# Kalman filter localisation equations

I am doing mobile robot localisation as a project. Now I stuck in obtaining the equations of EKF localisation. My robot moves straight for 10 seconds parallel to x-axis and robot equipped with 2 sonars - in front and in right side. As a landmark I have two lines in front of the robot and on the right side parallel to x-axis. Could you please help me to obtain the equations?! The map looks like this:

The robot is in the origin (0, 0), the landmark line parallel to X-axis coordinate is y=-2000mm, the landmark parallel to y-axis is x=4000. I already implemented the motion-based control which returns estimated pose of the robot and covariance matrix. The estimated pose of the robot is given by S=[Sx, Sy, Sth]. Please help me to find matrices of the correction step

What is my observation model Jacobian matrix?! The papers in internet gives me only Jacobian matrix form for nonlinear model, but in my case as my teacher said the model is linear, but I dont know how to obtain this Jacobian matrix which has dimension H[2][3] matrix

• Welcome to Robotics, user17633. Could you please explain more what your terms are and what source you're working from? You seem to be confused about the same terms I am (z_real?) and I think it would be helpful to read the publication that used it.
– Chuck
Commented Jul 23, 2017 at 13:37
• Hi Chuck! I am working with localisation as my dissertation topic, this is the link for the material that I am using: docs.google.com/… I am doing implementation in C++ using Aria library and Amigobot, and the last thing left is this localisation method. Cannot obtain Jacobian matrix for the model described above Commented Jul 23, 2017 at 22:08
• I totally agree with @Chuck, it is not clear what you are trying to do. Please share more info. Be clear and precise. We don't know what you've done and you are trying to do. Commented Jul 26, 2017 at 13:15
• ok. My primary task is to do mobile robot localisation in MobileSim. Firstly, my supervisor asked me to do motion-based localisation(or dead-reckoning) and it works fine now. Now my next task is to do Extended Kalman filter localisation. I have estimated pose and covariance matrix(from motion-based localisation). Now I need to find the matrices of correction step, especially the observation model Jacobian matrix Commented Jul 26, 2017 at 15:46
• Then if I know the observation model Jacobian matrix, I can find a Kalman gain and update the pose and covariance matrix of the robot. I don't know the observation model Jacobian matrix in my example described above, please help me, deadline is coming soon Commented Jul 26, 2017 at 15:51