Special Topics - The Kalman Filter (6 of 55) A Simple Example of the Kalman Filter (Continued)

[@MirekKrenc]

OMG! I finally found a teacher who understands what he says and allows other people to understand some non trivial topics:) Thank you very much for your effort. Keep going Mr Michael van Biezen !!!

[@yayser]

Exactly!!. Prof Gilbert Strant (Linear Algebra) and Prof Arthur Mattuch (Dif. Equations) from the MIT falls into the same category just incase you may need.

[@alonealonesupervisor537]

Sir Michel Van Biezen i don't know how to express my appreciation for your great effort to teach us. i really grateful to you and not only me by maybe hundreds of thousand people share the same feeling with me just i would like to give a hint about the C matrix its role is convert the estimation unit to the measured unit for example if you estimate the position in the Cartesian Coordinates while you measure it in Polar then we have to convert the estimated to polar using the C matrix i hope that my comment was insightful for you sir once again many thanks

[@MichelvanBiezen]

Thank you for your input. It is much appreciated.

[@giovannibruner8455]

Michel please keep doing what you doing, the simplicity of your explanation to concept that are simple but that people seem to be indulging in representing with tonnes of complexity is disarming. People that can spread knowledge such effectively like you are a gift to humanity.

[@timdarrah2677]

This is by far the best tutorial on any topic I've ever came across and definitely the best tutorial on the kaman filter!!

[@mariadubyaga6261]

I wish I could make hundreds of likes for your video. And wish my teachers in university were like you. I've started to read a few tutorials on Kalman filter and in the process was either falling asleep or developed a headache (And I love math and always worked in corporate financial analytics). You've made it so understandable and now I see why it's a such a great method! Thank you!

[@TheEugnio]

You are an amazing teacher. Books and videos are full of theory but only a few selected ones knows how to get into the mind of struglling students: sometimes all we want is an example with solved problem. Congratulations!

[@gvvvv2300]

you are a good teacher - "surprisingly" there are not many of them in the current education system...

[@rush00121]

Beautifully explained . This is one of the most awesome and simplified explanations ever for something that can be such a complicated topic

[@fredwu6604]

you are the clearest lecturer I met so far sir! very nice! thanks!

[@석영수-j1h]

Thanks! You're the best teacher who I've ever seen!

[@Cc-go5ov]

Best explanation of all the internet.

[@MichelvanBiezen]

Glad you found our videos.

[@pollenbarua5450]

wow! how simple it is as per your lecture. the only way that has taught me KALMAN filtering. SALUTATION !

[@MichelvanBiezen]

Thank you. Did you watch the rest of the videos? They show you how the iteration works for a simple tracking scheme.

[@pollenbarua5450]

@@MichelvanBiezen Yes, I am going through whole series as I am to work on grid side inverter dynamics to improve control strategies. Thanks a lot for making such wonderful lectures, Sir!

[@MichelvanBiezen]

You are welcome. All the best on your project.

[@qcnck2776]

Thanks so much for doing the calculations by hand (calculator): so much better than just plugging it into a program and drawing a graph!

[@MichelvanBiezen]

Happy to help!

[@karihardarson1234]

Thank you very very much for this! The Internet can be an inspiring place sometimes!

[@kanaga7027]

Great job Mr Michael! Finally I could understand the kalman filter 👍

[@EvilSpeculator]

This is so cool. Your method of explaining mathematical concepts is extremely lucid and easy to follow. I never had so much fun watching math tutorials! :-)

[@thitran9637]

You are an excellent teacher. Thank you very much.

[@MichelvanBiezen]

Thank you. Glad you found our videos. 🙂

[@6935g]

Thank you very much! Never understood how this works, until your video. Keep up!

[@MichelvanBiezen]

Glad it helped!

[@JMRG2992]

I think I'm going to stick up all the night viewing your videos hehee, thank you, they're very clear.

[@MichelvanBiezen]

Glad you like them!

[@sriramkrishnamurthy9881]

Your lectures are very clear and explanative.

[@souravde6116]

Here my question is True measurement is fixed to 72. Now as each time step measurement reading by the sensor is also changing from 75 -71-70-74 as explained. If so, then how would you say that the Error in the measurement will always remain the same? It basically depends on its error probability distribution.

