Date: January 28, 2024

Topic: Comparing Filters

Recall

Notes

Comparison of Filters

Considering m intervals (or m state spaces) 1D → m^1 intervals 2D → m^2 intervals 3D → m^3 intervals … | Approximate as the world is not discrete | | Kalman | Continuous | Unimodal | Quadratic: Due to covariance matrix which is quadratic (more efficient filter) | Approximate as the world is non-linear | | Particle | Continuous | Multimodal | Sometimes scale exponentially. Used for ≤ 4 dims | Approximate |

Particle filters initialize with random particle clouds all over the environment with differing densities.

Higher density areas show higher probabilities.

After enough measurements, the clouds with the best estimations remain, until there is only one cloud left, which shows the position of the robot.

Particle Filters

• Generate clouds of particles, and the best estimates will survive (survival of the fittest)
• Particles more consistent with the measurements are more likely to survive
• A place of high probability collects more particles, and more representative of the robot’s posterior belief

During Localization

Many clouds are present, these will diminish when we get more measurements Places with higher probabilities have denser clouds

After Localization

Only one cloud remains, representing the best guess of where the robot is

We initialize particles by giving them random locations and headings. These particles can then move in any direction

Using random guesses

Vector showing random particle’s coordinates

• Each dot is a vector containing: $x$-coord, $y$-coord, heading (angle relative to $x$-axis)
• To get 1000 particles, we randomly generate 1000 $x$, $y$ and heading vectors and put them in a list

When we initalize random particles, they will be all over the environment.

We check the difference between the actual measurement of the true robot’s position ($Z$) vs the predicted measurement from the particle.

This difference gives us the weighting.

<aside> 📌 SUMMARY: Particle filters work by having randomly initialized particles that

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