PX4飞控中利用EKF估计姿态角代码详解
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PX4飞控中利用EKF估计姿态角代码详解
PX4飞控中主要用EKF算法来估计飞行器三轴姿态角,具体c文件在px4\Firmware\src\modules\attitude_estimator_ekf\codegen\目录下
- 具体原理
- 程序详解
- 下一步
1.具体原理
EKF算法原理不再多讲,具体可参见上一篇blog http://blog.csdn.net/lizilpl/article/details/45289541.
这篇讲EKF算法执行过程,需要以下几个关键式子:
飞行器状态矩阵:
这里表示三轴角速度,
表示三轴角加速度,
表示加速度在机体坐标系三轴分量,
,表示磁力计在机体坐标系三轴分量。
测量矩阵
分别由三轴陀螺仪,加速度计,磁力计测得。状态转移矩阵:
飞行器下一时刻状态预测矩阵如下:
其中W项均为高斯噪声, 为飞行器在姿态发生变化后,坐标系余旋变换矩阵,对该函数在处求一阶偏导,可得到状态转移矩阵:
此时可得到飞行器状态的先验估计:
利用测量值修正先验估计:
这里测量矩阵H与状态矩阵X为线性关系,故无需求偏导。
卡尔曼增益:
状态后验估计:
方差后验估计:
2.程序详解
整个EKF的代码挺长的,大部分是矩阵运算,而且使用嵌套for循环来执行的,所以读起来比较费劲,但是要是移植到自己工程上的话必然离不开这一步,所以花了一个下午把各个细节理清楚,顺便记录分享。
/* Include files */#include "rt_nonfinite.h"#include "attitudeKalmanfilter.h"#include "rdivide.h"#include "norm.h"#include "cross.h"#include "eye.h"#include "mrdivide.h"/* '输入参数:updateVect[3]:用来记录陀螺仪,加速度计,磁力计传感器数值是否有效 z[9] :测量矩阵 x_aposteriori_k[12]:上一时刻状态后验估计矩阵,用来预测当前状态 P_aposteriori_k[144]:上一时刻后验估计方差 eulerAngles[3] :输出欧拉角 Rot_matrix[9] :输出余弦矩阵 x_aposteriori[12] :输出状态后验估计矩阵 P_aposteriori[144] :输出方差后验估计矩阵'*/void attitudeKalmanfilter(const uint8_T updateVect[3],real32_T dt, const real32_T z[9], const real32_T x_aposteriori_k[12], const real32_T P_aposteriori_k[144], const real32_T q[12], real32_T r[9], real32_T eulerAngles[3], real32_T Rot_matrix[9],real32_T x_aposteriori[12], real32_T P_aposteriori[144]){/*以下这一堆变量用到的时候再解释*/ real32_T wak[3]; real32_T O[9]; real_T dv0[9]; real32_T a[9]; int32_T i; real32_T b_a[9]; real32_T x_n_b[3]; real32_T b_x_aposteriori_k[3]; real32_T z_n_b[3]; real32_T c_a[3]; real32_T d_a[3]; int32_T i0; real32_T x_apriori[12]; real_T dv1[144]; real32_T A_lin[144]; static const int8_T iv0[36] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; real32_T b_A_lin[144]; real32_T b_q[144]; real32_T c_A_lin[144]; real32_T d_A_lin[144]; real32_T e_A_lin[144]; int32_T i1; real32_T P_apriori[144]; real32_T b_P_apriori[108]; static const int8_T iv1[108] = { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 }; real32_T K_k[108]; real32_T fv0[81]; static const int8_T iv2[108] = { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 }; real32_T b_r[81]; real32_T fv1[81]; real32_T f0; real32_T c_P_apriori[36]={ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; real32_T fv2[36]; static const int8_T iv4[36] = { 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; real32_T c_r[9]; real32_T b_K_k[36]; real32_T d_P_apriori[72]; static const int8_T iv5[72] = { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 }; real32_T c_K_k[72]; static const int8_T iv6[72] = { 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; real32_T b_z[6]; static const int8_T iv7[72] = { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 }; static const int8_T iv8[72] = { 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 }; real32_T fv3[6]; real32_T c_z[6]; /*开始计算*/ /*'wak[]为当前状态三轴角加速度'*/ wak[0] = x_aposteriori_k[3]; wak[1] = x_aposteriori_k[4]; wak[2] = x_aposteriori_k[5];
/* ‘欧拉角旋转矩阵’
这里的O矩阵相当于A矩阵中的的转置矩阵!
