mahony算法c语言

Mahony算法是一种常见的姿态估计算法，C语言的实现如下：

#include <math.h>

#define PI 3.14159265358979323846f

typedef struct {
    float q0;
    float q1;
    float q2;
    float q3;
} Quaternion;

void MahonyAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az, Quaternion *q, float sampleFreq, float Kp, float Ki) {
    float recipNorm;
    float hx, hy, bx, bz;
    float vx, vy, vz, ex, ey, ez;
    float qa, qb, qc;
    float integralFBx = 0.0f, integralFBy = 0.0f, integralFBz = 0.0f;
  
    // Convert gyroscope degrees/sec to radians/sec
    gx *= PI/180.0f;
    gy *= PI/180.0f;
    gz *= PI/180.0f;
  
    // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
    if(!(ax == 0.0f && ay == 0.0f && az == 0.0f)) {
        // Normalise accelerometer measurement
        recipNorm = 1.0f/sqrtf(ax*ax + ay*ay + az*az);
        ax *= recipNorm;
        ay *= recipNorm;
        az *= recipNorm;
    
        // Estimated direction of gravity and magnetic field
        vx = 2.0f*(q->q1*q->q3 - q->q0*q->q2);
        vy = 2.0f*(q->q0*q->q1 + q->q2*q->q3);
        vz = q->q0*q->q0 - q->q1*q->q1 - q->q2*q->q2 + q->q3*q->q3;
    
        // Error is cross product between estimated direction and measured direction of gravity
        ex = (ay*vz - az*vy);
        ey = (az*vx - ax*vz);
        ez = (ax*vy - ay*vx);

        // Compute and apply integral feedback if enabled
        if(Ki > 0.0f) {
            integralFBx += Ki*ex/sampleFreq;
            integralFBy += Ki*ey/sampleFreq;
            integralFBz += Ki*ez/sampleFreq;
            gx += integralFBx;
            gy += integralFBy;
            gz += integralFBz;
        }
        else {
            integralFBx = 0.0f;
            integralFBy = 0.0f;
            integralFBz = 0.0f;
        }
    
        // Apply proportional feedback
        gx += Kp*ex;
        gy += Kp*ey;
        gz += Kp*ez;
    }
  
    // Integrate rate of change of quaternion
    gx *= (0.5f/sampleFreq);   // pre-multiply common factors
    gy *= (0.5f/sampleFreq);
    gz *= (0.5f/sampleFreq);
    qa = q->q0;
    qb = q->q1;
    qc = q->q2;
    q->q0 += (-qb*gx - qc*gy - q->q3*gz);
    q->q1 += (qa*gx + qc*gz - q->q3*gy);
    q->q2 += (qa*gy - qb*gz + q->q3*gx);
    q->q3 += (qa*gz + qb*gy - qc*gx);
  
    // Normalise quaternion
    recipNorm = 1.0f/sqrtf(q->q0*q->q0 + q->q1*q->q1 + q->q2*q->q2 + q->q3*q->q3);
    q->q0 *= recipNorm;
    q->q1 *= recipNorm;
    q->q2 *= recipNorm;
    q->q3 *= recipNorm;
}

其中，`gx, gy, gz`为陀螺仪测量值，`ax, ay, az`为加速度计测量值，`q`为四元数，`sampleFreq`为采样频率，`Kp`为比例增益，`Ki`为积分增益。调用该函数即可对四元数进行更新，从而得到姿态估计结果。