Object Inertial Extrinsics Error

Created by: IMU

Overview

These metrics refer to the error between a sequence of measured and optimized extrinsics involving the IMU. Put in mathematical terms:

$$\Gamma^{E}_{O} \approx \Gamma^{E}_{\text{IMU}} \cdot \Gamma^{\text{IMU}}_{C} \cdot \Gamma^{C}_{O}$$

• $E$ is the inertial frame, a gravity-aligned frame with its origin coincident with the first IMU navigation state
• $O$ is the object space
• $\text{IMU}$ is the current IMU navigation state
• $C$ is any component that can observe the object space directly, e.g. a camera

The transform $\Gamma^{\text{E}}_{O}$ is the object inertial extrinsic. This calculation is performed for every navigation state of the IMU, since a navigation state directly corresponds to a synced component's observations to the object space in question.

Note that only one of these metrics is created per object space. This metric is closely related to Composed Relative Extrinsics; the strategy is basically the same. However, since IMU cannot directly observe objects, we use the navigation states to infer the relative extrinsics.

Definition

Object inertial extrinsics error metrics contain the following fields:

Field	Type	Description
nav_component_id	UUID	The UUID of the IMU component this metric was generated from.
navigation_states	An array of extrinsics-velocity objects	The inferred navigation states of the object inertial extrinsic cost.
world_extrinsics	An array of world extrinsics objects	The inferred world pose (component from world) of the object inertial extrinsic, $\Gamma^{\text{C}}_{O}$
component_relative_extrinsics	An array of extrinsics objects	The inferred component relative extrinsics, $\Gamma^{\text{IMU}}_{C}$
object_inertial_extrinsics	An array of extrinsics objects	The inferred object inertial extrinsics, $\Gamma^{\text{IMU}}_{O}$
misalignments	An array of extrinsics objects	The residual error of each object inertial extrisnic.