{"id":60443,"date":"2026-01-15T16:05:21","date_gmt":"2026-01-15T08:05:21","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/60443.html"},"modified":"2026-01-15T16:05:21","modified_gmt":"2026-01-15T08:05:21","slug":"ar%e7%9c%bc%e9%95%9c-ahrs-%e7%ae%97%e6%b3%95%e6%8a%80%e6%9c%af%e6%96%87%e6%a1%a3-%e4%ba%8c","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/60443.html","title":{"rendered":"AR\u773c\u955c AHRS \u7b97\u6cd5\u6280\u672f\u6587\u6863 (\u4e8c)"},"content":{"rendered":"

AR\u773c\u955c AHRS \u7b97\u6cd5\u6280\u672f\u6587\u6863 (\u4e8c)<\/h2>\n

\u8be6\u7ec6\u6570\u5b66\u63a8\u5bfc<\/h3>\n

\u76ee\u5f55<\/h3>\n
  • \u56db\u5143\u6570\u57fa\u7840<\/li>\n
  • Madgwick \u7b97\u6cd5\u5b8c\u6574\u63a8\u5bfc<\/li>\n
  • Mahony \u7b97\u6cd5\u5b8c\u6574\u63a8\u5bfc<\/li>\n
  • \u6536\u655b\u6027\u4e0e\u7a33\u5b9a\u6027\u5206\u6790<\/li>\n
    \n

    1. \u56db\u5143\u6570\u57fa\u7840<\/h3>\n

    1.1 \u56db\u5143\u6570\u5b9a\u4e49<\/h4>\n

    \u56db\u5143\u6570\u662f\u4e00\u79cd\u6269\u5c55\u7684\u590d\u6570\u7cfb\u7edf,\u7528\u4e8e\u8868\u793a\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u65cb\u8f6c:<\/p>\n

    q = q w + q x i + q y j + q z k q = q_w + q_x i + q_y j + q_z k <\/span><\/span>q<\/span><\/span>=<\/span><\/span><\/span><\/span>q<\/span><\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>q<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span>+<\/span><\/span><\/span><\/span>q<\/span><\/span>y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span>+<\/span><\/span><\/span><\/span>q<\/span><\/span>z<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u6216\u5411\u91cf\u8868\u793a: q = [ q w q x q y q z ] = [ q w q v ] q = \\\\begin{bmatrix} q_w q_x q_y q_z \\\\end{bmatrix} = \\\\begin{bmatrix} q_w \\\\mathbf{q_v} \\\\end{bmatrix} <\/span><\/span>q<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>q<\/span><\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>z<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>q<\/span><\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u5176\u4e2d:<\/p>\n

      \n
    • q w q_w <\/span><\/span>q<\/span><\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>: \u6807\u91cf\u90e8\u5206 (scalar part)<\/li>\n
    • q v = [ q x , q y , q z ] T \\\\mathbf{q_v} = [q_x, q_y, q_z]^T <\/span><\/span>q<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>q<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>q<\/span><\/span>y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>q<\/span><\/span>z<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>: \u5411\u91cf\u90e8\u5206 (vector part)<\/li>\n<\/ul>\n

      \u865a\u6570\u5355\u4f4d\u6027\u8d28: i 2 = j 2 = k 2 = i j k = \u2212 1 i^2 = j^2 = k^2 = ijk = -1 <\/span><\/span>i<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>j<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>ijk<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      i j = k , j k = i , k i = j ij = k, \\\\quad jk = i, \\\\quad ki = j <\/span><\/span>ij<\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span>,<\/span><\/span><\/span>jk<\/span><\/span>=<\/span><\/span><\/span><\/span>i<\/span>,<\/span><\/span><\/span>ki<\/span><\/span>=<\/span><\/span><\/span><\/span>j<\/span><\/span><\/span><\/span><\/span><\/span> j i = \u2212 k , k j = \u2212 i , i k = \u2212 j ji = -k, \\\\quad kj = -i, \\\\quad ik = -j <\/span><\/span>ji<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>k<\/span>,<\/span><\/span><\/span>kj<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>i<\/span>,<\/span><\/span><\/span>ik<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>j<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      1.2 \u56db\u5143\u6570\u57fa\u672c\u8fd0\u7b97<\/h4>\n

