ekf 六轴陀螺仪 c语言

以下是基于EKF算法的六轴陀螺仪C语言代码示例：

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

//定义常量 #define PI 3.14159265358979323846 #define TWO_PI 6.28318530717958647692

//定义陀螺仪和加速度计的测量值和噪声方差 double gyro_x, gyro_y, gyro_z; double accel_x, accel_y, accel_z; double gyro_noise = 0.1; double accel_noise = 0.1;

//定义状态向量和协方差矩阵 double state[4] = {1, 0, 0, 0}; double cov[16] = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1};

//定义采样时间和计数器 double dt = 0.01; int count = 0;

//定义旋转矩阵和角速度向量 double R[9]; double w[3];

//定义函数原型 void update_state(); void predict_state(); void update_covariance(); void predict_covariance(); double norm(double *v); void cross_product(double *a, double *b, double *c); void matrix_multiply(double *a, double *b, int m, int n, int p, double *c); void quat_to_rot(double *q, double *R); void rot_to_quat(double *R, double *q); void gyro_meas(double *w, double *q, double dt); void accel_meas(double *a, double *q); void normalize(double *q);

int main(void) { //读取陀螺仪和加速度计的测量值，进行初始化 gyro_x = 0.1; gyro_y = 0.2; gyro_z = 0.3; accel_x = 0.01; accel_y = 0.02; accel_z = 0.03;

//循环更新状态和协方差
while (count < 1000)
{
    update_state();
    predict_state();
    update_covariance();
    predict_covariance();
    count++;
}

//输出结果
printf("Final state vector: %.4f %.4f %.4f %.4f\n", state[0], state[1], state[2], state[3]);
printf("Final covariance matrix:\n");
printf("%.4f %.4f %.4f %.4f\n", cov[0], cov[1], cov[2], cov[3]);
printf("%.4f %.4f %.4f %.4f\n", cov[4], cov[5], cov[6], cov[7]);
printf("%.4f %.4f %.4f %.4f\n", cov[8], cov[9], cov[10], cov[11]);
printf("%.4f %.4f %.4f %.4f\n", cov[12], cov[13], cov[14], cov[15]);

return 0;

}

//更新状态向量 void update_state() { //计算旋转矩阵和角速度向量 quat_to_rot(state, R); w[0] = 2 * (state[1] * gyro_x + state[2] * gyro_y + state[3] * gyro_z); w[1] = 2 * (-state[0] * gyro_x + state[2] * gyro_z - state[3] * gyro_y); w[2] = 2 * (-state[0] * gyro_y - state[1] * gyro_z + state[3] * gyro_x);

//用陀螺仪的测量值更新状态向量
gyro_meas(w, state, dt);

//用加速度计的测量值更新状态向量
accel_meas(&accel_x, state);

//对状态向量进行归一化
normalize(state);

}

//预测状态向量 void predict_state() { //计算旋转矩阵和角速度向量 quat_to_rot(state, R); w[0] = 2 * (state[1] * gyro_x + state[2] * gyro_y + state[3] * gyro_z); w[1] = 2 * (-state[0] * gyro_x + state[2] * gyro_z - state[3] * gyro_y); w[2] = 2 * (-state[0] * gyro_y - state[1] * gyro_z + state[3] * gyro_x);

//用陀螺仪的测量值预测状态向量
gyro_meas(w, state, dt);

}

//更新协方差矩阵 void update_covariance() { //计算雅可比矩阵 double J[16] = {0}; J[0] = -state[1]; J[1] = state[0]; J[2] = state[3]; J[3] = -state[2]; J[4] = -state[3]; J[5] = state[2]; J[6] = state[0]; J[7] = -state[1]; J[8] = -state[2]; J[9] = -state[3]; J[10] = state[0]; J[11] = state[1]; J[12] = -state[3]; J[13] = -state[2]; J[14] = -state[1]; J[15] = state[0];

//计算卡尔曼增益
double K[12] = {0};
double S[9] = {0};
matrix_multiply(J, cov, 4, 4, 4, S);
S[0] += gyro_noise;
S[4] += gyro_noise;
S[8] += gyro_noise;
matrix_multiply(S, J, 4, 4, 4, K);
K[0] /= (K[0] + accel_noise);
K[1] /= (K[0] + accel_noise);
K[2] /= (K[0] + accel_noise);
K[3] /= (K[0] + accel_noise);
K[4] /= (K[4] + accel_noise);
K[5] /= (K[4] + accel_noise);
K[6] /= (K[8] + accel_noise);
K[7] /= (K[8] + accel_noise);
K[8] /= (K[8] + accel_noise);
K[9] /= (K[8] + accel_noise);

//更新协方差矩阵
double I[16] = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1};
double temp[16] = {0};
matrix_multiply(I, K, 4, 4, 3, temp);
cov[0] -= temp[0];
cov[1] -= temp[1];
cov[2] -= temp[2];
cov[3] -= temp[3];
cov[4] -= temp[4];
cov[5] -= temp[5];
cov[6] -= temp[6];
cov[7] -= temp[7];
cov[8] -= temp[8];
cov[9] -= temp[9];
cov[10] -= temp[10];
cov[11] -= temp[11];
cov[12] -= temp[12];
cov[13] -= temp[13];
cov[14] -= temp[14];
cov[15] -= temp[15];

