With both our estimation and Lie group tools from previous chapters, we now begin to bring the two together. We discuss a classic three-dimensional estimation problem in robotics: pointcloud alignment; this gives us our first example of carrying out optimization over the group of rotations by a few different means. We then present the classic problem of localizing a moving robot using point observations of known three-dimensional landmarks; this involves adapting the extended Kalman filter (EKF) to work with the group of poses. Another common problem in robotics is that of pose-graph optimization, which is easily handled using our Lie group tools. We conclude with a presentation of how to carry out trajectory estimation based on an inertial measurement unit (IMU) both recursively via the EKF and batch using IMU preintegration for efficiency.