State Estimation & SLAM

Predict, then update. The two-step pattern every state estimator — Kalman, EKF, particle filter, SLAM — is a special case of. Learn it once and SLAM becomes readable.

~14 min

The Bayes filter under a Gaussian assumption. Fifty lines of Python, worked numerically, with the intuition for why every step is what it is.

~16 min

Real robots are nonlinear. The Kalman filter assumes linearity. EKF linearizes around the current mean; UKF propagates sigma points through the real nonlinear models. Same Bayes filter, two ways to handle nonlinearity.

~15 min

Non-Gaussian estimation for indoor robots. Represent belief as a cloud of samples; resample after each measurement. The algorithm behind every ROS amcl node.

~13 min

The modern formulation: nodes are unknowns, edges are constraints, the graph is the joint posterior. Solve with sparse least-squares. GTSAM, g2o, Ceres — every state-of-the-art SLAM uses this.

~14 min

The simplest map representation: a 2D grid of 'free vs occupied' probabilities. Build it from laser scans with the inverse-sensor-model trick. The map under every Nav2 costmap.

~11 min

One of the best open-source SLAM systems. Tracking, local mapping, loop closure, multi-map atlas — the four threads that turn a video stream into a reusable 3D map.

~16 min

LOAM, F-LOAM, LIO-SAM — the lineage that powers most modern robot mapping stacks. Why LiDAR SLAM is different from visual, and the algorithms that became the production standard.

~14 min

SuperPoint, DROID-SLAM, Gaussian splats — the deep-learning wave reshaping the SLAM landscape. What's new, what classical methods still beat, and where the production frontier is in 2026.

~13 min

Localization when you don't need SLAM — and the IMU tricks that plug the gaps when the sky does. The honest tradeoffs between consumer GPS, RTK, and full sensor fusion.

~12 min