Robust and accurate pose estimation of moving systems is a challenging task that is often tackled by combining information from different sensor subsystems in a multi-sensor fusion setup. To obtain robust and accurate estimates, it is crucial to respect the exact time of each measurement. Data fusion is additionally challenged when the sensors are running at different rates and the information is subject to processing- and transmission delays. In this paper, we present an optimization-based moving horizon estimator which allows to estimate and compensate for time-varying measurement delays without the need for any synchronization signals between the sensors. By adopting a direct collocation approach, we find a continuous-time solution for the navigation states which allows us to incorporate the discrete-time sensor measurements in an optimal way despite the presence of unknown time delays. The presented sensor fusion algorithm is applied to the problem of pose estimation by fusing data of a high-rate inertial measurement unit and a low-rate centimeter-accurate global navigation satellite system receiver using simulated and real-data experiments.

Inertial sensors are used in an increasing number of autonomous applications. Integrating such sensors into dynamic systems, the problem of their calibration arises naturally. Existing methods often require the sensor to be accurately placed in certain poses, which can be infeasible in practice. In this paper, we present an optimization-based estimator for in-field identification of inertial biases and scale factors. Instead of predefined poses, we use measurements of an accurate global navigation satellite system receiver in the calibration algorithm. By adopting a moving horizon scheme, the resulting estimator has the potential to run on embedded hardware allowing for online calibration without sacrificing robustness. We also present an approach for the simulation of realistic sensor data. The resulting datasets are used to analyze the performance of the optimization-based estimator. The evaluated statistics clearly show that moving horizon estimation improves the robustness and accuracy of the presented calibration approach in the presence of uncertain initial conditions and outperforms traditional recursive filters.