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Extended Kalman Filter Tracking Object in 3-D

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Using Kalman filter to track object in 3D. Comparing Extended Kalman filter to its linear version.

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Assume that we want to track an object moving in 3-D space with constant velocity. Our instruments observe bearing, range and high(cylindrical coordinates). However, of an interest are rectangular coordinates. Since transformation is non-linear this requires use of extended Kalman filter.
Because transformation is non-linear between X,Y and Range,Bearing and linear between Z and high(Z is height), this problems serves as a good comparason of how well extended Kalman filter can perform. By comparing its linear estimation error in Z to non-linear estimations in X and Y, we can judge how non-familiarities effect estimation.

MATLAB release MATLAB 7.6 (R2008a)
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Comments and Ratings (11)
14 May 2014 Ahsan

I give the X(:,1)=MAT(1,:)' as actual initial condition, where MAT is the matrix of [501x6] and i'm confusing about initial observation `Z` and assumed initial condition `Xh`

14 May 2014 Ahsan

The value of Z is unused from argument in proccesANDobserve and Jacobian function.

14 May 2014 Ahsan

I know this is the observation vector, I edited a bit of your code for my purpose, but it crosses the actual trajectory and calculating in its opposite way. I have a matrix `MAT` of [501x6] having 1:3 for position and 4:6 for velocities, How can I set the initial observation vector and also what other initial assumptions would be set?

07 May 2014 Alex Dytso

'Z' Stands for the observation vector and it is used in number of places for example when you compute quantity called innovation.

07 May 2014 Ahsan

Hello, I didn't understand the Use of `Z` as this is unused in your code. Its always calculating but didn't use the initial array.

30 Sep 2013 yatie SUAIB

ok,thank you very much

26 Sep 2013 Alex Dytso

Yes, here is the document this is based on
https://dl.dropboxusercontent.com/u/12025879/Extended%20Kalman%20Filter.pdf

26 Sep 2013 yatie SUAIB

Hi Alex
Do you have the article/journal paper that you are referring to in order to write these Matlab codes?

31 Mar 2013 Alex Dytso

In order to convert to 2-D you just have to change the appropriate dimensions of matrices. You can also use the code as is and ignore one of the outputs.

31 Mar 2013 Atef

please how apply this code for 2-D ?

30 Dec 2012 W. Chong  

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