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

ekfsatellite

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?

Best Answer

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);

Related Solutions

MATLAB: How to access the current iteration number in the program where we supply the non-linear equations,F =0 and the Jacobian for FSOLVE

Something like this will work

global iter_number % global variable for a quick example, i recommend creating a handle class object
iter_number = 0;
fun = @root2d;
x0 = [0,0];
opts = optimoptions('fsolve', 'OutputFcn', @outputFcn);
x = fsolve(fun,x0, opts);
root2d(x)
function F = root2d(x)
global iter_number
current_iteration = iter_number
F(1) = exp(-exp(-(x(1)+x(2)))) - x(2)*(1+x(1)^2);
F(2) = x(1)*cos(x(2)) + x(2)*sin(x(1)) - 0.5;
end
function stop = outputFcn(x, optimValues, state)
    global iter_number
    iter_number = optimValues.iteration;
    stop = 0;
end

MATLAB: RK4 orbit problem

dvxdt=@(t,x,vx) GM*x./(x.^2+y.^2).^3;

that accepts vx as a parameter but does not use it.

It does not have any parameter named y but uses y. In that case, it is going to use the variable value that the variable y had at the time the anonymous function was created, which comes from

y = zeros(1,1825);

This is a vector, and even though it only contributes 0 at all components, it makes the result of dvxdt be a vector. That becomes a problem because it means that

    k1vx = dvxdt(t(i)     ,x(i)     ,vx(i));

gives a vector result, so

vx(i+1)=vx(i)+h/6*(k1vx+2*k2vx+2*k3vx+k4vx);

has a vector on the right hand side, but designates a scalar output location.

Best Answer

Related Solutions

MATLAB: How to access the current iteration number in the program where we supply the non-linear equations,F =0 and the Jacobian for FSOLVE

MATLAB: RK4 orbit problem

Related Question