Problem 44838. Pose from bearing angles in 2D

A robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors P1 and P2 . The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are th1 and th2 respectively. The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is thb .

Determine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame. In surveying this is known as a resection problem.