I have a set of nonlinear equations (run by rk4 method). How can I compute the Jacobian for those?
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The nonlinear equations give attitude quaternion and angular velocity of small satellite.
How may I compute the Jacobian matrices to use in a Kalman filter?
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Benjamin Großmann
2020-2-26
Assume you have the set of nonlinear eqations
and the vector of independent variables defined in Matlab, then you can use the jacobian function to compute the jacobian matrices, e.g.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/273812/image.png)
clearvars, close all
clc
% the variables
x = sym('x',[3,1]);
% some random functions
f = [x(1)^2 + x(2); ...
sin(x(3)); ...
cos(x(1) + x(2))];
% jacobian calculation
J = jacobian(f,x);
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