Nonlinear Multi-Sensor Observability and Estimation of Rigid Body Inertial Parameters
Ena Sundquist, Carey Whitehair, Kristi A. Morgansen · 2024
Inertial parameters are key to understanding a system’s dynamics, yet are difficult to estimate for rigid bodies with nonlinear dynamics. We use Lie algebraic observability to determine the analytic observability using the rank condition on the observability codistribution. We then use the empirical observability Gramian to determine the degree of observability of each inertial parameter under variable conditions: we modify force inputs, sensor package locations, and number of sensor packages. These results are then validated through simulation where we also consider the effects of noise and assess the performance of an Extended Kalman Filter and an Unscented Kalman Filter. Our results indicate that with two inertial measurement units (IMU), and no particular control input, we can observe and estimate three inertial parameters. Additionally, a single IMU, judiciously placed within the rigid body is sufficient in estimating all inertial parameters, under an appropriate forcing function. These results hold for a 2D aircraft model.