In this simulation-based assignment, you will utilize MATLAB to implement two different procedures for mobile robot simultaneous localization and mapping (SLAM) in discrete time, utilizing both linear least squares and the linear, discrete-time Kalman filter.
Consider the mobile robot illustrated in the figure below. It moves at constant velocity in a single degree of freedom, along a hallway. It is equipped with a bi-directional laser range beam with maximum range r, which is capable of sensing the doors in the hallway. The robot is also equipped with wheel encoders that provide a source of odometry sensing. The three doors depicted will serve as our navigation landmarks - we will assume they are point-landmarks of negligible width at locations ??1, ??2, ??3. We know with very high confidence that the robot starts moving from the origin, at the beginning of the hallway. However, we do not have a prior map of the hallway, and we do not know the locations of the three landmarks – the robot will need to discover them and estimate their locations through its measurement process. It will also, in turn, use those landmark measurements to curb the growth of its own localization uncertainty