A Gaussian error model for triangulation-based pose estimation using noisy landmarks

As multiple robot approaches to localisation become more prevalent, existing triangulation methods involving fixed location landmarks are inadequate to accurately determine a robot's pose. We present an error model for a robot's pose based on triangulation from three landmarks. The model represents each landmark position as a Gaussian distribution and, consequently, factors landmark positional uncertainty into robot pose error. We demonstrate the performance and accuracy of this model through a series of experiments and use the results to explain some of the inconsistencies in earlier results. We also present four metrics for analysing the output of any Gaussian-based localisation error model, demonstrating the metrics' particular applicability to multiple robot localisation problems.