[@joseferrer8334]

In this time series matrix the Error Estimate (t-1) should be the same column than Error Estimate (t), being the t-1 row the initial values provided. Also the formula for KG should utilize the (t) since is t dependent, in the same way than the Estimate and Error Estimate. Thank you soo much for this. Despite studying Kalman filter 25 years ago in the university and finding it many times in my life you explain it clearly for one single variable. Thank you

[@Crazycatwhiskers]

Thank you so much for this! I really appreciate the time and effort you put into creating these videos.

[@tjetjepdjuwarsa5824]

an excellent presentation, make points interesting and much easier to grasp, amazing job.

[@martintorres5829]

Muy bien explicado, sobre el final queda mas que claro que siendo el valor real de temperatura de 72°c y teniendo las 4 mediciones ruidosas kalman en la 4 iteracion ya estima mejor al valor real que los valores entregados por el sensor. Genial explicación.

[@hamzakarim7377]

very useful indeed. This guy knows what he is saying! excellent work, keep it going.

[@MichelvanBiezen]

Glad it was helpful!

[@alantroncosomorales3731]

Mr Van Biezen, I would like to say you thank you for your explication! It really helps me to understand

[@TheACCmy]

I think it's worth emphasizing that the kalman gain is essentialy based on a formula of multiplating two gaussians (The measurment one and the current estimate one). Other than that, I think this videos serie is absolutely phenomenal and really helps people

[@delcapslock100]

Well there are 49 more videos in the series, so perhaps he gets to that at some point.

[@mathisart]

convolution?

[@user-mj4111]

I'm too excited to go to sleep after watching a few episodes, I can't stop watching, even though I still need to go to work tomorrow, and not it's already 1:30a.m....

[@MichelvanBiezen]

Sleep is important too.

[@coroline205]

Thank you so much for your awesome work. You have no idea how i appriciate. Wish you all the best

[@baldbaby2000]

Good lecture but a question. This works well for a constant input with noise, but what does it do with a varying input plus noise which would be the real world case? For example, an aircraft measuring temperature during ascent or descent. Will it try to remove the actual variations?

[@zeratulofaiur2589]

If you run your filter fast enough, the filter will converge. The [MEA - EST] in (2) save your day. When there is deviation, this number may become positive or negative. If you run your filter fast enough the changes "appear" to be constant. How fast is fast enough? There is the theory... But you can also create a fast changing signal, your worst case, and feed it into the filter. See how fast you need to run the filter in order to track your signal.

[@estradacantu]

The best explanation of Kalman Filter...thanks,

[@MitulSuthar]

This was so easy to understand and I was able to program this too.

[@nkale2000]

Amazing Awesome .. you have made it so simple that i can teach this to my second grade child

[@wolfcoin3905]

and after all i found something useful on kalman filter THANK YOU

[@MichelvanBiezen]

Glad to hear that. Enjoy the rest of the playlist.

[@GwnTim92]

Really love the tutorials. It will help me create a more accurate positioning program based on IMU (accellerometers)... Please keep up the great work 👍

[@lyn200q]

Your lectures are awesome. Well done. I have one question. How did you get the initial values 68 and 2? How to select this initial values in a real implementation?

[@MichelvanBiezen]

This was just an example. In a real application you should pick a reasonable value. In the end it doesn't matter what value you pick since the filter will quickly converge to the correct value.

[@lyn200q]

Thanks a lot for your quick response.

[@gravitycuda]

Amazing Lecture! Very good presentation, Thank you!

[@aymakam3789]

Thank you very much Sir, your way of teaching and explanation is really great.... but i have two questions and i would truly appreciate your answer..... first we all know (mathematically speaking) that the value of the error in the measured value(s) is normally +/- (plus or minus) a certain value i.e range of values and not a fixed single value like you used here in the measured value(s) (which is 4 in the video example) , because simply if we know the measured value and we know exactly the error in the measuring apparatus so we can very simply calculate the true value i.e True value = measured value + error, and the Kalman filter calculations will have no meaning !!. Second if the error is a range (between a negative and a positive values for example from -3 to 3) not a single fixed value so the question here is which value to use ??.

[@ashl1669]

Hello Michel, can you explain how new valid measurements are accepted into the estimate? If you continue the calculation, KG will keep getting smaller, which results in the filter "rejecting" any valid reading of higher or lower temperature.