      \u52a0\u6cd5<\/h5>\n

      q 1 + q 2 = [ q 1 w + q 2 w q 1 x + q 2 x q 1 y + q 2 y q 1 z + q 2 z ] q_1 + q_2 = \\\\begin{bmatrix} q_{1w} + q_{2w} q_{1x} + q_{2x} q_{1y} + q_{2y} q_{1z} + q_{2z} \\\\end{bmatrix} <\/span><\/span>q<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>q<\/span><\/span>1<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>2<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>1<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>2<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>1<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>2<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>1<\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>2<\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u4e58\u6cd5 (Hamilton Product)<\/h5>\n

      q 1 \u2297 q 2 = [ q 1 w q 2 w \u2212 q 1 x q 2 x \u2212 q 1 y q 2 y \u2212 q 1 z q 2 z q 1 w q 2 x + q 1 x q 2 w + q 1 y q 2 z \u2212 q 1 z q 2 y q 1 w q 2 y \u2212 q 1 x q 2 z + q 1 y q 2 w + q 1 z q 2 x q 1 w q 2 z + q 1 x q 2 y \u2212 q 1 y q 2 x + q 1 z q 2 w ] q_1 \\\\otimes q_2 = \\\\begin{bmatrix} q_{1w}q_{2w} – q_{1x}q_{2x} – q_{1y}q_{2y} – q_{1z}q_{2z} q_{1w}q_{2x} + q_{1x}q_{2w} + q_{1y}q_{2z} – q_{1z}q_{2y} q_{1w}q_{2y} – q_{1x}q_{2z} + q_{1y}q_{2w} + q_{1z}q_{2x} q_{1w}q_{2z} + q_{1x}q_{2y} – q_{1y}q_{2x} + q_{1z}q_{2w} \\\\end{bmatrix} <\/span><\/span>q<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2297<\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>q<\/span><\/span>1<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>1<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>1<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>1<\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>1<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>1<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>1<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>1<\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>1<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>1<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>1<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>1<\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>1<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>1<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>1<\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>1<\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u5411\u91cf\u5f62\u5f0f: q 1 \u2297 q 2 = [ q 1 w q 2 w \u2212 q 1 v \u22c5 q 2 v q 1 w q 2 v + q 2 w q 1 v + q 1 v \u00d7 q 2 v ] q_1 \\\\otimes q_2 = \\\\begin{bmatrix} q_{1w}q_{2w} – \\\\mathbf{q_{1v}} \\\\cdot \\\\mathbf{q_{2v}} q_{1w}\\\\mathbf{q_{2v}} + q_{2w}\\\\mathbf{q_{1v}} + \\\\mathbf{q_{1v}} \\\\times \\\\mathbf{q_{2v}} \\\\end{bmatrix} <\/span><\/span>q<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2297<\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>q<\/span><\/span>1<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>1v<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span>q<\/span><\/span>2v<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>1<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2v<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>2<\/span>w<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>1v<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>1v<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>q<\/span><\/span>2v<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u6ce8\u610f: \u56db\u5143\u6570\u4e58\u6cd5\u4e0d\u6ee1\u8db3\u4ea4\u6362\u5f8b: q 1 \u2297 q 2 \u2260 q 2 \u2297 q 1 q_1 \\\\otimes q_2 \\\\neq q_2 \\\\otimes q_1 <\/span><\/span>q<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2297<\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2297<\/span><\/span><\/span><\/span>q<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u5171\u8f6d (Conjugate)<\/h5>\n

      q \u2217 = [ q w \u2212 q x \u2212 q y \u2212 q z ] = [ q w \u2212 q v ] q^* = \\\\begin{bmatrix} q_w -q_x -q_y -q_z \\\\end{bmatrix} = \\\\begin{bmatrix} q_w -\\\\mathbf{q_v} \\\\end{bmatrix} <\/span><\/span>q<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>q<\/span><\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>z<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>q<\/span><\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>q<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u6a21\u957f (Norm)<\/h5>\n

