Numerical integration RK4 for the given data

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HN 2020-8-18

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https://ww2.mathworks.cn/matlabcentral/answers/581256-numerical-integration-rk4-for-the-given-data

编辑： HN 2020-8-18

采纳的回答： James Tursa

在 MATLAB Online 中打开

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 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 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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采纳的回答

James Tursa 2020-8-18

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/581256-numerical-integration-rk4-for-the-given-data#answer_481809

编辑：James Tursa 2020-8-18

在 MATLAB Online 中打开

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.