[@brunoj8903]

Hi Michel, thank you so much for making these videos! They have been very helpful and informative. I just have one question regarding the third equation (the error in the estimate at time t). Is it missing a term? When you are doing the math, for example at time t, the error in the estimate comes out to 1.33. The estimated temperature at t is 70.33 and the true temperature is 72. Shouldn't the error in the estimate be 1.67? This behavior is consistent at t+1, t+2, t+3, etc. Am I misunderstanding equation 3? Thank you.

[@MrDEVSHARMALAKHAN]

Nice Lecture! Very well presented, You made it simple to understand,Thank you!

[@hannawei924]

Hi, your tutorial is pretty useful and excellent! Thanks! I am wondering how do you set the initialized value of a)the error of measurement, b)the value of estimate, and c)the Error of estimate?

[@MichelvanBiezen]

That depends on the actual situation you are dealing with. It usually is your best guess. It turns out that even if you pick values that are much to large, the Kalman FIlter converges quickly to the correct numbers.

[@hannawei924]

Got u! Thanks! I wanna use it to do prediction, and yes, I will try to figure out how to make a good guess as the initial value. Thank you!

[@madamkeshmur1500]

Thanks for the detailed explanation and calculations.

[@MichelvanBiezen]

You are welcome.

[@shiveklekhi5371]

I doubt that the Kalman Gain calculated each time is computed by taking in the same Error in Measurement, but the fact is every time the measurement is different and hence the Error in measurement is. So, the Kalman Filter will converge to accurate estimations sooner than explained.

[@lossmoss]

Excellent job. Hope to see the next show soon.

[@yunusyurtturk]

Of course I'll like, share and subscribe! Those lectures are great

[@SharonKlinkenberg]

Hi Michel, Nice videos. Could you tell me why the error in the measurement is constant? When we measure the temperature we only know what the degrees are, not what the error is. With only one measure taken how do we know the error? Or should we take multiple measures of temp end calculate the error in those measures? Or is it an assumption?

[@mohankrishnan2022]

The error in the measurement is really described in a statical sense and not a precise value. So one should interpret what is called "error" in this video as the standard deviation of the (assumed Gaussian) error distribution for the measurement device. If it is some temperature measuring device, we can have a reasonable expectation that this error distribution is fixed for this device. If it is a GPS measurement of a robot's location, it is possible to have the distribution change based on location (near tall buildings, under a big tree, etc.).

[@sohamprajapati8784]

Hello Sir. Great lecture. One doubt, where did we add the parameter of true temperature here? I tried in matlab for bigger data points, it does not converge at 72 deg, but somewhere in the middle of measurement values. Please explain, where did you tell the filter that our true temperature is 72? Thanks!

[@MichelvanBiezen]

Typically the filter does not know the correct value, and keeps getting inputs from the sensors, and depending on the volatility of those inputs, will determine how much weight to put on each of the inputs.

[@shakirullah5840]

Dear sir, thank you so much for your nicely explained videos on Kalman Filter. I want to ask you a question. Can the KF be helpful for forecasting the future demand of products using the historical data from time series?

[@MichelvanBiezen]

the Kalman Filter is typically used for predicting where something will be based on behavior that can be formulated with an equation, like the position of a projectile, not so much for something that can be influenced by many unpredictable factors.

[@shakirullah5840]

@@MichelvanBiezen Thank you, dear sir for your quick reply. Would you please comment on the paper that is available in the following link where KF is used to fit time series? ieeexplore.ieee.org/document/8302108

[@fingeroffang]

However, taking the mean of the 4 values (72.5) gets you closer to the true temperature. Also what do you do if you don't know (as is usual) the error in the measurement? Also is there a rule of thumb for choosing an initial value for the error in the estimate?

[@MichelvanBiezen]

This is just an example, to show how the filter works. As it turns out, with the Kalman filter, it doesn't actually matter what initial error we pick, since the filter will zero in to the correct value very quickly. Typically, we pick an initial error estimate that seems reasonable for the particular application.

[@cyriljourdan1023]

Great course, thank you ! I have a question, here E_MEA is constant for the simplicity of the example I guess, but how is it calculated in practice ? Is it linked to the standard deviation ?

