GMM model in factor graph based multiple object tracking papers.

[hojunson]

Hi Tim.

My research team is struggling the GMM part in your paper, "Factor Graph based 3D Multi-Object Tracking in Point Clouds".

I believe the $w_j$ is the weights from GMM based on measurements.
Here is my question.
There are 5 lidar measurements, the number of $w_j$ is 5. When the number of components for the GMM is equal to the number of measurements, the $w_j$ will be uniform.
In addition to that, the information matrix representing the detector's accuracy but it is fixed.
If then, $c_j$ must be even.

In addition to that, if $c_j$ is even, the upper error term in the detection factor is going to be always zero because $c_j$ is equal to $r_m$.

I would like to understand this part, so could you help with this?

Sincerely,
Hojun Son

[tipf]

Hi Hojun,
sorry for the late answer, I was quite occupied the last months.

Let's take a look at your example:

1. With 5 detections, the constant $w_j$ will be $\frac{1}{6}$. Why that?
   Well, there is the "null-hypothesis" component, which we included to handle detections that are not related to any known object from previous observations.
2. All $w_j$ are equal, but due to the much broader null-hypothesis, the $c_j$ are not. Therefore, the upper term of the cost function is usually not zero.

I hope that clarifies that a bit. Don't hesitate to ask further questions - I will try to be faster next time. ;-)