I have a set of nonlinear equations (run by rk4 method). How can I compute the Jacobian for those?

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?

[darova]

Do you have any formulas?

Answer 1

[Benjamin Großmann]

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.

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);