What does the 'Information' attribute of the factor 'factorPoseSE3Prior' mean in the factor graph?

The prior Factor node is defined in the example 'Factor Graph-Based Pedestrian Localization with IMU and GPS Sensors', which includes the attribute 'Information'.

In the help document of these three prior factors, the description of this attribute is also very vague, and its default value differs greatly from the default value in the example. My question is as follows:

1. What is the specific meaning of the 'Information' attribute?

2. What should the value of the 'Information' attribute refer to?

PosePrior = factorPoseSE3Prior(currNodeIDs(t0IndexPose),Measurement=prevPose, ...
    Information=diag([4e4 4e4 4e4 1e4 1e4 1e4]));
fVelPrior = factorVelocity3Prior(currNodeIDs(t0IndexVel),Measurement=prevVel, ...
    Information=100*eye(3));
fBiasPrior = factorIMUBiasPrior(currNodeIDs(t0IndexBias),Measurement=prevBias, ...
    Information=1e6*eye(6));

Answer 1

[Altaïr]

Hey @Cao,

The factorPoseSE3Prior object in MATLAB is a specialized factor used in a factorGraph to represent a full-state prior for a pose in the SE(3) state space. SE(3) refers to the Special Euclidean group in three dimensions, which encompasses all possible positions and orientations in 3D space.

Like other factor objects, factorPoseSE3Prior utilizes an information matrix to indicate the confidence level in the prior. A high information value suggests strong confidence in the prior pose, while a lower value indicates more uncertainty.

Here's a line from the Factor Graph-Based Pedestrian Localization with IMU and GPS Sensors example:

fPosePrior = factorPoseSE3Prior(currNodeIDs(t0IndexPose),Measurement=prevPose,...
    Information=diag([4e4 4e4 4e4 1e4 1e4 1e4]));

The six elements in the diag function represent the confidence in the translational and orientation position measurements. As mentioned in the example, the information matrix has large values because they are derived from ground truth measurements.

For more information on functionalities related to Factor Graphs, kindly check out this link:

https://www.mathworks.com/help/releases/R2022b/nav/localization-algorithms.html?searchHighlight=%22Factor%20Graph%22