The tuning is done for process and measurement covariances only. The Innovation covariance is the sum of the transformed state covariance in measurement space (H P H^T) and the measurement covariance R. S = H P H^T + R

@@al-khwarizmi It is crystal clear now. I also read your articles. These are some of the best contents on the earth about the Kalman filter. Take love brother.

P is the estimated state covariance so far which is how much do you actually trust the estimated state. while Q is the additional amount of error you add every time to state covariance P when you predict the state. The purpose of covariance matrix Q is to model the unknown external noises that influence the system which you couldn't model in the prediction model equations because of lack of knowledge.

It is the covariance matrix of the input vector u. Basically the noise of the external inputs of the prediction model.

@@al-khwarizmi Thank you. I really appreciate your videos. Thanks to them, I was able to understand the kalman filter much better. But I'm still having problems with some issues. The most important of these is how you determined the Q and R vectors and are they constantly changing? And again, does the input covariance matrix U change because the input changes every cycle? Finally, is there a chance to explain the dimensions of all the variables here with an example (for example xk 3*1 vector, uk 2*1 vector so Uk is 3*3 matrice, etc.)

Given there are n state variables and m input variables then the Dimension would be: Vec x: n*1 - state vector Vec u: m*1 - input vector Cov U: m*m - input noise covariance Cov Q: n*n - process noise covariance Cov P: n*n - state covariance Mat F: n*n - state transition matrix Mat B: n*m - input transition matrix

Glad it helped

Best of luck!

This c++ library is designed for multi-dimension state kalman filter. n-dimension for state space vector and m-Dimension for measurement space vector.

@@al-khwarizmi do you have linkedin?

www.linkedin.com/in/mohanad-youssef-5b69013a/

The measurement Model H depends on the "sensor" you are going to use and in what space or coordinates its delivering it's values. For example, If you use GPS sensor and measurement are delivered as position x & y which matches to some of already existing elements in our state vector then it will be direct mapping and hence a linear measurement Model. The same for magnetometer which delivery heading angle or accelerometer which can be used to obtain absolute roll and pitch angles.

If you are tracking an external moving object using sensors like (e.g. Radar or LiDAR) you can still use a state vector including both velocity and position states (could be in 2D or 3D even). The LiDAR sensor can measure the position directly of the object which you will use to correct the position state in the state vector (modeled by the measurement model). But, as explained in the video since the velocity and position states are correlated (as modeled in the prediction model), then even when fusing position measurement the Kalman gain will update the estimate of the velocity to match the new measured position. However for Radar, it can measure the relative radial velocity of the moving object using the doppler effect. In such case, you can correct the velocity state directly in the state vector once you receive a Radar measurement.

Glad it was helpful!

ممكن تبدأ بالفديوهات اللي أتكلمت فيها عن ال linear Kalman filter لفهم الأساسيات و ممكن توضح لي ما هي القرائات او ال sensors الي بتستخدمها و التطبيق؟

بأذن الله أعمل فديو أتكلم عن الموضوع دة