thanks for your video. I want to apply the KF to predict the future temp of a heating termoblock to be able to know when in the future i will reach the desired T°, then I will be able to control it from this prediction. But I have a problem, how can I estimate the both Q and R matrix ? have you some method for me ? or a program (like Matlab) ? or perhaps some proposal of typical matrix for that ? for your information the SSM of thermoblocks is a linear system of second order, so A matrix of SSM is rang 2.
the problem with the given example is that the GPS itself in real life has an error (covariance) that also needs to be taken into account. Would have been better if the some more effort went into coming up with a better example
Good question! I think the reason is the way how the control vector "u" is defined in the example. In your case the "u" can be thought of being defined as [acceleration, acceleration]^T (but G_{k-1} would then need to be a 2x2 matrix in order for the matrix multiplication to return a 2d vector back). However, the video is not clear about how they define "u". If you take a look at 6:52 you see that the video creator did not pay attention when "u" was defined because suddenly the vector became a scalar value?! So where should the scalar acceleration be put in the vector "u"? At 7:22 we can see that (in this example) "u" is indeed a scalar for simplicity sake and the math works properly. So you are actually right about your definition of G_{k-1}. However, it seems that it was not the goal to let the control vector contribute to the position state, but only to the velocity state and hence G_{k-1}=[0, DT]^T in this example. In contrast, here www.cs.cmu.edu/~motionplanning/papers/sbp_papers/kalman/kleeman_understanding_kalman.pdf on Slide 15, when the authors model a free-falling body motion, they actually use your formulation of the control matrix (with DT=1s). To be honest, I do not know what the implications of this different control input modeling are (and this is probably the reason why you are asking). But I think that it has something to do with how reliable the control input is, i.e. how much do you trust the input. If, for example, the control input is very noisy / jerky, then applying it to your position state would lead to a more noisy position estimate. If, however, it is a natural law (such as gravity) it would not harm your estimate but actually improve it. Even Wikipedia uses the model you have mentioned for explaining the Kalman filter and they reason about whether your input is "controlled" (definition from this video) or "uncontrolled" (your definition). Hope this helps a little.
Two things: 1. What the H matrix is has not been described. 2. One non s1x1 matrix cannot be smaller or greater then another. This is sloppy. Besides that, it is a great work.
Nice explaining! Much easier than the Book “Probabilistic Robotics”
It would be useful to drive the equations and calculations for the example, instead of just showing them in a few seconds.
The Gk vector is clearly wrong. Its first term should be 0.5 * dt^2, so that the position equation becomes p_k = p_{k-1} + p_dot*dt + 0.5*a^2*(dt)^2
Thanks for the correction.
Thanks, I can more understand about KF.
Where is the video on recursive least squares though ?
thanks for your video. I want to apply the KF to predict the future temp of a heating termoblock to be able to know when in the future i will reach the desired T°, then I will be able to control it from this prediction. But I have a problem, how can I estimate the both Q and R matrix ? have you some method for me ? or a program (like Matlab) ? or perhaps some proposal of typical matrix for that ? for your information the SSM of thermoblocks is a linear system of second order, so A matrix of SSM is rang 2.
Hi! Is it a series of which this course is a part of?
State Estimation and Localization for Self-Driving Cars by Toronto University (Coursera)
the prediction step, should the F maxtrix muitiply hat x instead of x?
whow did you choose the covriance matrix at ua-cam.com/video/LioOvUZ1MiM/v-deo.html ?
What are the basic requirements to understand KF?
You need to know what is Bayes Rule and the Gaussisn distribution.
the problem with the given example is that the GPS itself in real life has an error (covariance) that also needs to be taken into account. Would have been better if the some more effort went into coming up with a better example
Can someone please help me, in 7:22, why isn't the matrix Gk-1 = ((1/2)DT^2 , DT)) = (0.125, 0.5) ??
Good question!
I think the reason is the way how the control vector "u" is defined in the example. In your case the "u" can be thought of being defined as [acceleration, acceleration]^T (but G_{k-1} would then need to be a 2x2 matrix in order for the matrix multiplication to return a 2d vector back). However, the video is not clear about how they define "u". If you take a look at 6:52 you see that the video creator did not pay attention when "u" was defined because suddenly the vector became a scalar value?! So where should the scalar acceleration be put in the vector "u"? At 7:22 we can see that (in this example) "u" is indeed a scalar for simplicity sake and the math works properly. So you are actually right about your definition of G_{k-1}.
However, it seems that it was not the goal to let the control vector contribute to the position state, but only to the velocity state and hence G_{k-1}=[0, DT]^T in this example. In contrast, here www.cs.cmu.edu/~motionplanning/papers/sbp_papers/kalman/kleeman_understanding_kalman.pdf on Slide 15, when the authors model a free-falling body motion, they actually use your formulation of the control matrix (with DT=1s).
To be honest, I do not know what the implications of this different control input modeling are (and this is probably the reason why you are asking). But I think that it has something to do with how reliable the control input is, i.e. how much do you trust the input. If, for example, the control input is very noisy / jerky, then applying it to your position state would lead to a more noisy position estimate. If, however, it is a natural law (such as gravity) it would not harm your estimate but actually improve it. Even Wikipedia uses the model you have mentioned for explaining the Kalman filter and they reason about whether your input is "controlled" (definition from this video) or "uncontrolled" (your definition).
Hope this helps a little.
Best video on Kalman filter on UA-cam, great job and thanks for making it freely available
Absolutely not
@@AlexandreLefaure it was the most helpful for me at the time, but feel free to share if you found something better ;)
Two things:
1. What the H matrix is has not been described.
2. One non s1x1 matrix cannot be smaller or greater then another. This is sloppy.
Besides that, it is a great work.
Great job, thank you!