What is the Kalman Filter?

[@SPD15]

This has to be one of the best kf tutorial I have been trying to understand what exactly was going on for a long time. I'm still a bit lost when it came to calculating kf gain but it's a good start. Thank you so much.

[@iain_explains]

Glad it helped!

[@MGTOW-nn9ls]

Dear Sir I watched your video about convoluted integral some time ago. It is the best explanation I have seen. Your Kalman filter video is also one of the best.Thank you.

[@iain_explains]

I'm so glad you found both videos helpful!

[@agarvipul]

The recursive process you explain was pure gold as it cleared the doubt completely relating to previous and current time analysis. Keep posting such videos.

[@iain_explains]

I'm so glad it was helpful!

[@agarvipul]

@@iain_explains Can you please post a video on extended Kalman filters.

[@iain_explains]

Thanks for the suggestion, it’s on my “to do” list.

[@naveedbhuiyan9855]

awesome video man. The graphical example really helped me understand the concept much better. thanks a lot

[@iain_explains]

Glad you liked it and found it useful.

[@mentallama9123]

Thank you so much! Truly you are the best educators on this platform in the area of signals, control, estimation, etc... Please keep posting videos!

[@iain_explains]

I'm so glad you like the videos. Thanks for your nice comment.

[@matteomaggi4515]

Hello Professor, thanks for the explanation. Would it be possible to use Kalman Filter in an autonomous robotic application to estimate Tool Center Point parameters in an iterative measurement process? Starting from an ideal estimate of the parameters, given from CAD quotes, I would like to refine the Estimate in a touch probing procedure. I understand the question is a bit out of the blue, but I would love to know your perspective on the matter.

[@Apstergos]

I think this is the best vidoe that explained KF. Thank you so much, this is great help.

[@iain_explains]

Glad it was helpful!

[@jjr1028]

Great video! I have reached a point where I understand the concept and implementation of a kalman filter, but what is unclear is how to place my data, observations and measurements into matrix form to carry out the these calculations. Do you have any suggestion for the concepts that I should study to understand this?

[@iain_explains]

Perhaps these videos might help: "How does a Radar Track Manoeuvring Targets?" kzbin.info/www/bejne/n5PZnX6KfLZnsLM and "What is Least Squares Estimation?" kzbin.info/www/bejne/eIuch5-jotqiqq8

[@jjr1028]

@@iain_explains Thank you!

[@LuisFuentes1771]

This video is great! Super clear. Thank you!

[@iain_explains]

Glad it was helpful!

[@marksbelay9643]

I really appreciate the way you explain the algorithms technically. I am kindly waiting EKF which is used for 3D tracking. Many thanks!

[@iain_explains]

Glad yo found it helpful. Yes, the EKF is on my "to do" list.

[@ashkan1974]

At minute 4:41, concerning delta_kl, should not instead R_k within the matrix the term R_l to be appeared? Thanks!

[@iain_explains]

It's correct as shown. After that matrix gets multiplied by the delta function delta_{kl}, it will "pick out" the value R_l

[@ashkan1974]

I think, I understood 😊. The video is just super fantastic explaining and revealing the logic behind KF. I appreciate it❤❤

[@iain_explains]

I'm so glad to hear it.

[@kamele0865]

Dear Iain, thanks for the simple and informative lecture. I really enjoyed it. I wonder if you have a lecture on the Extended Kalman filter. Thank you.

[@iain_explains]

Thanks for the suggestion. It's on my "to do" list.

[@yannickmorin4472]

best kalman filter explanation I could find! tk so much :)

[@iain_explains]

I'm so glad you found it helpful.

[@renaldomoon3097]

Iain is such a bossman! Thanks alot, your work is very appreciated

[@iain_explains]

Glad you like it!

[@Demonithese]

Thank you for all the effort and thought that went into making this! Much appreciated

[@iain_explains]

Glad you found it useful!

[@MarkusLenzing]

What is H compare to H'? Excellent video!

[@iain_explains]

H' is the matrix transpose of H. I'm glad you like the video.

[@hongkyulee9724]

Thank you for making this intuitive video. :D I have learned many things from your KZbin channel.

[@iain_explains]

Thanks for your nice comment. I'm glad you're finding the channel to be helpful.

