Process model parameterisation in posegraphs

Through propagating information over time, process models serve a vital in any multi-time step estimation algorithm. However, they can introduce nonlinearities which can significantly degrade the performance of an estimator. In this paper, we investigate the impact of the parameterisation of the process model in posegraph-based formulations of filtering and estimation algorithms. Exploiting the flexibility and conditional independence structure of a posegraph, we develop two formulations of a process noise model of a vehicle - one in Euclidean space, the other in polar space. Using moment-matching, we develop exact closed form solutions for the first two moments of a Gaussian distribution propagated through both models. We analyse the effects of both formulations in the context of a Simultaneous Localisation and Mapping (SLAM) problem. We show that, by representing the “arc-like” nature of the prediction error more accurately, the polar form is more accurate, more robust, and is less computationally expensive than the Euclidean form.