CSCE 452/752 Robotics and Spatial Intelligence, Fall 2025

Homework 11

Elsa builds a cave exploring robot that moves forward along a one-dimensional tunnel with a flat floor. The height of the ceiling varies throughout the tunnel. The robot has a simple range sensor aimed at the ceiling of the cave. This sensor returns the ceiling height at the robot's position (measured from the floor), subject to zero-mean Gaussian random noise.
a cave robot
Elsa knows the shape of the cave's ceiling. She uses a particle filter to localize her robot. The figure below shows the ceiling height along the tunnel, the current positions of six of the particles. The most recent observation, $y_k$, is marked on the right. (The robot itself is not shown, because it is not certain of its own position; this is a localization problem after all.)
particles in a cave
At this point, the particle filter executes its resampling step.
  1. Circle the particles that have some non-zero chance to be selected in this resampling step.
  2. Mark an 'X' next to the particle that is most likely to be selected in this resampling step. Explain your answer in one sentence.
[Submit via Canvas.]