Questions: Particle Filter Localization (Monte Carlo Localization)
1 questions to test your understanding
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Question 1 Multiple Choice
A mobile robot localizes using 1,000 particles and a LiDAR sensor. After motion, particles are propagated using odometry with added Gaussian noise. Then particle weights are updated based on LiDAR beam measurements. Which step is most computationally expensive and why?
APropagating particles because odometry must be verified against wheel encoders for each particle
BResampling particles because systematic resampling requires sorting all 1,000 particles
CWeight computation because each particle must compare its expected LiDAR scan (ray-cast through a map) against the actual measured scan, requiring ray-casting for each particle
DNormalizing weights because normalizing 1,000 floating-point values is inherently slow
This three-step structure (predict, weight, resample) is the core of sequential importance resampling (SIR). The motion model pushes uncertainty outward (particles spread); the measurement pulls uncertainty inward (particles concentrate); resampling focuses computational resources on promising hypotheses. The algorithm is named 'particle filter' because it filters out bad hypotheses and concentrates particles around good ones, asymptotically converging to the true posterior as the number of particles increases.