2d radar kalman filter [r r_dot theta theta_dot]

Hi Hello,

I have a system state vector defined as [r,r˙,θ,θ˙] and a measurement vector that includes [r θ.] I would like to apply a Extended Kalman filter to this system. However, I have some questions:

1. Since both my system and measurement matrices are nonlinear, how should I proceed with the Jacobian?
2. How can I find the system transition matrix (F)?
3. I am not very familiar with these concepts; could you please guide me through the process of setting up and implementing the Kalman filter for this type of system?
4. Should I convert the system matrix to Cartesian coordinates, or should I continue using polar coordinates?

[Aquatris]

1) Jacobian is nothing more than linearizing your dynamic model and measurement model at a particular point. So once you write your models, it will be easy to construct the Jacobians.

2) This depends on what assumptions you want to use. If you are tracking a moving object, there are various models, e.g., constant turn rate and acceleration, constant turn rate and velocity, constant acceleration...

so in your case, if you assume constant velocity (r_dot does not change during the time step), r(k+1) = r(k)+r_dot(k)*dt

3) There are many academic papers on this topic. Search in google scholar for 'extended kalman filter motion tracking' and take a look. They generally give you the equations as well. Pick one that is easy to understand for you.

4) Both are equally viable. It will only change how your equation looks, and the pysical interpretation of the tunable parameters of the Kalman filter, noise levels etc.

Answer 1

[nick]

Hi @kalmanfilterlearner,

In the code shared, it is assumed that acceleration of the object is 0 which led F to be a linear matrix. The H matrix depends on the type of sensor data obtained from the object. If the assumption is sensor relays radius and angle wrt the observer, then the H matrix will be nonlinear. However, if on the contrary it relays absolute coordinates 'x' and 'y' then the H matrix will be linear.