forked from logzhan/NotesUESTC
28 lines
693 B
Markdown
28 lines
693 B
Markdown
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# **Mahony姿态解算**
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## 一、Mahony算法中载体系的重力投影到地理系
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常见代码的写法如下图所示：
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```C
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// 写法1
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float halfvx = q1 * q3 - q0 * q2;
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float halfvy = q0 * q1 + q2 * q3;
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float halfvz = q0 * q0 - 0.5f + q3 * q3;
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// 写法2
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float vx = 2.0f*(q1*q3 - q0*q2);
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float vy = 2.0f*(q0*q1 + q2*q3);
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float vz = q0*q0 - q1*q1 - q2*q2 + q3*q3;
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```
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比较有差异的主要在于vz的写法，这两种的写法其实是一样的，推导如下所示
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$$
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\begin{align*}
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vz &= q_0^2-0.5+q_3^2 \\
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2vz &= 2q_0^2-1+2q_3^2 \\
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&= 2q_0^2+2q_3^2-q_0^2-q_1^2-q_2^2-q_3^2 \\
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&= q_0^2-q_1^2-q_2^2+q_3^2 \\
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\end{align*}
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$$
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