[@tubejhe]

This is a so great class series that I enjoyed watching. One thing I like to make sure I understand is the Error in Measurement, 4 in this example. Is it correct that each particular measurement setup has its own error in measurement witch is a constant? And how do we find out the value of it? Thank you!

[@MichelvanBiezen]

There are several sources of errors in measurment (error caused by the internal electronics of the application, errors in the SW algorithms, errors in the actual measurement, etc.) These are dependent of the system you are dealing with (radar, tracking, GPS, automated measuring devices, etc.) Most of the errors are known, and are used in the Filter. Some errors are random.

[@tubejhe]

@@MichelvanBiezen Thank you for the answer!

[@leonjbr]

Excelent video Mr. Van Biezen, but I have a question: if instead of applying the Kalman Filter you simply calculate the SMA on the measured data, i.e. (75+71+70+74/4) you get 72,5 wich is more close to 72 than 71. Would it be better to calculate the SMA than the Kalman Filter?

[@MichelvanBiezen]

This is just a simple example (along with the following videos) to show how the KF works. In an actual application we don't know what the actual (true) value is and the KF will get us closer to the true value than any other method. (It places a weighting factor on the assumed errors and the measurements)

[@leonjbr]

@@MichelvanBiezen Well, Mr. van Bienzen, I understand, but then I have another doubt: if we dont know what the true value is how can we know that KF is faster than any other method?

[@MichelvanBiezen]

The KF has been used in many applications all over the world and it works like a charm. It is particular useful in tracking algorithms and we use it on radar technology and GPS technology as an example.

[@leonjbr]

@@MichelvanBiezen Ok, thanks a lot. Your videos are very, very clear. I think those are the first internet material in wich I really can understand Kalman Filter.

[@GustavoHJ6]

Excelent lecture! I am also waiting for the next 6 videos. If possible, 3D examples with signals from more than one source would be great.

[@MichelvanBiezen]

+GustavoHJ6 They are being prepared. My time is limited, but they are in the making and will appear in the near future.

[@GustavoHJ6]

+Michel van Biezen Oh, that's great. I will make sure to share your channel with my colleagues. Thanks from Brazil!

[@derunkarabeyoglu3527]

Hi, great tutorial!!! Can we predict the temperature at (t+5) time by just only taking measurements at the time [t:t+3]? I mean can we estimate room temperature in 5 minutes later? Is it possible by analyzing previous measurements?

[@MichelvanBiezen]

The KF is not used for prediction, but for smoothing out uncertainties and random variation in the process. For predicting future values, we use a math modeling technique extrapolating the current calculated curve.

[@dadou3024]

Thanks a lot for this lecture, it is very useful and helping. However, i'd like to understand something. How did you get the "2" and "4" ? I understand that it is just a random example you chose but i do not get how myself i can find the "initial error in the estimate" and the "initial error in the measurement" in the model i am estimating. Could you please help me on this point ?

[@MichelvanBiezen]

+Dalia Ibrahim In this example the error estimates were just randomly chosen. In a real world example, the initial errors are chosen based on the knowledge of estimated errors on your system. For example, when you are tracking a satellite, you may assume a timing error of 10 nanoseconds to start or 100 nanoseconds depending on your assumed design parameters. The beauty of the Kalman FIlter is that it doesn't matter much on what you choose for the initial errors, even if they are very far off, because the filter zeroes in to the correct values quickly.

[@dadou3024]

Thanks a lot ! it appears very clear to me now ! Big big thank you for your help.

[@bocao3491]

Great videos! Are errors in measurements predefined?

[@MichelvanBiezen]

Thank you. It depends. In some cases the errors are known or can be estimated, in other cases they must be approximated.

[@dohyeongkim9730]

Awesome lecture!

[@VoltaicoDevelopment]

Thanks for this lecture, it really helped me understanding the Kalman filter. Unfortunately I can't fing the next lectures (7 to 12), are they already online? Anyway, great job!

[@MichelvanBiezen]

+João Cabeleira Not yet. I am still working on those. Working 3 jobs doesn't leave me much time to make videos. I should have them up in 3 weeks or so.

[@horneproject]

+Michel van Biezen Please upload them :) We need your knowledge !

[@krangw6755]

+Michel van Biezen Thank you for explaining so well how the Kalman filter works and also for underlining why the Kalman filter is so effective (my university teacher didn't manage to do either of these) Anyway I hope you will upload the remaining Kalman videos asap, I will have a test on this soon and your help would be much appreciated!

