How to model the noise in a range sensor's return?

Question

Range sensors (for example sonar, infrared, and lidar) are notoriously noisy. How can I characterize the noise characteristics to include these in a probabilistic localization sensor model?

Answer 1

This subject is covered quite nicely in the Probabilistic Robotics book by Thrun et. al. I don't have a direct reference, but there are some of his papers (such as Robust Monte Carlo Localization for Mobile Robots, pdf) essentially include the same information. Usually what is used is a mixed error model, where the probability density function consists of different parts

• A Gaussian error around the true distance reading
• A part which accounts for false positives like dynamic obstacles and so on. This is larger with smaller distances.
• A constant part which accounts for false negative readings, where the sensor gives an out of range reading.

The model needs to be fitted to your sensor and application.

Answer 2

Almost everybody just assumes the noise is gaussian because that way the math is relatively easy.

If you really wanted, you could experimentally determine the distribution of sensor noise, fit a model to it, and use that but it would be a lot of work for potentially no gain.