Robotics estimation course

LiDAR–inertial estimation

From IMU measurements and LiDAR geometry to a joint state estimate.

Learn the models and ideas behind LiDAR–inertial odometry, then apply them to a working estimator. Each of the nine core lessons includes recall prompts, quizzes, and a short reference card.

The equations and design choices apply beyond any one codebase. glass-lio is a running case study: its source and measured failures make abstract ideas concrete. Sensor values, gates, and performance results are examples, not settings to copy.

Allow 30–45 minutes per lesson on first study (45–60 for the capstone), the 15–20 minute estimates are for revision. Start with the mathematical toolkit if matrices, derivatives, or covariance are unfamiliar.

By the end, aim to derive the IMU updates, explain covariance and bias correction, differentiate a point-to-plane residual, identify unobservable motions, and audit the complete solve.

Take them in order: each one builds on the last. Terms are defined in the glossary.

  1. Start here · 45–60 minutesThe mathematical toolkitFrames, rotations, Jacobians, covariance, and the normal equations.
  2. Lesson 1 · 30–45 minutes first studyWhat an IMU actually measuresSpecific force, angular rate, and the limits of stationary initialization.

    Reference card

  3. Lesson 2 · 30–45 minutes first studyIntegrating one IMU stepWhere gravity comes back in, and the update-order trap.

    Reference card

  4. Lesson 3 · 30–45 minutes first studyWhy preintegrateFrom eq. (31) iterated, to three deltas reusable when the starting pose changes.

    Reference card

  5. Lesson 4 · 30–45 minutes first studyThe bias correctionWhy the deltas go stale when the bias moves, and the first-order fix.

    Reference card

  6. Lesson 5 · 30–45 minutes first studyThe noise preintegration carriesOne covariance, propagated a sample at a time, and why it decides who wins.

    Reference card

  7. Lesson 6 · 30–45 minutes first studyThe point-to-plane factorOne residual per laser return, its Jacobian, and how thousands of them build one linear system.

    Reference card

  8. Lesson 7 · 30–45 minutes first studyPlanes and degeneracyOne skill, used twice: reading the smallest eigenvalue of a 3×3 matrix.

    Reference card

  9. Lesson 8 · 30–45 minutes first studyFilter, window, or current-state solveWhat each estimator keeps, what it re-linearises, and what marginalization buys.

    Reference card

  10. Lesson 9 · 45–60 minutes first studyThe tight solve, end to endTrace a scan through prediction, association, joint optimization, and map update.

    Reference card