[@youngdukseo9383]

Great lectures. Thank you.

[@MichelvanBiezen]

Glad you like them!

[@tehnoplus1]

Great explanation Sir!

[@uditarpit]

Why should error in measurement be fixed? KG and Error in estimate is bound to decrease as we have - { error estimate at t= (1-kg)*error estimate at t-1 } Can same kind of smoothing achieved by moving average ?

[@MichelvanBiezen]

Typically the error in measurement remains fixed, as the uncertainties are known. There are other contributor which are handled differently in the filter if there are variations to the input.

[@uditarpit]

thanks, I am unable to think how kalman filter is better than other smoothing algorithms ?

[@RyanGoessl94]

Thank you very much for making this series, it is very clear so far and very helpful. One question I have: Will this example only work when the true temperature stays constant? It seems as though the Kalman Gain will tend towards 0 in a set number of sets purely influenced by the constant measurement error. Then when the KG is near zero, if the true temp were to rise to 85 let's say, the system would effectively ignore any incoming measurements and never converge near the true temp.

[@MichelvanBiezen]

The Kalman filter is designed to track a constantly changing "number" or "thing". It is commonly used to track satellites, radar targets, etc.

[@jokerrxl]

well this makes me think that even it is designed to track constantly changing things/numbers, the error of estimation will still always converge no matter what, then it will finally still reach to a point where it starts ignoring new measurements right? then how it is gonna work with new measurements even given there are no huge change? Appreciate in advance for any explanations here for my question

[@chenghaofeng7779]

EST = 68 error_in_estimate = 2 error_in_measurement = 4 MEA = [75,71,70,74] for i in range(4): print("the {} update".format(i)) KG = error_in_estimate/(error_in_estimate+error_in_measurement) print("KG is {}".format(KG)) error_in_estimate = (1-KG)*(error_in_estimate) print("error_in_estimate is {}".format(error_in_estimate)) EST = EST+KG*(MEA[i]-EST) print("new estimate is {}".format(EST)) print("_________________________________") I wrote the code in Python3,maybe it's more convenient to understand.

[@nyinyinyanlin1656]

Thank you

[@nyinyinyanlin1656]

EST = 68.0 error_in_estimate = 2.0 error_in_measurement = 4.0 MEA = [75,71,70,74,73,75,72,70,69,73,70,71,74,72,75,76,71,70,70,73,74] for mea in MEA: print("Update: {}".format(mea)) KG = error_in_estimate/(error_in_estimate+error_in_measurement) print("KG: {}".format(KG)) error_in_estimate = (1-KG)*(error_in_estimate) EST = EST+KG*(mea-EST) print("Estimate: {}".format(EST)) print("________________________") Extended MEA list to several more iterations and the estimate really gets close to 72.

[@gaithazanky1487]

I am trying to use this control system for my ev3 robot , I am trying to let the robot follow the edge of black-white line by the action of light sensor readings . any ideas ?

[@BigPet-so5hp]

Great explanation, but I noticed that if I just take the simple average of all the measurement values + the initial estimate in each step, we get more accurate numbers in each step. I get the next values at each step: 71.5, 71.33, 71, 71.6, so while I understand the explanation, its hard to see why is it better at this point. Guess I need to watch the other vids as well :)

[@BigPet-so5hp]

An update to my comment: based on intuition I thought Kalman filter might actually be better when a big error comes in later. With two extra points: extra measurement 1: 79 KG 0.14 ESTt 72.12 EESTt 0.56 extra measurement 2: 75 KG 0.122 ESTt 72.4656 EESTt 0.49 The relevant values we got by averaging are 72.8, 73.14, so bingo, averging is worse for this case. So as far as I see Kalman filter actually handles better the unexpected big errors later on, thats where its better, it has a natural flattening built in due to the keep decreasing KG. But then the next obvious questions are: a) What happens if we get really unlucky at the start and we get 78,79,77,79 readings, so Kalman filter establishes itself up around those values and then it will be much slower coming down than the averaging method, as the KG factor will be also small by that time. b) Could we achieve a similar flattening with simpler methods, just by saying I give less weight to the datapoints coming later and somehow maximize this flattening effect based on the fix Error in measurement? Now thinking it through point b) KG calculation probably does exactly that.

