# IMU-Free Body-Frame State Estimation with Sparse Scene Flow for Quadcopters

arXiv: https://arxiv.org/abs/2608.20891 · HTML: https://mlsanity.com/paper/2608.20891/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 21 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 5 of 5)

- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Bayes-Newton Methods for Approximate Bayesian Inference with PSD Guarantees](https://mlsanity.com/paper/2111.01721/) (2021)
- [The Visual-Inertial-Dynamical Multirotor Dataset](https://mlsanity.com/paper/2103.11152/) (2021)
- [A Quick Guide for the Iterated Extended Kalman Filter on Manifolds](https://mlsanity.com/paper/2307.09237/) (2023)
- [Notes on Kalman Filter (KF, EKF, ESKF, IEKF, IESKF)](https://mlsanity.com/paper/2406.06427/) (2024)

## Abstract (arXiv)

We present a vision-only state estimation system for X-configuration quadcopters equipped with a canonical stereo camera pair and no inertial sensors. The system operates entirely in the body frame, requiring only synchronised stereo images and motor thrust commands. A continuous-discrete extended Kalman filter on a composite manifold state langle SE(3), ℝ3, ldots rangle maintains estimates of body-frame pose, velocity, angular velocity, gravity, and disturbances, using stationary scene points as implicit inertial references. Feature points are detected (FAST, Shi-Tomasi), tracked temporally (SSD, Lucas-Kanade) and matched across cameras (NCC), with search regions predicted from filter-derived pose and point uncertainty. Chi-squared gating on the normalised innovation admits only stationary points to the filter. The system also produces a sparse 3D point cloud carrying per-point position, velocity and joint covariance. These come from a 4-view (two stereo pairs at two timestamps) full bundle adjustment that jointly estimates position and velocity from stereo disparity and temporal parallax, with the filter-derived relative pose as a prior. Feature points in the EKF do not enter the solver; their information is reflected through the pose prior. Point cloud density is spatially adaptive: an external focus point directs allocation, producing dense coverage in the region of attention and sparse coverage elsewhere. The output is a body-frame state estimate, a calibrated pose change, and a sparse scene flow. It is intended as a measurement source for a downstream world model anchored in the current body frame, without dependence on GPS, IMU, or any world-frame infrastructure, though the architecture accommodates their future integration.