Observable GNSS-IMU Sliding Window Filtering Using Differential Flatness

Measurements from the global navigation satellite system (GNSS) and inertial measurement units (IMU) complement one another. Global position is observed from GNSS at low frequencies, and attitude and angular velocity are estimated from IMU data at high frequencies. However, in order to observe global attitude, there must be sufficient motion to excite each axis of the IMU, which may not be possible for large vehicles with constrained dynamics. We propose to model the trajectory estimate on the flat output space of a motion model whose heading is constrained to be in the direction of motion. This mitigates the need to observe heading from the measurements. In this method we use a continuous-time spline and optimize the control points such that the flat output trajectory fits the available GNSS and IMU measurements. We validate the proposed method with simulated data and show that it achieves a higher accuracy and lower solve time than continuous-time estimation on the configuration manifold SE(3).