Stanford OnlineStanford AA274A Principles of Robotic Autonomy | Autumn 2019 | Extra Session - Particle Filter SLAM
Stanford Online
Particle filter SLAM 0:05
Particle filter SLAM uses a particle belief instead of a single Gaussian. That helps when the belief has several modes or when the motion and sensor models are strongly nonlinear. The goal is full SLAM: estimate the whole robot path from the start time to the present, together with the map. A naive particle filter over the full robot trajectory and all map features would be too high-dimensional to scale.
Factoring the posterior 4:31
The key step is that, once you condition on the robot’s true path, the map features become conditionally independent. So you do not keep one huge posterior over everything. You represent the robot trajectory with particles, and for each particle you run EKF filters, one per feature. If you have M particles and N features, that gives M times N feature filters, but each one is small and easier to update.
Induction for feature factorization 24:01
The factorization of the posterior over all features is proved by induction. The base case is trivial at time one. Assuming it holds through time t minus one, Bayes’ rule is applied to the new measurement at time t. The Markov assumption and the fact that the state only affects the map through the measurement let the terms simplify. The new factor for the measured feature is updated, while the others stay the same.
Particle filter SLAM update 32:00
Particle filter SLAM splits the problem into two pieces. A particle tracks the robot path, and each particle carries one EKF per feature, so there are M times N EKFs in total. To move from time t minus one to time t, you first sample a new path state from the control input. Then you update only the EKF for the feature that matches the measurement, using the usual linearized EKF Gaussian update, and leave the others unchanged.
Feature and robot belief 43:31
The robot state is kept as particles, so there is no Gaussian sigma for the robot itself. Each particle carries its own hypothesis about the robot and its own Gaussian for each feature. The speaker walks through the notation to make that split clear: particles represent where the robot might be, while the attached EKF filters represent the mapped features.
Resampling with measurements 46:00
After prediction, the particles are resampled so the set matches the latest measurement. The weight for each particle is the compatibility term, written as the probability of the measurement given the current state. That comes from Bayes rule and a linearized sensor model. Unknown correspondences are chosen by maximum likelihood, and each particle keeps its own correspondence history, which makes failures local instead of global.
Filter tradeoffs and context 56:30
Gaussian filters are fast and familiar, but they assume one Gaussian belief and one correspondence history, so they work best when uncertainty is low. Particle filters handle multimodal beliefs, arbitrary noise, and data association errors better, but they need many particles and can suffer starvation. The lecture closes by pointing to graph SLAM, open-source tools, benchmarks, and the shift from classical EKF work to more robust perception methods.
Course wrap-up 1:03:01
The talk closes by revisiting the main ways to make SLAM feasible: linearization, particle filters, and factorizing the posterior. It then shifts to logistics. The next class will cover state machines and decision making, and the midterm is on Friday. The exam is meant to be easy, with simple true-false style questions.
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