Nonlinear State Estimators | Understanding Kalman Filters, Part 5

Download our Kalman Filter Virtual Lab to practice linear and extended Kalman filter design of a pendulum system with interactive exercises and animations in MATLAB and Simulink: bit.ly/3g5AwyS
This video explains the basic concepts behind nonlinear state estimators, including extended Kalman filters, unscented Kalman filters, and particle filters.
A Kalman filter is only defined for linear systems. If you have a nonlinear system and want to estimate system states, you need to use a nonlinear state estimator. This video explores different nonlinear filters to help you choose the one that will work for your nonlinear system. Extended Kalman filters linearize the distribution around the mean of the current estimate and then use this linearization in the predict and update states of the Kalman filter algorithm. An unscented Kalman filter selects a minimal set of sample points (also referred to as sigma points) from the Gaussian distribution, and it propagates them through the nonlinear system. It then computes the mean and covariance of the new set of transformed sample points and uses these to find the new state estimate. The working principles behind particle filters are similar to unscented Kalman filters, but particle filters can approximate any arbitrary distribution. For this, particle filters require a larger set of points (referred to as particles).
Check out additional resources:
• Extended and Unscented Kalman Filter Algorithms for Online State Estimation: goo.gl/MtS6B0
‌• Particle Filter Workflow: goo.gl/KiB5DB
‌• Using Nonlinear Kalman Filtering to Estimate Signals(PDF): bit.ly/3jj8Rzv
‌• The Unscented Kalman Filter for Nonlinear Estimation(PDF): goo.gl/rp1F8w
‌• An introduction to particle filters(PDF): goo.gl/oBcamD
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[@tomjanson4004]

Absolutely stunned by the quality of this explanation series on Kalman Filters. Thank you so much!

[@ahmedgaafar5369]

the series of those 5 videos did really an excellent job...thank you.

[@07kandarp]

Very simple and easy to understand tutorial. A couple of “mind blown” moments make it fun. Kudos to the team

[@elvispiss]

Was your mind blown?

[@ksjksjgg]

excellent lecture to have big picture of kalman filter, EKF, UKF and particle filter.

[@what_about_mike]

I'm loving these videos

[@NoNTr1v1aL]

0:19 I like the fact that it shows the person travelling back in time 😂

[@claudioricciardiello9601]

I loved these videos! Thank you very much! :))

[@kurtschuepfer7548]

Very helpful video series. Thanks!

[@Mayitzin]

Watch it at velocity x1.25 with subtitles to understand it better

[@saipavankumarreddy.y6537]

The Best video on Kalman Filters. Thanks a lot matlab.

[@mangooc4958]

Very nice. Keep doing it!

[@ahammadfahad3852]

Thank you for these awesome vedios .Great job.

[@DRAMBgo]

Impressive explanation, thanks

[@mohammadabedalrahmanhammou2990]

Very interesting series, can you add a part for the Ensemble Kalman Filter

[@0sm1um76]

I actually find the EnKF more intuitive than the Kalman Filter. Its easier for me to understand what an ensemble of samples is doing than to visualize what the whole gaussian distribution is doing if you know what mean.

[@yoga.sasmita]

Hi@@0sm1um76, where can I learn the EnKF? I need to understand the basic concept and how to implement it in my method. Thanks 🙏

[@slothochdonut3099]

very well explained! Even though I don’t use matlab, it’s still helpful’

[@claudiuradu7551]

thank you!

[@xiaoyandai9482]

many thanks!

[@alimazinani8436]

very goooooooood

[@fifaham]

This video could be the answer I commented in the previous video.

[@ahmedayman6787]

1- in the literature, there's always emphasis on the weights of the sigma points in UKF, could you elaborate the importance of weights for the sigma points in the prediction and update of the next state P ? 2- is their a solution for the non-positive definite P in the sigma points generation step ?

[@meldaulusoy8389]

1. Weights of the sigma points depend on a few unscented transformation parameters (such as alpha, beta, kappa), which in turn control the spread of the sigma points around the mean state estimate. How the sigma points are spread is important because UKF can only track unimodal (single-peak) state distributions. If the state distribution is not unimodal, but you would like to track one of the peaks, adjusting the spread of the sigma points so that they are all near this peak can yield reasonable results. Weights can also impact the results due to numerical issues. For instance, large weights (typically corresponds to tightly packed sigma points) is more likely to cause numerical issues. 2. A non-positive definite P can only arise due to numerical issues. If P is not positive definite, one solution is to perturb it to make it positive-definite. An alternative approach is reducing the chance of numerical issues by ensuring the state estimation is well scaled (states have similar magnitudes). For more information, I'd recommend the references on the following page: en.wikipedia.org/wiki/Unscented_transform

[@Cacnx34]

Why we need batch state estimation ? What are the differences batch estimation and Kalman?

[@Aleksandr_Kashirin]

In original Kalman paper there is absolutely no one assumption that the noise is distributed normally. Covariance of the noise is only matters.

[@gabrieloliveira3044]

I have a problem that only my C matrix presents nonlinearities, can i use the extended kalman filter using jacobians only in the C matrix? What should i do ?

[@vaks2l]

2:28 The linearized state-space equation should be delta x_k = F * [delta x_k-1 delta u_k] + w_k, right?

[@mirhamza4123]

They say that prof hugh stinked and so it was called the unscemted kalman filter. :D

[@stefano8936]

for a not anguishing version, play 1.75x

[@valyavalya9744]

На русский можете перевести

[@IntelLectualChip]

Poor narrator. It's hard to listen.