使用matlab编写将一个三维方向余弦矩阵转换为四元数,并对四元数进行单位化
时间: 2023-12-10 22:38:29 浏览: 80
在MATLAB中,可以使用以下代码将一个3x3的方向余弦矩阵转换为四元数:
```matlab
function q = dcm2quat(dcm)
% DCM2QUAT Convert direction cosine matrix to quaternion
% q = DCM2QUAT(dcm) converts a 3x3 direction cosine matrix (DCM) to a 1x4
% quaternion. The DCM input represents the rotation from frame 2 to frame
% 1, where frame 1 is the global frame and frame 2 is the rotated frame.
%
% Reference: Eq. 2.65 and 2.67, "Quaternion Kinematics for the Error-State
% Kalman Filter", Joan Solà, 2017.
% Check input size
if any(size(dcm) ~= [3 3])
error('Input matrix must be 3x3.')
end
% Compute quaternion elements
q0 = 0.5 * sqrt(1 + dcm(1,1) + dcm(2,2) + dcm(3,3));
q1 = (dcm(3,2) - dcm(2,3)) / (4*q0);
q2 = (dcm(1,3) - dcm(3,1)) / (4*q0);
q3 = (dcm(2,1) - dcm(1,2)) / (4*q0);
% Return quaternion as a row vector
q = [q0 q1 q2 q3];
```
然后,可以使用以下代码将四元数单位化:
```matlab
function q_unit = quatnormalize(q)
% QUATNORMALIZE Normalize quaternion
% q_unit = QUATNORMALIZE(q) normalizes the quaternion q to have unit
% magnitude.
% Check input size
if any(size(q) ~= [1 4])
error('Input vector must be 1x4.')
end
% Compute quaternion magnitude
q_mag = norm(q);
% Normalize quaternion
q_unit = q / q_mag;
```
现在,您可以将这两个函数组合在一起,使用以下代码将方向余弦矩阵转换为单位四元数:
```matlab
% Example DCM
dcm = [0.7071 -0.7071 0; 0.7071 0.7071 0; 0 0 1];
% Convert DCM to quaternion
q = dcm2quat(dcm);
% Normalize quaternion
q_unit = quatnormalize(q);
```
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