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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.

Hien Pham

Ahsan

### Ahsan (view profile)

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`

Ahsan

### Ahsan (view profile)

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

Ahsan

### Ahsan (view profile)

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?

Alex Dytso

### Alex Dytso (view profile)

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

Ahsan

### Ahsan (view profile)

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.

yatie SUAIB

### yatie SUAIB (view profile)

ok,thank you very much

Alex Dytso

yatie SUAIB

### yatie SUAIB (view profile)

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

Alex Dytso

### Alex Dytso (view profile)

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.

Atef

### Atef (view profile)

please how apply this code for 2-D ?

W. Chong

### W. Chong (view profile)

##### MATLAB Release
MATLAB 7.6 (R2008a)