*/
O[0] = 0.0F; O[1] = -x_aposteriori_k[2]; O[2] = x_aposteriori_k[1]; O[3] = x_aposteriori_k[2]; O[4] = 0.0F; O[5] = -x_aposteriori_k[0]; O[6] = -x_aposteriori_k[1]; O[7] = x_aposteriori_k[0]; O[8] = 0.0F; /* 预测转过一个小角度之后的重力向量三轴投影 */ /* a = [1, -delta_z, delta_y; * delta_z, 1 , -delta_x; * -delta_y, delta_x, 1 ]'; */ eye(dv0); //dv0矩阵单位化 for (i = 0; i < 9; i++) { a[i] = (real32_T)dv0[i] + O[i] * dt; } /* 预测转过一个小角度之后的磁力向量三轴投影 */ eye(dv0); for (i = 0; i < 9; i++) { b_a[i] = (real32_T)dv0[i] + O[i] * dt; }
/*
其实就是这个大家都很眼熟的的余弦矩阵的转置, 用来更新机体转过一个角度之后的重力和磁力三轴投影,只不过两次计算间隔时间很短,变化角度很小,因此忽略高阶小量之后就变成了这个样子。这里还少一个时间系数dt,下面会补上。
*/
x_n_b[0] = x_aposteriori_k[0]; //角速度 x_n_b[1] = x_aposteriori_k[1]; x_n_b[2] = x_aposteriori_k[2]; b_x_aposteriori_k[0] = x_aposteriori_k[6]; // 加速度 b_x_aposteriori_k[1] = x_aposteriori_k[7]; b_x_aposteriori_k[2] = x_aposteriori_k[8]; z_n_b[0] = x_aposteriori_k[9]; //磁力计 z_n_b[1] = x_aposteriori_k[10]; z_n_b[2] = x_aposteriori_k[11]; for (i = 0; i < 3; i++) { c_a[i] = 0.0F; for (i0 = 0; i0 < 3; i0++) { c_a[i] += a[i + 3 * i0] * b_x_aposteriori_k[i0]; } d_a[i] = 0.0F; for (i0 = 0; i0 < 3; i0++) { d_a[i] += b_a[i + 3 * i0] * z_n_b[i0]; } x_apriori[i] = x_n_b[i] + dt * wak[i]; } for (i = 0; i < 3; i++) { x_apriori[i + 3] = wak[i]; } for (i = 0; i < 3; i++) { x_apriori[i + 6] = c_a[i]; } for (i = 0; i < 3; i++) { x_apriori[i + 9] = d_a[i]; } //得到状态先验估计
/*
根据上述矩阵运算,可以得到:
从而:
从而:
其中
得到状态先验估计:
Xk+1[12∗1]=x_apriori[1∗12]T =[x_n_b+wak∗dtwakc_ad_a]T
*/
/* '开始计算A矩阵'*/ b_eye(dv1); for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 3; i0++) { A_lin[i0 + 12 * i] = (real32_T)iv0[i0 + 3 * i]; } /*1 2 3列*/ for (i0 = 0; i0 < 3; i0++) { A_lin[(i0 + 12 * i) + 3] = 0.0F; } /*3 4 5列*/ } /*6 7 8 列*/ A_lin[6] = 0.0F; A_lin[7] = x_aposteriori_k[8]; A_lin[8] = -x_aposteriori_k[7]; A_lin[18] = -x_aposteriori_k[8]; A_lin[19] = 0.0F; A_lin[20] = x_aposteriori_k[6]; A_lin[30] = x_aposteriori_k[7]; A_lin[31] = -x_aposteriori_k[6]; A_lin[32] = 0.0F; for (i = 0; i < 3; i++) { for (i0 = 0; i0 < 3; i0++) { A_lin[(i0 + 12 * (i + 3)) + 6] = 0.0F; } } for (i = 0; i < 3; i++) { for (i0 = 0; i0 < 3; i0++) { A_lin[(i0 + 12 * (i + 6)) + 6] = O[i0 + 3 * i]; } } for (i = 0; i < 3; i++) { for (i0 = 0; i0 < 3; i0++) { A_lin[(i0 + 12 * (i + 9)) + 6] = 0.0F; } } /*6 7 8 列*/ /*9 10 11 列*/ A_lin[9] = 0.0F; A_lin[10] = x_aposteriori_k[11]; A_lin[11] = -x_aposteriori_k[10]; A_lin[21] = -x_aposteriori_k[11]; A_lin[22] = 0.0F; A_lin[23] = x_aposteriori_k[9]; A_lin[33] = x_aposteriori_k[7]; A_lin[34] = -x_aposteriori_k[9]; A_lin[35] = 0.0F; for (i = 0; i < 3; i++) { for (i0 = 0; i0 < 3; i0++) { A_lin[(i0 + 12 * (i + 3)) + 9] = 0.0F; } } for (i = 0; i < 3; i++) { for (i0 = 0; i0 < 3; i0++) { A_lin[(i0 + 12 * (i + 6)) + 9] = 0.0F; } } for (i = 0; i < 3; i++) { for (i0 = 0; i0 < 3; i0++) { A_lin[(i0 + 12 * (i + 9)) + 9] = O[i0 + 3 * i]; } } /*9 10 11 列*/
/*
根据上述矩阵运算,可以得到A_lin矩阵:
同样
*/
