Mahony.js
function mahonyAHRSupdateIMU(gx, gy, gz, ax, ay, az) {
    let recipNorm;
    let halfvx, halfvy, halfvz;
    let halfex, halfey, halfez;

    // Compute feedback only if accelerometer measurement valid (afunctions NaN in accelerometer normalisation)
    if (ax !== 0 && ay !== 0 && az !== 0) {
      // Normalise accelerometer measurement
      recipNorm = (ax * ax + ay * ay + az * az) ** -0.5;
      ax *= recipNorm;
      ay *= recipNorm;
      az *= recipNorm;

      // Estimated direction of gravity and vector perpendicular to magnetic flux
      halfvx = q1 * q3 - q0 * q2;
      halfvy = q0 * q1 + q2 * q3;
      halfvz = q0 * q0 - 0.5 + q3 * q3;

      // Error is sum of cross product between estimated and measured direction of gravity
      halfex = ay * halfvz - az * halfvy;
      halfey = az * halfvx - ax * halfvz;
      halfez = ax * halfvy - ay * halfvx;

      // Compute and apply integral feedback if enabled
      if (twoKi > 0.0) {
        integralFBx += twoKi * halfex * recipSampleFreq; // integral error scaled by Ki
        integralFBy += twoKi * halfey * recipSampleFreq;
        integralFBz += twoKi * halfez * recipSampleFreq;
        gx += integralFBx; // apply integral feedback
        gy += integralFBy;
        gz += integralFBz;
      } else {
        integralFBx = 0.0; // prevent integral windup
        integralFBy = 0.0;
        integralFBz = 0.0;
      }
      // Apply proportional feedback
      gx += twoKp * halfex;
      gy += twoKp * halfey;
      gz += twoKp * halfez;
    }

    // Integrate rate of change of quaternion
    gx *= 0.5 * recipSampleFreq; // pre-multiply common factors
    gy *= 0.5 * recipSampleFreq;
    gz *= 0.5 * recipSampleFreq;
    const qa = q0;
    const qb = q1;
    const qc = q2;
    q0 += -qb * gx - qc * gy - q3 * gz;
    q1 += qa * gx + qc * gz - q3 * gy;
    q2 += qa * gy - qb * gz + q3 * gx;
    q3 += qa * gz + qb * gy - qc * gx;

    // Normalise quaternion
    recipNorm = (q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3) ** -0.5;
    q0 *= recipNorm;
    q1 *= recipNorm;
    q2 *= recipNorm;
    q3 *= recipNorm;
  }
function mahonyAHRSupdateIMU(gx, gy, gz, ax, ay, az) {
    let recipNorm;
    let halfvx, halfvy, halfvz;
    let halfex, halfey, halfez;

    // Compute feedback only if accelerometer measurement valid (afunctions NaN in accelerometer normalisation)
    if (ax !== 0 && ay !== 0 && az !== 0) {
      // Normalise accelerometer measurement
      recipNorm = (ax * ax + ay * ay + az * az) ** -0.5;
      ax *= recipNorm;
      ay *= recipNorm;
      az *= recipNorm;

      // Estimated direction of gravity and vector perpendicular to magnetic flux
      halfvx = q1 * q3 - q0 * q2;
      halfvy = q0 * q1 + q2 * q3;
      halfvz = q0 * q0 - 0.5 + q3 * q3;

      // Error is sum of cross product between estimated and measured direction of gravity
      halfex = ay * halfvz - az * halfvy;
      halfey = az * halfvx - ax * halfvz;
      halfez = ax * halfvy - ay * halfvx;

      // Compute and apply integral feedback if enabled
      if (twoKi > 0.0) {
        integralFBx += twoKi * halfex * recipSampleFreq; // integral error scaled by Ki
        integralFBy += twoKi * halfey * recipSampleFreq;
        integralFBz += twoKi * halfez * recipSampleFreq;
        gx += integralFBx; // apply integral feedback
        gy += integralFBy;
        gz += integralFBz;
      } else {
        integralFBx = 0.0; // prevent integral windup
        integralFBy = 0.0;
        integralFBz = 0.0;
      }
      // Apply proportional feedback
      gx += twoKp * halfex;
      gy += twoKp * halfey;
      gz += twoKp * halfez;
    }

    // Integrate rate of change of quaternion
    gx *= 0.5 * recipSampleFreq; // pre-multiply common factors
    gy *= 0.5 * recipSampleFreq;
    gz *= 0.5 * recipSampleFreq;
    const qa = q0;
    const qb = q1;
    const qc = q2;
    q0 += -qb * gx - qc * gy - q3 * gz;
    q1 += qa * gx + qc * gz - q3 * gy;
    q2 += qa * gy - qb * gz + q3 * gx;
    q3 += qa * gz + qb * gy - qc * gx;

    // Normalise quaternion
    recipNorm = (q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3) ** -0.5;
    q0 *= recipNorm;
    q1 *= recipNorm;
    q2 *= recipNorm;
    q3 *= recipNorm;
  }
--------------------------------------------------------------------------------------------------- IMU algorithm update