Dual-IMU State Estimation for Relative Localization of Two Mobile Agents

TL;DR

This work considers the Dual-IMU system, where each agent is equipped with one IMU, and employs relative pose observations between them, and focuses on the observability analysis, for the observability under general motion and the unobserved directions arising from various special motions.

Abstract

In this paper, we address the problem of relative localization of two mobile agents. Specifically, we consider the Dual-IMU system, where each agent is equipped with one IMU, and employs relative pose observations between them. Previous works, however, typically assumed known ego motion and ignored biases of the IMUs. Instead, we study the most general case of unknown biases for both IMUs. Besides the derivation of dynamic model equations of the proposed system, we focus on the observability analysis, for the observability under general motion and the unobservable directions arising from various special motions. Through numerical simulations, we validate our key observability findings and examine their impact on the estimation accuracy and consistency. Finally, the system is implemented to achieve effective relative localization of an HMD with respect to a vehicle moving in the real world.

Figures (13)

• Figure 1: The system comprises a static global coordinate frame {$G$}, and the moving reference and target IMU coordinate frames {$I_1$} and {$I_2$}. $\prescript{I_1}{}{\mathbf{p}}_{I_2}$ and $\prescript{I_1}{}{\mathbf{q}_{I_2}}$ are the relative position and orientation of the target IMU with respect to the reference IMU.
• Figure 2: The RMSE and 3$\sigma$ bound of the motion that the reference IMU remains still and the target IMU moves generally with respect to the reference IMU in Cell I-S of Table (\ref{['table-dpq']}) with both $\mathbf{dp}$ and $\mathbf{dq}$ measurements. The red line represents RMSE, and the green background represents 3$\sigma$ bound. The definition of each subplot is that: (a) and (d) represent the relative orientation and relative position errors, (b) and (c) represent the gyroscope bias errors of reference IMU and target IMU, (e) and (f) represent the accelerometer bias errors of reference IMU and target IMU, (g) and (h) represent the errors of $\mathbf{b}_{g-}$ and $\mathbf{b}_{a-}$, (i) and (j) represent the errors of $\mathbf{b}_{g+}$ and $\mathbf{b}_{a+}$, respectively. All states are observable.
• Figure 3: The RMSE and 3$\sigma$ bound of the motion that the reference IMU moves on a horizontal plane and the target IMU moves only rotates with respect to the reference IMU in Cell V-M of Table (\ref{['table-dpq']}) with both $\mathbf{dp}$ and $\mathbf{dq}$ measurements. The red line represents RMSE, and the green background represents 3$\sigma$ bound. The definition of each subplot is the same as in Fig. \ref{['dpq_static_pxyz_vxvyvz_wxwywz']}. All states are observable.
• Figure 4: The RMSE and 3$\sigma$ bound of the motion that the reference IMU moves on a horizontal plane and the target IMU remains still with respect to the reference IMU in Cell V-K of Table (\ref{['table-dpq']}) with both $\mathbf{dp}$ and $\mathbf{dq}$ measurements. The red line represents RMSE, and the green background represents 3$\sigma$ bound. The definition of each subplot is the same as in Fig. \ref{['dpq_static_pxyz_vxvyvz_wxwywz']}. There are 3 unobservable directions: 3 directions of $\mathbf{b}_{a+}$.
• Figure 5: The RMSE and 3$\sigma$ bound of the motion that the reference IMU moves along a straight line (the X direction) and the target IMU remains still with respect to the reference IMU in Cell III-K of Table (\ref{['table-dpq']}) with both $\mathbf{dp}$ and $\mathbf{dq}$ measurements. The red line represents RMSE, and the green background represents 3$\sigma$ bound. The definition of each subplot is the same as in Fig. \ref{['dpq_static_pxyz_vxvyvz_wxwywz']}. There are 6 unobservable directions: 3 directions of $\mathbf{b}_{g+}$ and 3 directions of $\mathbf{b}_{a+}$.