Nonlinear Optimization, Interactively
Gradient descent, Newton's method, Gauss-Newton and Levenberg-Marquardt, built up around one running example - a robot working out where it is - and ending in full 3D rotation and SLAM.
The same four solvers carry the whole series; what changes is the thing being estimated - a position, then a full pose, then a map, then a trajectory, then a 3D orientation. The math primer is the companion for Part 5 and can be read at any point, and Lie Groups & Lie Algebras develops the same machinery in full, for rotations and rigid poses alike. This is also the machinery behind bundle adjustment in the multi-view geometry guide.
These parts use calculus as a tool. If the gradient, Jacobian or Hessian are not yet second nature - or were always asserted rather than derived - Calculus, Interactively builds single-variable and multivariable calculus from local linearity up, and Calculus in Motion, Interactively covers the curvature and convergence this guide relies on.
The parts
Gradient descent, Newton's method, Gauss-Newton and Levenberg-Marquardt, built around one running example: a robot figuring out where it is.
Extending the four methods to a robot's full 2D pose (x, y, heading) using range-and-bearing observations to landmarks.
Landmarks are no longer known. The robot must jointly estimate its own pose and every landmark's position from observations alone.
Chaining many robot poses with noisy odometry, watching dead-reckoning drift accumulate, and how one loop closure corrects the whole trajectory.
Moving from a 2D heading to full 3D orientation, where rotations don't commute and can't simply be added.