      \u2223 \u2223 q \u2223 \u2223 = q w 2 + q x 2 + q y 2 + q z 2 ||q|| = \\\\sqrt{q_w^2 + q_x^2 + q_y^2 + q_z^2} <\/span><\/span>\u2223\u2223<\/span>q<\/span>\u2223\u2223<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>w<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>x<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>y<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>q<\/span><\/span>z<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> <\/p>\n

      <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u9006 (Inverse)<\/h5>\n

      q \u2212 1 = q \u2217 \u2223 \u2223 q \u2223 \u2223 2 q^{-1} = \\\\frac{q^*}{||q||^2} <\/span><\/span>q<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2223\u2223<\/span>q<\/span>\u2223<\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u5bf9\u4e8e\u5355\u4f4d\u56db\u5143\u6570 ( \u2223 \u2223 q \u2223 \u2223 = 1 ||q|| = 1 <\/span><\/span>\u2223\u2223<\/span>q<\/span>\u2223\u2223<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>): q \u2212 1 = q \u2217 q^{-1} = q^* <\/span><\/span>q<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

      AR\u773c\u955c AHRS \u7b97\u6cd5\u6280\u672f\u6587\u6863 (\u4e8c)
      \n\u8be6\u7ec6\u6570\u5b66\u63a8\u5bfc
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      \n1.1 \u56db\u5143\u6570\u5b9a\u4e49
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      \n\u6216\u5411\u91cf\u8868\u793a: q = [ q w q x q y <\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[4276,3244,427],"topic":[],"class_list":["post-60443","post","type-post","status-publish","format-standard","hentry","category-server","tag-ar","tag-3244","tag-427"],"yoast_head":"\nAR\u773c\u955c AHRS \u7b97\u6cd5\u6280\u672f\u6587\u6863 (\u4e8c) - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/60443.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"AR\u773c\u955c AHRS \u7b97\u6cd5\u6280\u672f\u6587\u6863 (\u4e8c) - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"AR\u773c\u955c AHRS \u7b97\u6cd5\u6280\u672f\u6587\u6863 (\u4e8c) \u8be6\u7ec6\u6570\u5b66\u63a8\u5bfc \u76ee\u5f55 \u56db\u5143\u6570\u57fa\u7840 Madgwick \u7b97\u6cd5\u5b8c\u6574\u63a8\u5bfc Mahony \u7b97\u6cd5\u5b8c\u6574\u63a8\u5bfc \u6536\u655b\u6027\u4e0e\u7a33\u5b9a\u6027\u5206\u6790 1. \u56db\u5143\u6570\u57fa\u7840 1.1 \u56db\u5143\u6570\u5b9a\u4e49 \u56db\u5143\u6570\u662f\u4e00\u79cd\u6269\u5c55\u7684\u590d\u6570\u7cfb\u7edf,\u7528\u4e8e\u8868\u793a\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u65cb\u8f6c: q = q w + q x i + q y j + q z k q = q_w + q_x i + q_y j + q_z k q=qw\u200b+qx\u200bi+qy\u200bj+qz\u200bk \u6216\u5411\u91cf\u8868\u793a: q = [ q w q x q y\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/60443.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-01-15T08:05:21+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/60443.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/60443.html\",\"name\":\"AR\u773c\u955c AHRS \u7b97\u6cd5\u6280\u672f\u6587\u6863 (\u4e8c) - 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