This page contains a collection of various notes, slides, and derivations that I have created over the years. Please take them with a grain of salt in their correctness, but I hope some people will find them helpful.

Visual-Inertial Sensor Calibration Videos

Recently I have been trying to spread my knowledge of performing visual-inertial calibration for future students in the lab and have recorded two long-form videos on the subject. They are mostly informal, but have my ramblings on the process, how to collect data, and how to interpret the results. The videos have been made public in the hope that this can help new students and practitioners reduce the time spent on this (time consuming) process.

Covariance Intersection Delayed Feature Initialization

Notes on how to perform delayed state initialization when using covariance intersection. This is of particular interest if you have a set of measurements that are a function of two states that are related through covariance intersection (CI). We wish to find the correlation between the current state and the to-be-initialized state along with its marginal covariance. These notes also show shows some equivalence of two different initialization methodologies (very informally).

Visual-Inertial Navigation Systems: An Introduction

This talk was presented at the ICRA21 Workshop on Visual-Inertial Navigation Systems organized by my advisor Guoquan (Paul) Huang. This presentation served as an introduction to the topic of visual-inertial research. The main goal was to provide both a nice introduction to the rest of the workshop talks, but also discuss some of the key challenge areas which research has focused on. Additionally, a high level introduction into the camera and inertial measurement models along with traditional estimation methods was presented. The presentation finally closed with an overview of available open sourced systems, datasets, and evaluation techniques that a research could start using today.

Kalman Filter Derivations and the MSCKF

Unfinished notes on Kalman filtering in 2D and 3D on the focus on clarifying the steps needed to formally derive its propagation and update equations. First discrete linear filter is explain, then nonlinear filtering. An unfinished JPL quaternion example is included. Towards the end the MSCKF filter is looked at with details on the camera cloning, measurement update, Jacobians, nullspace operation, and measurement compression. These notes where created to help my understanding, so take them with a grain of salt in their correctness.

Real-Time 3D Reconstruction and 6-DoF Tracking with an Event Camera

Details on the ray-triangle intersection and details on how this can then be used in an update. Jacobians are derived for these barycentric coordinates and then the inverse depth update for inclusion into the state.

Continuous-Time Visual-Inertial Trajectory Estimation with Event Cameras

Goes into detail on how the B-spline is formally created. Starts with the standard definition of a spline and then focuses on the matrix representation of a uniform B-spline, showing how the matrices in the paper are found. The initial measurement is noted, and it is noted that Jacobians for this measurement are computed numerically.

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