EKF c语言 六轴姿态融合算法

根据提供的引用内容，EKF C语言六轴姿态融合算法是一种使用扩展卡尔曼滤波器（EKF）进行六轴姿态融合的算法。该算法使用加速度计和磁力计来估计姿态，并使用EKF来融合两个感器的数据。在加速度计为0的条件下，该算法可以准确地估计姿态。在后续的融合算法中，加速度计和磁力计只起到修正的作用，影响不大。

以下是一个简单的EKF C语言六轴姿态融合算法的示例：

#include <stdio.h>
#include <math.h>

#define PI 3.14159265358979323846

// 定义加速度计和磁力计的数据结构
typedef struct {
    double x;
    double y;
    double z;
} Vector3;

// 定义姿态的数据结构
typedef struct {
    double roll;
    double pitch;
    double yaw;
} Attitude;

// 定义EKF的数据结构
typedef struct {
    double q0;
    double q1;
    double q2;
    double q3;
    double p[3];
    double k[4];
    double h[4];
    double f[16];
    double q[16];
    double r[4];
    double x[4];
    double z[4];
    double y[4];
    double s[4];
    double t[16];
} EKF;

// 初始化EKF
void EKF_Init(EKF *ekf) {
    ekf->q0 = 1.0;
    ekf->q1 = 0.0;
    ekf->q2 = 0.0;
    ekf->q3 = 0.0;
    ekf->p[0] = 0.0;
    ekf->p[1] = 0.0;
    ekf->p[2] = 0.0;
    ekf->k[0] = 0.0;
    ekf->k[1] = 0.0;
    ekf->k[2] = 0.0;
    ekf->k[3] = 0.0;
    ekf->h[0] = 0.0;
    ekf->h[1] = 0.0;
    ekf->h[2] = 0.0;
    ekf->h[3] = 0.0;
    ekf->f[0] = 1.0;
    ekf->f[1] = 0.0;
    ekf->f[2] = 0.0;
    ekf->f[3] = 0.0;
    ekf->f[4] = 0.0;
    ekf->f[5] = 1.0;
    ekf->f[6] = 0.0;
    ekf->f[7] = 0.0;
    ekf->f[8] = 0.0;
    ekf->f[9] = 0.0;
    ekf->f[10] = 1.0;
    ekf->f[11] = 0.0;
    ekf->f[12] = 0.0;
    ekf->f[13] = 0.0;
    ekf->f[14] = 0.0;
    ekf->f[15] = 1.0;
    ekf->q[0] = 0.01;
    ekf->q[1] = 0.0;
    ekf->q[2] = 0.0;
    ekf->q[3] = 0.0;
    ekf->q[4] = 0.0;
    ekf->q[5] = 0.01;
    ekf->q[6] = 0.0;
    ekf->q[7] = 0.0;
    ekf->q[8] = 0.0;
    ekf->q[9] = 0.0;
    ekf->q[10] = 0.01;
    ekf->q[11] = 0.0;
    ekf->q[12] = 0.0;
    ekf->q[13] = 0.0;
    ekf->q[14] = 0.0;
    ekf->q[15] = 0.01;
    ekf->r[0] = 0.1;
    ekf->r[1] = 0.0;
    ekf->r[2] = 0.0;
    ekf->r[3] = 0.1;
    ekf->x[0] = 1.0;
    ekf->x[1] = 0.0;
    ekf->x[2] = 0.0;
    ekf->x[3] = 0.0;
}

// 更新EKF
void EKF_Update(EKF *ekf, Vector3 acc, Vector3 mag, double dt) {
    double ax = acc.x;
    double ay = acc.y;
    double az = acc.z;
    double mx = mag.x;
    double my = mag.y;
    double mz = mag.z;
    double q0 = ekf->q0;
    double q1 = ekf->q1;
    double q2 = ekf->q2;
    double q3 = ekf->q3;
    double p0 = ekf->p[0];
    double p1 = ekf->p[1];
    double p2 = ekf->p[2];
    double k0 = ekf->k[0];
    double k1 = ekf->k[1];
    double k2 = ekf->k[2];
    double k3 = ekf->k[3];
    double h0 = ekf->h[0];
    double h1 = ekf->h[1];
    double h2 = ekf->h[2];
    double h3 = ekf->h[3];
    double f0 = ekf->f[0];
    double f1 = ekf->f[1];
    double f2 = ekf->f[2];
    double f3 = ekf->f[3];
    double f4 = ekf->f[4];
    double f5 = ekf->f[5];
    double f6 = ekf->f[6];
    double f7 = ekf->f[7];
    double f8 = ekf->f[8];
    double f9 = ekf->f[9];
    double f10 = ekf->f[10];
    double f11 = ekf->f[11];
    double f12 = ekf->f[12];
    double f13 = ekf->f[13];
    double f14 = ekf->f[14];
    double f15 = ekf->f[15];
    double q0q0 = q0 * q0;
    double q0q1 = q0 * q1;
    double q0q2 = q0 * q2;
    double q0q3 = q0 * q3;
    double q1q1 = q1 * q1;
    double q1q2 = q1 * q2;
    double q1q3 = q1 * q3;
    double q2q2 = q2 * q2;
    double q2q3 = q2 * q3;
    double q3q3 = q3 * q3;
    double norm;
    double hx;
    double hy;
    double hz;
    double bx;
    double bz;
    double vx;
    double vy;
    double vz;
    double wx;
    double wy;
    double wz;
    double ex;
    double ey;
    double ez;
    double qa;
    double qb;
    double qc;
    double qd;
    double s0;
    double s1;
    double s2;
    double s3;
    double s4;
    double s5;
    double s6;
    double s7;
    double s8;
    double s9;
    double s10;
    double s11;
    double s12;
    double s13;
    double s14;
    double s15;
    double t0;
    double t1;
    double t2;
    double t3;
    double t4;
    double t5;
    double t6;
    double t7;
    double t8;
    double t9;
    double t10;
    double t11;
    double t12;
    double t13;
    double t14;
    double t15;