[@MichelvanBiezen]

The first few videos are just there to gain a basic understanding. To see how the KF really works see the rest of the playlist.

[@martintorres5829]

Hay un comentario interesante sobre como esta resolviendo se la ganancia de kalman, que mas adelante seguramente se explica. Y es como prevenir que KG llegue a cero.

[@muntedme203]

Are you able to provide an update to tbe Kalman filter for time series prediction. I see a lot of papers setting distributions etc, or even arma like models with Kalman. It would be appreciated if you could consider this please.

[@MichelvanBiezen]

Currently my schedule is too full to work on the KF videos. (They take a lot of prep time). Probably when I retire from my day job.

[@muntedme203]

@@MichelvanBiezen can we do an example via patreon and donation?

[@MichelvanBiezen]

We appreciate the offer, but my personal sitation and schedule just doesn't allow me to work on this now. We'll pick it back up as soon as possible.

[@dibmon]

Special Scenario: Suppose KG become stable near zero after long run, and E(est) stable, now temperature going to increases so E(meas) will increases, then KG will be tends to zero, and E(est)t almost equal to E(est)t-1 so EST(t) will not increases.

[@ro-kg5vb]

I'd like to know that too. The algorithm will stop to accept new values because kalman gain gets zero. It seems to me that there is something missing that prevents it or increases kg depending on the measurements. Without any additional step, kg doesn't depend on the measurements but is predefined by the chosen parameters and and reaches zero asymptotic.

[@ro-kg5vb]

Ok I read all comments and found the answer. Just repeating it here so that everyone can find in the top comments. This is oversimplified and in reality the "process noise" needs to be taken into account which will prevent kg decrease to zero!

[@ndnygren]

I looked threw the comments and didn't find this question.. I built these equations into an arduino and faked all the measurements to make sure they calculated out the same as yours. I then took out the fake measurements and took real measurements. The filter converged really quickly, but afterward I stuck my finger on the sensor and the measured readings went up by 10 degrees, but the current estimate moves really slowly toward the new measurements, probably about a minute or so. I watched the Kalman gain and the error in the estimate and they both stay at 0.00. Am I wrong in thinking that the current estimate is the output of the filter? Shouldn't the Kalman gain and error in the estimate ramp up with a 10 degree change in the measured value? It seems like once they reach zero they get stuck. I'm not very smart with math or arduino, but am trying to learn. Thanks for the lectures and any response you may offer.

[@zeratulofaiur2589]

Heuristics can help you. If the temperature changes by more than the "error" of the sensor, reset your estimate to somewhere within the temperature error! The universe does not limit you to the theory :)

[@christerranaldo906]

How can one find the error in the measurement? Do you calculate the median or average of the measured value and subtract it from the real value?

[@MichelvanBiezen]

The details of how to do that are in the videos following this. (Often the error is not known and will be deduced as shown in those videos. )

[@christerranaldo906]

@@MichelvanBiezen allright, thank you!

[@johnsonlee2243]

Excuse me. I think that the Kalman Gain Value and the Error Estimate do not relay on the value of the measurement, do they? This means that when the true value changes, the Kalman Filter cannot solve it.

[@johnsonlee2243]

Thanks

[@johnsonlee2243]

I am feeling a little bit confused.

[@akashasthana277]

Hi, your tutorial is very useful and every concept is well explained . My doubt is , how do you know about true temperature? May be true temperature is 75.

[@MichelvanBiezen]

In real applications you usually do not know the actual true values, but the Kalman Filter has been shown to converge to the "true" value quickly in most circumstances.

[@koenschuurman9736]

Sir Michel van Biezen, thanks for explaining us all the Kalman Filter. I'm currently working on a subject in which this method is gonna play a major role. However I think you made a mistake in this video. By calculating the EST for T+2 you calculated 70.40, but shouldn't this be 70.60 because when i recalculate the following formula EST= 70,5 + 0.20(70-70,5 = 0,5) = 70,60. This would even make more sense that it will increase your "estimation" instead of decreasing it. Despite that, thank you for broadcasting this video's.

[@smithjohn589]

you are wrong

[@再來一碗]

This is a really good one! Thx for the interpretation!

