Probabilistic data association with a particle filter

[RichardJ]

Homework Statement

Hello everyone, I have to implement a probabilistic data association filter with a particle filter.
I have already implemented a PDAF based on the Kalman filter.
The assignment considers a radar (range,angle) tracker. With the state s containing the x, y position and the x and y velocity. $$s = [x,y,v_x,v_y]^T$$. The object is flying in a straight line and in some measurements false alarms occur.

Homework Equations

How does one integrate the particle filter in the probabilistic data association method?
How can you compute the association probability for each measurements and how to relate this to the particles.

The Attempt at a Solution

The current approach involves trying to compute the likelihood for each measurement (false measurements as well) and then trying to do a weighted average of the likelihoods with the association probabilities. However I am not able to get an expression for the association probabilities.

 

[KataKoniK]

I would suggest the following approach to integrate a particle filter in the probabilistic data association method:

1. Understand the basics of particle filters and probabilistic data association: Before attempting to integrate the two methods, it is important to have a thorough understanding of both particle filters and probabilistic data association. This will help in identifying the key components that need to be integrated and the potential challenges that may arise.

2. Develop a probabilistic data association filter with a particle filter: Start by implementing a basic particle filter for the given radar tracking problem. Then, incorporate the probabilistic data association technique into the particle filter. This can be achieved by modifying the measurement update step of the particle filter to incorporate the likelihood of the measurement being associated with the correct target.

3. Consider the state representation and measurement model: In the given problem, the state consists of the position and velocity of the object. The measurement model can be represented as a function of the state. Therefore, when integrating the particle filter and probabilistic data association, it is important to ensure that the state representation and measurement model are consistent.

4. Determine the association probabilities: The association probability for each measurement can be computed by comparing the likelihood of the measurement being associated with the correct target with the likelihood of the measurement being a false alarm. This can be done by considering the measurement noise and the distribution of the false alarms.

5. Relate the association probabilities to the particles: The association probabilities can be related to the particles by assigning a weight to each particle based on the likelihood of the measurement being associated with the correct target. This weight can then be used in the resampling step of the particle filter to update the particles.

In conclusion, integrating a particle filter in the probabilistic data association method requires a thorough understanding of both techniques and careful consideration of the state representation, measurement model, and association probabilities. By following these steps, you should be able to successfully implement a probabilistic data association filter with a particle filter.