    // 计算加速度计和磁力计的模
    norm = sqrt(ax * ax + ay * ay + az * az);
    ax /= norm;
    ay /= norm;
    az /= norm;
    norm = sqrt(mx * mx + my * my + mz * mz);
    mx /= norm;
    my /= norm;
    mz /= norm;

    // 计算磁力计的方向
    hx = mx * q0q0 - 2.0 * q0 * my * q3 + 2.0 * q0 * mz * q2 + mx * q1q1 + 2.0 * q1 * my * q2 + 2.0 * q1 * mz * q3 - mx * q2q2 - my * q1q1 + 2.0 * q2 * mz * q3 - mz * q0q0 - mz * q1q1;
    hy = 2.0 * q0 * mx * q3 + my * q0q0 - 2.0 * q0 * mz * q1 + 2.0 * q1 * mx * q2 - my * q2q2 + my * q3q3 + 2.0 * q2 * mz * q3 - mz * q1q1 - mz * q2q2;
    hz = 2.0 * q0 * my * q1 + 2.0 * q0 * mz * q0 + mz * q1q1 - my * q2q2 + 2.0 * q1 * mx * q3 - mz * q3q3 + 2.0 * q2 * my * q3 - mx * q1q1 - mx * q2q2;
    bx = sqrt((hx * hx) + (hy * hy));
    bz = hz;

    // 计算预测状态
    vx = 2.0 * (q1q3 - q0q2);
    vy = 2.0 * (q0q1 + q2q3);
    vz = q0q0 - q1q1 - q2q2 + q3q3;
    wx = 2.0 * bx * (0.5 - q2q2 - q3q3) + 2.0 * bz * (q1q3 - q0q2);
    wy = 2.0 * bx * (q1q2 - q0q3) + 2.0 * bz * (q0q1 + q2q3);
    wz = 2.0 * bx * (q0q2 + q1q3) + 2.0 * bz * (0.5 - q1q1 - q2q2);
    ex = (ay * vz - az * vy) + (my * wz - mz * wy);
    ey = (az * vx - ax * vz) + (mz * wx - mx * wz);
    ez = (ax * vy - ay * vx) + (mx * wy - my * wx);
    ekf->x[0] += dt * (q1 * ex + q2 * ey + q3 * ez);
    ekf->x[1] += dt * (q0 * ex + q2 * ez - q3 * ey);
    ekf->x[2] += dt * (q0 * ey - q1 * ez + q3 * ex);
    ekf->x[3] += dt * (q0 * ez + q1 * ey - q2 * ex);

    // 计算雅可比矩阵
    s0 = q0q0 + q1q1 - q2q2 - q3q3;
    s1 = 2.0 * (q1 * q2 + q0 * q3);
    s2 = 2.0 * (q1 * q3 - q0 * q2);
    s3 = 2.0 * (q1 * q2 - q0 * q3);
    s4 = q0q0 - q1q1 + q2q2 - q3q3;
    s5 = 2.0 * (q2 * q3 + q0 * q1);
    s6 = 2.0 * (q1 * q3 + q0 * q2);
    s7 = 2.0 * (q2 * q3 - q0 * q1);
    s8 = q0q0 - q1q1 - q2q2 + q3q3;
    t0 = 2.0 * (-q2q2 - q3q3);
    t1 = 2.0 * (q1q2 - q0q3);
    t2 = 2.0 * (q1q3 + q0q2);
    t3 = 2.0 * (q1q2 + q0q3);
    t4 = 2.0 * (-q1q1 - q3q3);
    t5 = 2.0 * (q