Decoupled Representation of the Error and Trajectory Estimates for Ef_cient Pose Estimation

In this paper we present a novel approach for the parameterization of the trajectory of a moving platform, which facilitates the development of real-time pose-estimation methods. The key idea of the proposed approach is the decoupling of the parameterization of the trajectory estimate from the parameterization of the error in this estimate. Specifically, we represent the trajectory estimate as usual, via a set of pose states, each associated with a sensor reading (e.g., a laser scan or an image). The novelty of our approach lies in the representation of the estimation errors, for which we employ B-splines. This decoupled formulation, which we term Decoupled Estimate-Error Parameterization (DEEP) offers two key advantages. First, the use of a pose-based representation of the trajectory allows us to represent arbitrarily complex trajectories. Second, the use of B-splines for error representation allows us to control the computational complexity of an estimator, by selecting the density of the knots of the B-spline. We empirically demonstrate that, in the problem of visual-inertial localization, the DEEP formulation leads to substantial computational gains, while incurring only a small loss of estimation performance.