for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { b_A_lin[i0 + 12 * i] = (real32_T)dv1[i0 + 12 * i] + A_lin[i0 + 12 * i] *dt; } } //最终A_link,k的逆矩阵
得到:
/*
开始根据计算过程方差
*/
b_q[0] = q[0]; b_q[12] = 0.0F; b_q[24] = 0.0F; b_q[36] = 0.0F; b_q[48] = 0.0F; b_q[60] = 0.0F; b_q[72] = 0.0F; b_q[84] = 0.0F; b_q[96] = 0.0F; b_q[108] = 0.0F; b_q[120] = 0.0F; b_q[132] = 0.0F; b_q[1] = 0.0F; b_q[13] = q[0]; b_q[25] = 0.0F; b_q[37] = 0.0F; b_q[49] = 0.0F; b_q[61] = 0.0F; b_q[73] = 0.0F; b_q[85] = 0.0F; b_q[97] = 0.0F; b_q[109] = 0.0F; b_q[121] = 0.0F; b_q[133] = 0.0F; b_q[2] = 0.0F; b_q[14] = 0.0F; b_q[26] = q[0]; b_q[38] = 0.0F; b_q[50] = 0.0F; b_q[62] = 0.0F; b_q[74] = 0.0F; b_q[86] = 0.0F; b_q[98] = 0.0F; b_q[110] = 0.0F; b_q[122] = 0.0F; b_q[134] = 0.0F; b_q[3] = 0.0F; b_q[15] = 0.0F; b_q[27] = 0.0F; b_q[39] = q[1]; b_q[51] = 0.0F; b_q[63] = 0.0F; b_q[75] = 0.0F; b_q[87] = 0.0F; b_q[99] = 0.0F; b_q[111] = 0.0F; b_q[123] = 0.0F; b_q[135] = 0.0F; b_q[4] = 0.0F; b_q[16] = 0.0F; b_q[28] = 0.0F; b_q[40] = 0.0F; b_q[52] = q[1]; b_q[64] = 0.0F; b_q[76] = 0.0F; b_q[88] = 0.0F; b_q[100] = 0.0F; b_q[112] = 0.0F; b_q[124] = 0.0F; b_q[136] = 0.0F; b_q[5] = 0.0F; b_q[17] = 0.0F; b_q[29] = 0.0F; b_q[41] = 0.0F; b_q[53] = 0.0F; b_q[65] = q[1]; b_q[77] = 0.0F; b_q[89] = 0.0F; b_q[101] = 0.0F; b_q[113] = 0.0F; b_q[125] = 0.0F; b_q[137] = 0.0F; b_q[6] = 0.0F; b_q[18] = 0.0F; b_q[30] = 0.0F; b_q[42] = 0.0F; b_q[54] = 0.0F; b_q[66] = 0.0F; b_q[78] = q[2]; b_q[90] = 0.0F; b_q[102] = 0.0F; b_q[114] = 0.0F; b_q[126] = 0.0F; b_q[138] = 0.0F; b_q[7] = 0.0F; b_q[19] = 0.0F; b_q[31] = 0.0F; b_q[43] = 0.0F; b_q[55] = 0.0F; b_q[67] = 0.0F; b_q[79] = 0.0F; b_q[91] = q[2]; b_q[103] = 0.0F; b_q[115] = 0.0F; b_q[127] = 0.0F; b_q[139] = 0.0F; b_q[8] = 0.0F; b_q[20] = 0.0F; b_q[32] = 0.0F; b_q[44] = 0.0F; b_q[56] = 0.0F; b_q[68] = 0.0F; b_q[80] = 0.0F; b_q[92] = 0.0F; b_q[104] = q[2]; b_q[116] = 0.0F; b_q[128] = 0.0F; b_q[140] = 0.0F; b_q[9] = 0.0F; b_q[21] = 0.0F; b_q[33] = 0.0F; b_q[45] = 0.0F; b_q[57] = 0.0F; b_q[69] = 0.0F; b_q[81] = 0.0F; b_q[93] = 0.0F; b_q[105] = 0.0F; b_q[117] = q[3]; b_q[129] = 0.0F; b_q[141] = 0.0F; b_q[10] = 0.0F; b_q[22] = 0.0F; b_q[34] = 0.0F; b_q[46] = 0.0F; b_q[58] = 0.0F; b_q[70] = 0.0F; b_q[82] = 0.0F; b_q[94] = 0.0F; b_q[106] = 0.0F; b_q[118] = 0.0F; b_q[130] = q[3]; b_q[142] = 0.0F; b_q[11] = 0.0F; b_q[23] = 0.0F; b_q[35] = 0.0F; b_q[47] = 0.0F; b_q[59] = 0.0F; b_q[71] = 0.0F; b_q[83] = 0.0F; b_q[95] = 0.0F; b_q[107] = 0.0F; b_q[119] = 0.0F; b_q[131] = 0.0F; b_q[143] = q[3]; for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { A_lin[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { A_lin[i + 12 * i0] += b_A_lin[i + 12 * i1] * P_aposteriori_k[i1 + 12 *i0]; } c_A_lin[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { c_A_lin[i + 12 * i0] += b_A_lin[i + 12 * i1] * b_q[i1 + 12 * i0]; } } for (i0 = 0; i0 < 12; i0++) { d_A_lin[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { d_A_lin[i + 12 * i0] += A_lin[i + 12 * i1] * b_A_lin[i0 + 12 * i1]; } e_A_lin[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { e_A_lin[i + 12 * i0] += c_A_lin[i + 12 * i1] * b_A_lin[i0 + 12 * i1]; } } }
