Numerical integration RK4 for the given data

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HN
HN 2020-8-18
编辑： HN 2020-8-18
I have the angular veocity data shown below and wanted to apply , where.
w
Columns 1 through 9
5.0468 0.1049 -0.1582 -0.4549 -0.7088 -0.8615 -0.8758 -0.7409 -0.4740
3.2405 0.6230 0.6264 0.5425 0.3348 0.0279 -0.3276 -0.6692 -0.9351
-0.0000 -0.0049 -0.0119 -0.0229 -0.0369 -0.0526 -0.0687 -0.0837 -0.0962
Columns 10 through 18
-0.1169 0.2715 0.6264 0.8889 1.0163 0.9908 0.8218 0.5447 0.2142
-1.0766 -1.0664 -0.9047 -0.6183 -0.2562 0.1194 0.4448 0.6665 0.7518
-0.1053 -0.1100 -0.1100 -0.1053 -0.0962 -0.0837 -0.0687 -0.0526 -0.0369
Columns 19 through 22
-0.1062 -0.3561 -0.4855 5.7553
0.6957 0.5261 0.3291 1.6874
-0.0229 -0.0119 -0.0049 -0.0000
%The skew matrix is given by
W= [ 0,-w(1),-w(2),-w(3);
w(1), 0, omg(3),-w(2);
w(2),-w(3), 0, w(1);
w(3), w(2),-w(1), 0];
Apperciated !
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James Tursa
James Tursa 2020-8-18
You stated that w is angular rate and you have that data. You have a formula for quaternion derivative as a function of angular rate w. Why can't you integrate that to give the quaternion as a function of time?
James Tursa
James Tursa 2020-8-18
编辑：James Tursa 2020-8-18
What are the units of your sampled w? Those numbers look way too large for rad/sec.

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James Tursa
James Tursa 2020-8-18
编辑：James Tursa 2020-8-18
E.g., a VERY SIMPLISTIC approach showing one step of Euler integration
dt = some delta time value
q = [1,0,0,0]; % Initial quaternion, scalar first
w = a 1x3 angular rate vector in rad/sec from your sampled data
qdot = 0.5 * quatmultiply( q, [0 w] ); % Assuming right chain convention
q = q + qdot * dt; % One Euler step
This is just to show a very basic idea. In practice, one would use more sophisticated methods of integration.
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James Tursa
James Tursa 2020-8-18
You want 10e-10 integration accuracy using noisy sampled data? Really?
HN
HN 2020-8-18
编辑：HN 2020-8-18
Don't you think RK4 can give that accuracy if we use small sample size. My actual data is 3x1001. Not noisy as it is shown above.

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