}

//预测协方差矩阵 void predict_covariance() { double A[16] = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1}; double B[12] = {0}; double Q[9] = {gyro_noise, 0, 0, 0, gyro_noise, 0, 0, 0, gyro_noise}; double temp[16] = {0}; matrix_multiply(A, cov, 4, 4, 4, temp); matrix_multiply(temp, A, 4, 4, 4, cov); matrix_multiply(A, B, 4, 4, 3, temp); cov[0] += temp[0] + Q[0] * dt * dt; cov[1] += temp[1] + Q[1] * dt * dt; cov[2] += temp[2] + Q[2] * dt * dt; cov[3] += temp[3]; cov[4] += temp[4] + Q[4] * dt * dt; cov[5] += temp[5] + Q[5] * dt * dt; cov[6] += temp[6]; cov[7] += temp[7]; cov[8] += temp[8] + Q[8] * dt * dt; cov[9] += temp[9]; cov[10] += temp[10]; cov[11] += temp[11]; cov[12] += temp[12]; cov[13] += temp[13]; cov[14] += temp[14]; cov[15] += temp[15]; }

//计算向量的模长 double norm(double *v) { return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]); }

//计算向量的叉积 void cross_product(double *a, double *b, double *c) { c[0] = a[1] * b[2] - a[2] * b[1]; c[1] = a[2] * b[0] - a[0] * b[2]; c[2] = a[0] * b[1] - a[1] * b[0]; }

//矩阵乘法 void matrix_multiply(double *a, double *b, int m, int n, int p, double *c) { for (int i = 0; i < m; i++) { for (int j = 0; j < p; j++) { c[i * p + j] = 0; for (int k = 0; k < n; k++) { c[i * p + j] += a[i * n + k] * b[k * p + j]; } } } }

//将四元数转换为旋转矩阵 void quat_to_rot(double *q, double *R) { double q0 = q[0]; double q1 = q[1]; double q2 = q[2]; double q3 = q[3]; R[0] = 1 - 2 * q2 * q2 - 2 * q3 * q3; R[1] = 2 * q1 * q2 - 2 * q0 * q3; R[2] = 2 * q1 * q3 + 2 * q0 * q2; R[3] = 2 * q1 * q2 + 2 * q0 * q3; R[4] = 1 - 2 * q1 * q1 - 2 * q3 * q3; R[5] = 2 * q2 * q3 - 2 * q0 * q1; R[6] = 2 * q1 * q3 - 2 * q0 * q2; R[7] = 2 * q2 * q3 + 2 * q0 * q1; R[8] = 1 - 2 * q1 * q1 - 2 * q2 * q2; }

//将旋转矩阵转换为四元数 void rot_to_quat(double *R, double *q) { double tr = R[0] + R[4] + R[8]; double S; if (tr > 0) { S = sqrt(tr + 1.0) * 2; q[0] = 0.25 * S; q[1] = (R[7] - R[5]) / S; q[2] = (R[2] - R[6]) / S; q[3] = (R[3] - R[1]) / S; } else if ((R[0] > R[4]) && (R[0] > R[8])) { S = sqrt(1.0 + R[0] - R[4] - R[8]) * 2; q[0] = (R[7] - R[5]) / S; q[1] = 0.25 * S; q[2] = (R[1] + R[3]) / S; q[3] = (R[2] + R[6]) / S; } else if (R[4] > R[8]) { S = sqrt(1.0 + R[4] - R[0] - R[8]) * 2; q[0] = (R[2] - R[6]) / S; q[1] = (R[1] + R[3]) / S; q[2] = 0.25 * S; q[3] = (R[5] + R[7]) / S; } else { S = sqrt(1.0 + R[8] - R[0] - R[4]) * 2; q[0] = (R[3] - R[1]) / S; q[1] = (R[2] + R[6]) / S; q[2] = (R[5] + R[7]) / S; q[3] = 0.25 * S; } }

//用陀螺仪的测量值更新状态向量 void gyro_meas(double *w, double *q, double dt) { double w_norm = norm(w); if (w_norm < 1e-8) { return; } double w_hat[3] = {w[0] / w_norm, w[1] / w_norm, w[2] / w_norm}; double q_dot[4] = {0}; q_dot[0] = -0.5 * (q[1] * w[0] + q[2] * w[1] + q[3] * w[2]); q_dot[1] = 0.5 * (q[0] * w[0] + q[2] * w[2] - q[3] * w[1]); q_dot[2] = 0.5 * (q[0] * w[1] - q[1] * w[2] + q[3] * w[0]); q_dot[3] = 0.5 * (q[0] * w[2] + q[1] * w[1] - q[2] * w[0]); q[0] += q_dot[0] * dt; q[1] += q_dot[1] * dt; q[2] += q_dot[2] * dt; q[3] += q_dot[3] * dt; normalize(q); }

//用加速度计的测量值更新状态向量 void accel_meas(double *a, double *q) { double g[3] = {0, 0, -1}; double a_norm = norm(a); if (a_norm < 1e-8) { return; } double a_hat[3] = {a[0] / a_norm, a[1] / a_norm, a[2] / a_norm}; double b_hat[3] = {0}; cross_product(g, a_hat, b_hat); double R[9] = {0}; R[0] = b_hat[0]; R[1] = b_hat[1]; R[2] = b_hat[2]; R[3] = a_hat[0]; R[4] = a_hat[1]; R[5] = a_hat[2]; R[6] = -g[0]; R[7] = -g[1]; R[8] = -g[2]; double q_temp[4] = {0}; rot_to_quat(R, q_temp); double q_error[4] = {0}; cross_product(q, q_temp, q_error); q[0] += 0.5 * q_error[0]; q[1] += 0.5 * q_error[1]; q[2] += 0.5 * q_error[2]; q[3] += 0.5 * q_error[3]; normalize(q); }

//将四元数归一化 void normalize(double *q) { double norm_q = norm(q); if (norm_q < 1e-8) { return; } q[0] /= norm_q; q[1] /= norm_q; q[2] /= norm_q; q[3] /= norm_q; }