根据上面的矩阵运算,可以得到:
for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { P_apriori[i0 + 12 * i] = d_A_lin[i0 + 12 * i] + e_A_lin[i0 + 12 * i]; } } //最终过程方差
最终得到过程方差::
P_apriori[12∗12]=d_A_lin[12∗12]+e_A_lin[12∗12];
/*
下面开始利用测量值修正先验估计:用到的公式为:
*/
if ((updateVect[0] == 1) && (updateVect[1] == 1) && (updateVect[2] == 1)) { /*都为1表示三个传感器测量值均有效*/ if ((z[5] < 4.0F) || (z[4] > 15.0F)) { r[1] = 10000.0F; } for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 9; i0++) { b_P_apriori[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { b_P_apriori[i + 12 * i0] += P_apriori[i + 12 * i1] * (real32_T)iv1[i1 + 12 * i0]; } } } for (i = 0; i < 9; i++) { for (i0 = 0; i0 < 12; i0++) { K_k[i + 9 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { K_k[i + 9 * i0] += (real32_T)iv2[i + 9 * i1] * P_apriori[i1 + 12 * i0]; } } for (i0 = 0; i0 < 9; i0++) { fv0[i + 9 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { fv0[i + 9 * i0] += K_k[i + 9 * i1] * (real32_T)iv1[i1 + 12 * i0]; } } }
同样是计算了一堆中间矩阵:
b_r[0] = r[0]; b_r[9] = 0.0F; b_r[18] = 0.0F; b_r[27] = 0.0F; b_r[36] = 0.0F; b_r[45] = 0.0F; b_r[54] = 0.0F; b_r[63] = 0.0F; b_r[72] = 0.0F; b_r[1] = 0.0F; b_r[10] = r[0]; b_r[19] = 0.0F; b_r[28] = 0.0F; b_r[37] = 0.0F; b_r[46] = 0.0F; b_r[55] = 0.0F; b_r[64] = 0.0F; b_r[73] = 0.0F; b_r[2] = 0.0F; b_r[11] = 0.0F; b_r[20] = r[0]; b_r[29] = 0.0F; b_r[38] = 0.0F; b_r[47] = 0.0F; b_r[56] = 0.0F; b_r[65] = 0.0F; b_r[74] = 0.0F; b_r[3] = 0.0F; b_r[12] = 0.0F; b_r[21] = 0.0F; b_r[30] = r[1]; b_r[39] = 0.0F; b_r[48] = 0.0F; b_r[57] = 0.0F; b_r[66] = 0.0F; b_r[75] = 0.0F; b_r[4] = 0.0F; b_r[13] = 0.0F; b_r[22] = 0.0F; b_r[31] = 0.0F; b_r[40] = r[1]; b_r[49] = 0.0F; b_r[58] = 0.0F; b_r[67] = 0.0F; b_r[76] = 0.0F; b_r[5] = 0.0F; b_r[14] = 0.0F; b_r[23] = 0.0F; b_r[32] = 0.0F; b_r[41] = 0.0F; b_r[50] = r[1]; b_r[59] = 0.0F; b_r[68] = 0.0F; b_r[77] = 0.0F; b_r[6] = 0.0F; b_r[15] = 0.0F; b_r[24] = 0.0F; b_r[33] = 0.0F; b_r[42] = 0.0F; b_r[51] = 0.0F; b_r[60] = r[2]; b_r[69] = 0.0F; b_r[78] = 0.0F; b_r[7] = 0.0F; b_r[16] = 0.0F; b_r[25] = 0.0F; b_r[34] = 0.0F; b_r[43] = 0.0F; b_r[52] = 0.0F; b_r[61] = 0.0F; b_r[70] = r[2]; b_r[79] = 0.0F; b_r[8] = 0.0F; b_r[17] = 0.0F; b_r[26] = 0.0F; b_r[35] = 0.0F; b_r[44] = 0.0F; b_r[53] = 0.0F; b_r[62] = 0.0F; b_r[71] = 0.0F; b_r[80] = r[2]; for (i = 0; i < 9; i++) { for (i0 = 0; i0 < 9; i0++) { fv1[i0 + 9 * i] = fv0[i0 + 9 * i] + b_r[i0 + 9 * i]; } }
/*矩 阵 除 法 ,计算出卡尔曼增益*/ mrdivide(b_P_apriori, fv1, K_k);
/* x_aposteriori=x_apriori+K_k*y_k; */ for (i = 0; i < 9; i++) { f0 = 0.0F; for (i0 = 0; i0 < 12; i0++) { f0 += (real32_T)iv2[i + 9 * i0] * x_apriori[i0]; } O[i] = z[i] - f0; } for (i = 0; i < 12; i++) { f0 = 0.0F; for (i0 = 0; i0 < 9; i0++) { f0 += K_k[i + 12 * i0] * O[i0]; } x_aposteriori[i] = x_apriori[i] + f0; }