[@pitmaler4439]

Thank You. On the right upper corner, in the third equation, where comes the supscript l (wl vl)? In the Dirac Impuls there are 2 subscripts again.

[@iain_explains]

"k" is one time value, and "l" is another time value. The Dirac delta function is at the location k-l=0, or in other words, the expectation equals 0 unless k=l, or in even more other words, the values at different times are independent of each other.

[@xuyang2776]

Thanks a lot. The video is so cool. But I have a question. If the Matrix F, H, and G are unknown, can kalman filter work? I guess maybe those matrix could be estimated, but I don't know how...

[@iain_explains]

That's right - you need to find some way to estimate F, H and G. In some applications you might know these from physics - for example, if x is the location of a car that's being driven along a highway, then you'd know something about the time domain correlation of x (ie. you could build a model for F) since you'd know the average speed of cars along a particular road, and the maximum speed, etc. In other cases, you might be able to use training to estimate F, H and G. For example, if you can input known "training" values of x, then you can use estimation techniques to estimate F, H and G. See this for more details: "What is Least Squares Estimation?" kzbin.info/www/bejne/eIuch5-jotqiqq8

[@xuyang2776]

Thanks a lot. But stata variable x is unobservable, how to use regression or other statistic method to estimate de F, H, and G? Could you provide some resouces that is talking about this topic? @@iain_explains

[@fifaham]

Do you have any code in C, or Assembly language, that execute Kalman filter? It would be nice to have a microcontroller progect with input from sensors, to measure the noise and present state, and a propeller blades acting as motion input? The deflection blades can act based on feedback produced from the mcu. Any sample code around?

[@iain_explains]

That's a great idea, but unfortunately I don't have any code. I might make it a project for my undergrad students next semester. Thanks for the suggestion.

[@fifaham]

@@iain_explains Thank you for the reply Iain. I have been searching all over the internet for a method that produces an estimate for k(z+1) with higher degree of accuracy, I didn't find any video like that. I then thought you are the king of system control and I will ask you: I have been thinking to combine both the Kalman filter with adaptive PID control mechanism with a microcontroller based gating technique, meaning I will use an MCU to produce an interrupt based TIC signal, say once every 10 ms on 40 MHz clock. The adaptive PID will be gating the Kalman filter output via MOSFET drivers, all the gausian estimations based on Kalman filter will be gated via PID adaptive control in a hybrid fashion. Have you ever seen anyone doing this kind of control? Or what do you think of such gating of PID to Kalman filter? Any idea or any book and weblink reference will be greatly appreciated.

[@iain_explains]

Sorry, I can't really visualise what you're describing.

[@fifaham]

@@iain_explains No problem, thank you for your reply. I am only thinking of a hybrid method to produce a more predictable estimate and this method may, or may not work. I am looking all around to find out about that.

[@casinarro]

hey, thank you so much, u are a phenomenal teacher

[@iain_explains]

Thanks so much. Glad you think so!

[@menoone2042]

Crystal clear thanks prof.

[@iain_explains]

Glad it helped.

[@VTdarkangel]

Interesting. This suggests that implementing a Kalman filter into a control scheme is extremely calculation intensive, and gets rapidly more intensive as the system order increases. Means selection of the control processor is very important.

[@iain_explains]

Yes, that's right. You make a good point.

[@likehemantha]

Dr can we use this Kalman filter to track where the storm is moving next?

[@iain_explains]

Yes, Kalman filters are often used for tracking. See this video for some more details: "How does a Radar Track Manoeuvring Targets?" kzbin.info/www/bejne/n5PZnX6KfLZnsLM

[@MLDawn]

Could you please do a tutorial on Kalman Bucy filger as well? Thanks a million.

[@iain_explains]

Thanks for the suggestion. The Kalman-Bucy filter is ("just") a continuous-time version of the discrete-time Kalman filter. I'll add it to my "to do" list.

[@MLDawn]

@@iain_explains Yep! My main issue is that if we are going to use Kalman Bucy filter for modelling a dynamic system, there is no concept of time step anymore and all is happening at the same time (I think)! Looking forward eagerly to your video! Also, I am really not sure why in Kalman Bucy filter, RIGHT OFF the BAT, we start with an equation describing the forst time derivative of our hidden variable!