[@darshuetube]

If we take the average of the 4 measurements, it is 72.5C. That is also close to true value w/o doing much math. Maybe this filter provides better stability if a 1 noisy measurement comes in.

[@MichelvanBiezen]

This is just a very simplistic example to show how the filter works. If you look at the next videos, you'll get a much better feel for it.

[@darshuetube]

@@MichelvanBiezen I intend to watch the whole series. I have to this for a class. Your videos are great. I donated via pay pal to pitch in my parts.

[@kareemahmad2389]

assuming white noise and the actual temperature is fixed we can estimate it by taking the mean of the readings overtime till it settle near to the actual temperature since the mean of the white noise is zero

[@gaabinubatrafinulifilit122]

Thanks for some very good videos on a hard subject! I just wonder how one get the "Error in measurement" value which seems very important for a reliable result through the whole iteration. I assume that decide this value is the "art" and the heart in making a reliable Kalman filter ?

[@MichelvanBiezen]

It turns out that you can start with a large error and the Kalman Filter will quickly zero in to the correct value. Although a good start would be the difference between the average and the largest value, or 2 or 3 sigma.

[@gaabinubatrafinulifilit122]

But if Emea stays constant the gain will only depend on Eest ?

[@MichelvanBiezen]

If the measured values very little to none, the Kalman Filter will put more weight onto the measured values.

[@arsenantonyan9875]

If our true temperature is 72 and measurment error is 4 ,does it mean that our measurments can not show values outside of this scope (68---76) ?Thank you

[@MichelvanBiezen]

No, the values being read can still be outside those values. The measurement error can be caused by the fluctuations in the equipment, or the accuracy of the sensor, or any number of known errors that can affect the measurement.

[@Mycreatedvideos]

In 3rd iteration the measurement is 70 which is 1 less than that of the previous iteration. So why you are considering measurement error as constant 4 for all iterations?

[@MichelvanBiezen]

Note, that this is just a simple (non-realistic) example in order to explain how the Kalman Filter works. Later more realistic (and more complicated) examples will be shown that show how the filter works.

[@iamredencio]

How do you get the initial errors for the error in estimates and error in measurements?

[@MichelvanBiezen]

It should be your best guess based on what you know. As it turns out, the initial errors do not affect the final outcome. Once you have programmed your model, put in different starting points and the filter will rather quickly converge to the near correct values.

[@iamredencio]

@@MichelvanBiezen Ah, I see. Thank you. So, that means that some prior knowledge would be nice, but it wouId still yield a good end result. Ps. I programmed this example in python, as I was following along with the video, and indeed the fast convergence occurred even when I accidentally entered a wrong estimate.

[@MichelvanBiezen]

Yes, the Kalman Filter is amazing.

[@50_Hz]

Sir, If I am to keep measurement error constant than why my meter Measured readings fluctuate from the true value. Need i not to keep the Measured vale constant or should change the measurement error as 72- measured value.

[@MichelvanBiezen]

Note that the first few videos in this series are over simplistic to show the basic principle of the Kalman Filter. If you watch the rest of the series you'll see more realistic examples.

[@andrewvirtual]

Once again, great video. This question may sound silly, but how would this method be superior to just taking the average between all measured values? (in this case, = 72.5)

[@MichelvanBiezen]

The KF is actually an amazing filter that alternates the weight it gives to the uncertainty vs the expected value (in a tracking situation for example). It is far superior to taking the average. (see the following videos).

[@stefanuswirdatmadja8702]

How do we know the value of "ERROR IN MEASUREMENT"? can we choose it arbitrarily too?

[@MichelvanBiezen]

Often we don't know, but we start with an estimate, and the filter will do the rest.

[@ro-kg5vb]

@@MichelvanBiezen but it's constant in the example. It seems that there is a step missing? KG will get zero and the filter stop working!

[@mohankrishnan2022]

Keep it up Michel Biezen! I am going to get a bow tie too!!

[@MichelvanBiezen]

We're not doing a tutorial on "How to Tie a Bow-Tie". LOL

[@rays14ful]

Something seems off. Looks like there is no connection between the estimated value and the error in the estimate I.e. I can’t see how the estimated value plays back into the error in the estimated value.

[@MichelvanBiezen]

This is just an oversimplistic example to get the basic concept. For those details, watch the rest of the videos where those details are explained.