计算状态后验估计:
/* 'attitudeKalmanfilter:137' P_aposteriori=(eye(12)-K_k*H_k)*P_apriori; */ b_eye(dv1); for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { f0 = 0.0F; for (i1 = 0; i1 < 9; i1++) { f0 += K_k[i + 12 * i1] * (real32_T)iv2[i1 + 9 * i0]; } b_A_lin[i + 12 * i0] = (real32_T)dv1[i + 12 * i0] - f0; } } for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { P_aposteriori[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { P_aposteriori[i + 12 * i0] += b_A_lin[i + 12 * i1] * P_apriori[i1 + 12 * i0]; } } } }
计算方差后验估计:
到此就把所有的量都计算出来了!
下面几种情形为某个传感器未更新的情况,只需改变H矩阵和测量噪声方差矩阵即可,其余运算均类似!
else { /* 'attitudeKalmanfilter:138' else */ /* 'attitudeKalmanfilter:139' if updateVect(1)==1&&updateVect(2)==0&&updateVect(3)==0 */ if ((updateVect[0] == 1) && (updateVect[1] == 0) && (updateVect[2] == 0)) { /* 'attitudeKalmanfilter:141' R=[r(1),0,0; */ /* 'attitudeKalmanfilter:142' 0,r(1),0; */ /* 'attitudeKalmanfilter:143' 0,0,r(1)]; */ /* observation matrix */ /* 'attitudeKalmanfilter:146' H_k=[ E, Z, Z, Z]; */ /* 'attitudeKalmanfilter:148' y_k=z(1:3)-H_k(1:3,1:12)*x_apriori; */ /* 'attitudeKalmanfilter:150' S_k=H_k(1:3,1:12)*P_apriori*H_k(1:3,1:12)'+R(1:3,1:3); */ /* 'attitudeKalmanfilter:151' K_k=(P_apriori*H_k(1:3,1:12)'/(S_k)); */ for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 3; i0++) { c_P_apriori[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { c_P_apriori[i + 12 * i0] += P_apriori[i + 12 * i1] * (real32_T) iv3[i1 + 12 * i0]; } } } for (i = 0; i < 3; i++) { for (i0 = 0; i0 < 12; i0++) { fv2[i + 3 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { fv2[i + 3 * i0] += (real32_T)iv4[i + 3 * i1] * P_apriori[i1 + 12 * i0]; } } for (i0 = 0; i0 < 3; i0++) { O[i + 3 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { O[i + 3 * i0] += fv2[i + 3 * i1] * (real32_T)iv3[i1 + 12 * i0]; } } } c_r[0] = r[0]; c_r[3] = 0.0F; c_r[6] = 0.0F; c_r[1] = 0.0F; c_r[4] = r[0]; c_r[7] = 0.0F; c_r[2] = 0.0F; c_r[5] = 0.0F; c_r[8] = r[0]; for (i = 0; i < 3; i++) { for (i0 = 0; i0 < 3; i0++) { a[i0 + 3 * i] = O[i0 + 3 * i] + c_r[i0 + 3 * i]; } } b_mrdivide(c_P_apriori, a, b_K_k); /* 'attitudeKalmanfilter:154' x_aposteriori=x_apriori+K_k*y_k; */ for (i = 0; i < 3; i++) { f0 = 0.0F; for (i0 = 0; i0 < 12; i0++) { f0 += (real32_T)iv4[i + 3 * i0] * x_apriori[i0]; } x_n_b[i] = z[i] - f0; } for (i = 0; i < 12; i++) { f0 = 0.0F; for (i0 = 0; i0 < 3; i0++) { f0 += b_K_k[i + 12 * i0] * x_n_b[i0]; } x_aposteriori[i] = x_apriori[i] + f0; } /* 'attitudeKalmanfilter:155' P_aposteriori=(eye(12)-K_k*H_k(1:3,1:12))*P_apriori; */ b_eye(dv1); for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { f0 = 0.0F; for (i1 = 0; i1 < 3; i1++) { f0 += b_K_k[i + 12 * i1] * (real32_T)iv4[i1 + 3 * i0]; } b_A_lin[i + 12 * i0] = (real32_T)dv1[i + 12 * i0] - f0; } } for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { P_aposteriori[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { P_aposteriori[i + 12 * i0] += b_A_lin[i + 12 * i1] * P_apriori[i1 + 12 * i0]; } } } } else { /* 'attitudeKalmanfilter:156' else */ /* 'attitudeKalmanfilter:157' if updateVect(1)==1&&updateVect(2)==1&&updateVect(3)==0 */ if ((updateVect[0] == 1) && (updateVect[1] == 1) && (updateVect[2] == 0)) { /* 'attitudeKalmanfilter:158' if z(6)<4 || z(5)>15 */ if ((z[5] < 4.0F) || (z[4] > 15.0F)) { /* 'attitudeKalmanfilter:159' r(2)=10000; */ r[1] = 10000.0F; } /* 'attitudeKalmanfilter:162' R=[r(1),0,0,0,0,0; */ /* 'attitudeKalmanfilter:163' 0,r(1),0,0,0,0; */ /* 'attitudeKalmanfilter:164' 0,0,r(1),0,0,0; */ /* 'attitudeKalmanfilter:165' 0,0,0,r(2),0,0; */ /* 'attitudeKalmanfilter:166' 0,0,0,0,r(2),0; */ /* 'attitudeKalmanfilter:167' 0,0,0,0,0,r(2)]; */ /* observation matrix */ /* 'attitudeKalmanfilter:170' H_k=[ E, Z, Z, Z; */ /* 'attitudeKalmanfilter:171' Z, Z, E, Z]; */ /* 'attitudeKalmanfilter:173' y_k=z(1:6)-H_k(1:6,1:12)*x_apriori; */ /* 'attitudeKalmanfilter:175' S_k=H_k(1:6,1:12)*P_apriori*H_k(1:6,1:12)'+R(1:6,1:6); */ /* 'attitudeKalmanfilter:176' K_k=(P_apriori*H_k(1:6,1:12)'/(S_k)); */ for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 6; i0++) { d_P_apriori[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { d_P_apriori[i + 12 * i0] += P_apriori[i + 12 * i1] * (real32_T) iv5[i1 + 12 * i0]; } } } for (i = 0; i < 6; i++) { for (i0 = 0; i0 < 12; i0++) { c_K_k[i + 6 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { c_K_k[i + 6 * i0] += (real32_T)iv6[i + 6 * i1] * P_apriori[i1 + 12 * i0]; } } for (i0 = 0; i0 < 6; i0++) { fv2[i + 6 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { fv2[i + 6 * i0] += c_K_k[i + 6 * i1] * (real32_T)iv5[i1 + 12 * i0]; } } } b_K_k[0] = r[0]; b_K_k[6] = 0.0F; b_K_k[12] = 0.0F; b_K_k[18] = 0.0F; b_K_k[24] = 0.0F; b_K_k[30] = 0.0F; b_K_k[1] = 0.0F; b_K_k[7] = r[0]; b_K_k[13] = 0.0F; b_K_k[19] = 0.0F; b_K_k[25] = 0.0F; b_K_k[31] = 0.0F; b_K_k[2] = 0.0F; b_K_k[8] = 0.0F; b_K_k[14] = r[0]; b_K_k[20] = 0.0F; b_K_k[26] = 0.0F; b_K_k[32] = 0.0F; b_K_k[3] = 0.0F; b_K_k[9] = 0.0F; b_K_k[15] = 0.0F; b_K_k[21] = r[1]; b_K_k[27] = 0.0F; b_K_k[33] = 0.0F; b_K_k[4] = 0.0F; b_K_k[10] = 0.0F; b_K_k[16] = 0.0F; b_K_k[22] = 0.0F; b_K_k[28] = r[1]; b_K_k[34] = 0.0F; b_K_k[5] = 0.0F; b_K_k[11] = 0.0F; b_K_k[17] = 0.0F; b_K_k[23] = 0.0F; b_K_k[29] = 0.0F; b_K_k[35] = r[1]; for (i = 0; i < 6; i++) { for (i0 = 0; i0 < 6; i0++) { c_P_apriori[i0 + 6 * i] = fv2[i0 + 6 * i] + b_K_k[i0 + 6 * i]; } } c_mrdivide(d_P_apriori, c_P_apriori, c_K_k); /* 'attitudeKalmanfilter:179' x_aposteriori=x_apriori+K_k*y_k; */ for (i = 0; i < 6; i++) { f0 = 0.0F; for (i0 = 0; i0 < 12; i0++) { f0 += (real32_T)iv6[i + 6 * i0] * x_apriori[i0]; } b_z[i] = z[i] - f0; } for (i = 0; i < 12; i++) { f0 = 0.0F; for (i0 = 0; i0 < 6; i0++) { f0 += c_K_k[i + 12 * i0] * b_z[i0]; } x_aposteriori[i] = x_apriori[i] + f0; } /* 