[@hrachya_khachatryan]

Another excellent lecture. Thank you Iain, you are amazing! I have two questions. 1. Do you use prime to denote matrix transpose? in particular the H'_k in the Kalman gain is the transpose of the H_k, I assume? 2. As mentioned omega_k and v_k are gaussian noise vectors. In the first equation omega_k is multiplied by a matrix G_k , while in the second equation we simply have v_k. I wonder what is the G_k, is it a characteristic of a system (like F_k and Gamma_k)? My feeling is that there is a noise omega_k at time=k and then we multiply it by G_k to define its effect on time=k+1. While, in the second equation we do observation at time k and the v_k being the gaussian noise of that observation doesn't need to be multiplied by any matrix. Is there a good example to illustrate this G_k factor? Thanks

[@iain_explains]

Thanks. Answers: 1) yes, and 2) G_k allows for different variances of noise to act on each of the elements of x.

[@hrachya_khachatryan]

@@iain_explains Thanks a lot :)

[@dinezeazy]

Hi, can you do a video on de/companding in imagers. I understand the function but not getting exactly how this is done.

[@iain_explains]

Sorry, I'm not exactly sure what you're referring to. Perhaps interpolation? "Interpolation of Discrete Time Signals" kzbin.info/www/bejne/eWaroIqfp7eEn7c

[@AJ-fo3hp]

For Image compression JPEG, JPEG 2000 standards used JPEG standard uses Discrete Cosine Transform for compression JPEG 2000 standard uses Discrete Wavelet Transform for compression. For audio and video compression following standards are used MPEG-1 Edition MPEG-2 Edition MPEG-4 Edition MPEG-7 Edition MPEG-21 Edition, etc. MPEG standard uses Discrete Cosine Transform for compression.

[@armandfossouo3546]

hello. can we estimate the unobservable component of the kalman filter by the least squares method?

[@iain_explains]

No, because Least Squares applies to constant parameters, whereas the Kalman Filter applies to time varying parameters (ie. the state x_k).

[@noname-uf1hr]

Thank you sir.. You are amazing as always..

[@iain_explains]

So nice of you

[@hariharanramamurthy9946]

Hi sir I trying to apply kalman filter for range bearing model, but I don't know correct method to implement, can you please derive it for me, or share that has , because I am having 5 books none of them explains how it can be applied

[@iain_explains]

Thanks for the suggestion. I've added it to my "to do" list.

[@malkemarouki3303]

Very helpful thanks a lot.

[@iain_explains]

Glad it was helpful!

[@AJ-fo3hp]

What measured value Zk Is Zk open loop measured value,I mean without feed back. As I understood Current output = Predicted Value + gain (open loop measured value Zk - Predicted Value) If open loop measured value Zk greater than Predicted value Then (open loop measured value Zk - Predicted Value) is positive that mean Predicted and open loop measured value are in same same direction So final current output is Predicted Value + difference between open loop measured value Zk and Predicted value. final current output is also in the direction of Zk If open loop measured value Zk equal to Predicted value Then (open loop measured value Zk - Predicted Value) is zero that mean Predicted and open loop measured value are same So final current output is Predicted Value + 0 final current output is also in the direction of Zk If open loop measured value Zk less than Predicted value Then (open loop measured value Zk - Predicted Value) is negative that mean Predicted and open loop measured value are in opposite direction So final current output is Predicted Value - difference between open loop measured value Zk and Predicted value. final current output is also in the opposite direction of Zk Once final current output is calculated then Zk(open loop measured value) becomes final calculated value hence Predicted value is equal to final current output but ship is moving always its measured value and direction value is keep changing so to filter out the error there is need of prediction based on previous experience, prediction and open loop measured value and direction to be minimum this is done by filter(high pass filter or difference fiter or derivative)to correct error. ---------- ------------------ ------------------ | PLANT | ---Zk---> | HPF | ---Xk---> | Ship | X^k-1--->| | ------------------- |^ ------------------- X^k -1 | |Xk ------------------------- | Prediction +| | Delay | --------------------------

[@knightx9405]

Hello professor could you please do a video about Wiener filters asap?.. There are literally no good resources of wiener filter for usage of audios available in the internet

[@iain_explains]

Thanks for the topic suggestion. It's on my "to do" list.