A Geometric Approach For Pose and Velocity Estimation Using IMU and Inertial/Body-Frame Measurements
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| Format: | Preprint |
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2025
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| author | Benahmed, Sifeddine Berkane, Soulaimane Hamel, Tarek |
| author_facet | Benahmed, Sifeddine Berkane, Soulaimane Hamel, Tarek |
| contents | This paper addresses accurate pose estimation (position, velocity, and orientation) for a rigid body using a combination of generic inertial-frame and/or body-frame measurements along with an Inertial Measurement Unit (IMU). By embedding the original state space, $\so \times \R^3 \times \R^3$, within the higher-dimensional Lie group $\sefive$, we reformulate the vehicle dynamics and outputs within a structured, geometric framework. In particular, this embedding enables a decoupling of the resulting geometric error dynamics: the translational error dynamics follow a structure similar to the error dynamics of a continuous-time Kalman filter, which allows for a time-varying gain design using the Riccati equation. Under the condition of uniform observability, we establish that the proposed observer design on $\sefive$ guarantees almost global asymptotic stability. We validate the approach in simulations for two practical scenarios: stereo-aided inertial navigation systems (INS) and GPS-aided INS. The proposed method significantly simplifies the design of nonlinear geometric observers for INS, providing a generalized and robust approach to state estimation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_03764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Geometric Approach For Pose and Velocity Estimation Using IMU and Inertial/Body-Frame Measurements Benahmed, Sifeddine Berkane, Soulaimane Hamel, Tarek Systems and Control Robotics This paper addresses accurate pose estimation (position, velocity, and orientation) for a rigid body using a combination of generic inertial-frame and/or body-frame measurements along with an Inertial Measurement Unit (IMU). By embedding the original state space, $\so \times \R^3 \times \R^3$, within the higher-dimensional Lie group $\sefive$, we reformulate the vehicle dynamics and outputs within a structured, geometric framework. In particular, this embedding enables a decoupling of the resulting geometric error dynamics: the translational error dynamics follow a structure similar to the error dynamics of a continuous-time Kalman filter, which allows for a time-varying gain design using the Riccati equation. Under the condition of uniform observability, we establish that the proposed observer design on $\sefive$ guarantees almost global asymptotic stability. We validate the approach in simulations for two practical scenarios: stereo-aided inertial navigation systems (INS) and GPS-aided INS. The proposed method significantly simplifies the design of nonlinear geometric observers for INS, providing a generalized and robust approach to state estimation. |
| title | A Geometric Approach For Pose and Velocity Estimation Using IMU and Inertial/Body-Frame Measurements |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2504.03764 |