[@rays14ful]

@@MichelvanBiezen Will do. Very good videos by the way.

[@rubenayla]

So then the second equation is independent of the other 2 equations

[@KatyKarineLee]

How do we determine the initial estimation error and measurement error?

[@MichelvanBiezen]

You make an estimate based on your knowledge and understanding of the equipment used. Even if you don't have a good estimate, the filter will quickly converge to the correct values.

[@mathisart]

If you take the simple average (75+71+70+74)/4 you get 72.5, which is even closer to the true value than the Kalman Filter. I wonder when is the simple average worse than the Kalman filter (for stationary values)?

[@MichelvanBiezen]

This is just for illustration. If you watch the next videos in the series you will see the value of the Kalman Filter. It works amazingly well.

[@javed2547]

So far i think i follow however, why is E_mea = 4 all the time? Is that an assumption that the sensor is off by +-4 degrees? Furthermore, in more complex examples, is the error in your measurement usually always a constant?

[@MichelvanBiezen]

This is just a simple example to show how the filter works. In a real world example the error will indeed change and will be calculated at every iteration.

[@davidg506]

According to the formula for "Error of the estimate", this value can never increase in magnitude. Not only that but it seems very possible that it could quickly go to zero. I'm running a simulation that is doing just that. The "Error of the estimate" goes to zero and therefore causes the Kalman gain to go to zero. Has anyone had the same problem, and if so, how can this be fixed?

[@jairam2788]

How to get the first estimate and error in estimate sir Thank you sir for your lecture❤

[@MichelvanBiezen]

Usually you will know something about your system that will help you determine that. If not, then you take you best guess. Any errors in the guess will be quickly nullified by the filter.

[@jairam2788]

@@MichelvanBiezen thank you sir

[@schoonerene8793]

actually saving me rn at 3:24am

[@francisbaffour-awuahjunior3099]

Does the error in the estimate have to go down every time?

[@MichelvanBiezen]

The error will fluctuate.

[@francisbaffour-awuahjunior3099]

@@MichelvanBiezen I have implemented the extended KF for the logistics differential equation. The error increases and the slowly reaches a maximum. I don't know if it's correct

[@MichelvanBiezen]

The Kalman filter is typically used on measurements of actual systems, such as radar signals, GPS signals, etc. the eliminate unpredictable input variations, and variations caused by system inaccuracies, etc.

[@manukulshreshtha5877]

one question.. In what case will the gain start increasing? What if the value change from 70 to 50? the values wont converge so fast. KG in not a function of new values?

[@MichelvanBiezen]

Depending on the choice of initial values, the KF will take a little longer to converge, but there isn't a lot of difference as the KF converges amazingly quickly.

[@hazemhelal7903]

Thank you very much, When will you upload the next 7 lectures? i need 3D Examples please

[@abhyuditjain]

How do you know that it will approach 72..... You haven't used 72 in calculations anywhere (the real temperature). So how does the system know that it will approach that temperature? Also, the error in measurement is 4 and initial measurement was 75, so the measurement can be from 71 to 79, but you have used 70 at t+2. Can you explain these 2 questions?

[@OttoFazzl]

The distribution of measurements is centered around the true value. In this sense, measurements themselves tell the system what the true value is. The only problem is that in real life measuring devices have measurement noise and so Kalman filter allows to deal with the noise and only keep the relevant information and thus quickly converge to the true value.

[@parthi2929]

So what I gather from replies here, the true value is hidden in measurements and kalman filter helps us to "see" that. Isn't it? But in his experiment, how does he already know true value is 72 in order to validate the experiment if it worked or not?

[@Schuller95]

The example is not very realistic since the initial estimate is 68, and the error of the estimate is 2, which would put the temperature between 66 and 70, even though the true value is 72. That's why it was so slow to converge, because the Kalman Gain started too small compared to the reality of the problem. Also, this method is not prepared for concept drift (change in the true temperature value). Why would you use this instead of, say, exponential smoothing, with the trigg & leach method?

[@minhajsixbyte]

how do you find out error in the measurement in the first place?

[@MichelvanBiezen]

Depending on the situation and the sensors used, the error may be known based on the known performance of the sensor. But if not known then we must guess.

[@minhajsixbyte]

@@MichelvanBiezen got it. thank you for this series!