dependent on the trajectory of the robot. Conclusions on the asymptotic growth rate of the bias continue to hold even with unbiased measurements or error-free translation measurements. Exact formulas for the bias and the variance of the position estimation error are provided for two specific 2-D trajectoriesstraight line and periodic. Experiments with a P3-DX wheeled robot and Monte-Carlo simulations are provided to verify the theoretical predictions. A method to reduce the bias is proposed based on the lessons learned.