'attitudeKalmanfilter:180' P_aposteriori=(eye(12)-K_k*H_k(1:6,1:12))*P_apriori; */ b_eye(dv1); for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { f0 = 0.0F; for (i1 = 0; i1 < 6; i1++) { f0 += c_K_k[i + 12 * i1] * (real32_T)iv6[i1 + 6 * i0]; } b_A_lin[i + 12 * i0] = (real32_T)dv1[i + 12 * i0] - f0; } } for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { P_aposteriori[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { P_aposteriori[i + 12 * i0] += b_A_lin[i + 12 * i1] * P_apriori[i1 + 12 * i0]; } } } } else { /* 'attitudeKalmanfilter:181' else */ /* 'attitudeKalmanfilter:182' if updateVect(1)==1&&updateVect(2)==0&&updateVect(3)==1 */ if ((updateVect[0] == 1) && (updateVect[1] == 0) && (updateVect[2] == 1)) { /* 'attitudeKalmanfilter:183' R=[r(1),0,0,0,0,0; */ /* 'attitudeKalmanfilter:184' 0,r(1),0,0,0,0; */ /* 'attitudeKalmanfilter:185' 0,0,r(1),0,0,0; */ /* 'attitudeKalmanfilter:186' 0,0,0,r(3),0,0; */ /* 'attitudeKalmanfilter:187' 0,0,0,0,r(3),0; */ /* 'attitudeKalmanfilter:188' 0,0,0,0,0,r(3)]; */ /* observation matrix */ /* 'attitudeKalmanfilter:191' H_k=[ E, Z, Z, Z; */ /* 'attitudeKalmanfilter:192' Z, Z, Z, E]; */ /* 'attitudeKalmanfilter:194' y_k=[z(1:3);z(7:9)]-H_k(1:6,1:12)*x_apriori; */ /* 'attitudeKalmanfilter:196' S_k=H_k(1:6,1:12)*P_apriori*H_k(1:6,1:12)'+R(1:6,1:6); */ /* 'attitudeKalmanfilter:197' K_k=(P_apriori*H_k(1:6,1:12)'/(S_k)); */ for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 6; i0++) { d_P_apriori[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { d_P_apriori[i + 12 * i0] += P_apriori[i + 12 * i1] * (real32_T) iv7[i1 + 12 * i0]; } } } for (i = 0; i < 6; i++) { for (i0 = 0; i0 < 12; i0++) { c_K_k[i + 6 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { c_K_k[i + 6 * i0] += (real32_T)iv8[i + 6 * i1] * P_apriori[i1 + 12 * i0]; } } for (i0 = 0; i0 < 6; i0++) { fv2[i + 6 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { fv2[i + 6 * i0] += c_K_k[i + 6 * i1] * (real32_T)iv7[i1 + 12 * i0]; } } } b_K_k[0] = r[0]; b_K_k[6] = 0.0F; b_K_k[12] = 0.0F; b_K_k[18] = 0.0F; b_K_k[24] = 0.0F; b_K_k[30] = 0.0F; b_K_k[1] = 0.0F; b_K_k[7] = r[0]; b_K_k[13] = 0.0F; b_K_k[19] = 0.0F; b_K_k[25] = 0.0F; b_K_k[31] = 0.0F; b_K_k[2] = 0.0F; b_K_k[8] = 0.0F; b_K_k[14] = r[0]; b_K_k[20] = 0.0F; b_K_k[26] = 0.0F; b_K_k[32] = 0.0F; b_K_k[3] = 0.0F; b_K_k[9] = 0.0F; b_K_k[15] = 0.0F; b_K_k[21] = r[2]; b_K_k[27] = 0.0F; b_K_k[33] = 0.0F; b_K_k[4] = 0.0F; b_K_k[10] = 0.0F; b_K_k[16] = 0.0F; b_K_k[22] = 0.0F; b_K_k[28] = r[2]; b_K_k[34] = 0.0F; b_K_k[5] = 0.0F; b_K_k[11] = 0.0F; b_K_k[17] = 0.0F; b_K_k[23] = 0.0F; b_K_k[29] = 0.0F; b_K_k[35] = r[2]; for (i = 0; i < 6; i++) { for (i0 = 0; i0 < 6; i0++) { c_P_apriori[i0 + 6 * i] = fv2[i0 + 6 * i] + b_K_k[i0 + 6 * i]; } } c_mrdivide(d_P_apriori, c_P_apriori, c_K_k); /* 'attitudeKalmanfilter:200' x_aposteriori=x_apriori+K_k*y_k; */ for (i = 0; i < 3; i++) { b_z[i] = z[i]; } for (i = 0; i < 3; i++) { b_z[i + 3] = z[i + 6]; } for (i = 0; i < 6; i++) { fv3[i] = 0.0F; for (i0 = 0; i0 < 12; i0++) { fv3[i] += (real32_T)iv8[i + 6 * i0] * x_apriori[i0]; } c_z[i] = b_z[i] - fv3[i]; } for (i = 0; i < 12; i++) { f0 = 0.0F; for (i0 = 0; i0 < 6; i0++) { f0 += c_K_k[i + 12 * i0] * c_z[i0]; } x_aposteriori[i] = x_apriori[i] + f0; } /* 'attitudeKalmanfilter:201' P_aposteriori=(eye(12)-K_k*H_k(1:6,1:12))*P_apriori; */ b_eye(dv1); for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { f0 = 0.0F; for (i1 = 0; i1 < 6; i1++) { f0 += c_K_k[i + 12 * i1] * (real32_T)iv8[i1 + 6 * i0]; } b_A_lin[i + 12 * i0] = (real32_T)dv1[i + 12 * i0] - f0; } } for (i = 0; i < 12; i++) { for (i0 = 0; i0 < 12; i0++) { P_aposteriori[i + 12 * i0] = 0.0F; for (i1 = 0; i1 < 12; i1++) { P_aposteriori[i + 12 * i0] += b_A_lin[i + 12 * i1] * P_apriori[i1 + 12 * i0]; } } } } else { /* 'attitudeKalmanfilter:202' else */ /* 'attitudeKalmanfilter:203' x_aposteriori=x_apriori; */ for (i = 0; i < 12; i++) { x_aposteriori[i] = x_apriori[i]; } /* 'attitudeKalmanfilter:204' P_aposteriori=P_apriori; */ memcpy(&P_aposteriori[0], &P_apriori[0], 144U * sizeof(real32_T)); } } } }
至此,EKF解算姿态过程全部结束,下面从姿态矩阵中提取欧拉角。其实本质就是计算新的余弦矩阵,然后根据下面的公式计算欧拉角
/* % euler anglels extraction */ /* 'attitudeKalmanfilter:213' z_n_b = -x_aposteriori(7:9)./norm(x_aposteriori(7:9)); */ for (i = 0; i < 3; i++) { x_n_b[i] = -x_aposteriori[i + 6]; } rdivide(x_n_b, norm(*(real32_T (*)[3])&x_aposteriori[6]), z_n_b); /* 'attitudeKalmanfilter:214' m_n_b = x_aposteriori(10:12)./norm(x_aposteriori(10:12)); */ rdivide(*(real32_T (*)[3])&x_aposteriori[9], norm(*(real32_T (*)[3])& x_aposteriori[9]), wak); /* 'attitudeKalmanfilter:216' y_n_b=cross(z_n_b,m_n_b); */ for (i = 0; i < 3; i++) { x_n_b[i] = wak[i]; } cross(z_n_b, x_n_b, wak); /* 'attitudeKalmanfilter:217' y_n_b=y_n_b./norm(y_n_b); */ for (i = 0; i < 3; i++) { x_n_b[i] = wak[i]; } rdivide(x_n_b, norm(wak), wak); /* 'attitudeKalmanfilter:219' x_n_b=(cross(y_n_b,z_n_b)); */ cross(wak, z_n_b, x_n_b); /* 'attitudeKalmanfilter:220' x_n_b=x_n_b./norm(x_n_b); */ for (i = 0; i < 3; i++) { b_x_aposteriori_k[i] = x_n_b[i]; } rdivide(b_x_aposteriori_k, norm(x_n_b), x_n_b); /* 'attitudeKalmanfilter:226' Rot_matrix=[x_n_b,y_n_b,z_n_b]; */ for (i = 0; i < 3; i++) { Rot_matrix[i] = x_n_b[i]; Rot_matrix[3 + i] = wak[i]; Rot_matrix[6 + i] = z_n_b[i]; } /* 'attitudeKalmanfilter:230' phi=atan2(Rot_matrix(2,3),Rot_matrix(3,3)); */ /* 'attitudeKalmanfilter:231' theta=-asin(Rot_matrix(1,3)); */ /* 'attitudeKalmanfilter:232' psi=atan2(Rot_matrix(1,2),Rot_matrix(1,1)); */ /* 'attitudeKalmanfilter:233' eulerAngles=[phi;theta;psi]; */ eulerAngles[0] = rt_atan2f_snf(Rot_matrix[7], Rot_matrix[8]); eulerAngles[1] = -(real32_T)asin(Rot_matrix[6]); eulerAngles[2] = rt_atan2f_snf(Rot_matrix[3], Rot_matrix[0]);}/* End of code generation (attitudeKalmanfilter.c) */
3.下一步
把EKF估计姿态原理和具体算法细节搞清楚之后就可以移植到自己的工程上了,完成后把代码放上来。
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