# Probability Density Functions (PDFs) over spatial transformations

These distributions can be used as to represent the robot positining belief and the map uncertainty in many localization and SLAM algorithms.

They include unimodal Gaussians, sum of Gaussians, sets of particles, and grid representations, methods to convert between them and to draw an arbitrary number of samples from any kind of distribution:

Points:

R^3 points: mrpt::poses::CPointPDF.

SE(2) poses:

SE(3) poses:

mrpt::poses::CPose3DPDF (for poses as rotation matrix and yaw/pitch/roll).

mrpt::poses::CPose3DQuatPDF (for poses as quaternions) poses.

Each of the above abstract classes has implementations for different kinds of representing the spatial uncertainty: particles using importance sampling, a single monomodal gaussian, or a sum of gaussians.

The technical report [Bla10] contains most of the derivations of the implemented Jacobians.