function mahonyAHRSupdate(gx, gy, gz, ax, ay, az, mx, my, mz, deltaTimeSec) {
    recipSampleFreq = deltaTimeSec || recipSampleFreq;
    let recipNorm;
    let q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
    let hx, hy, bx, bz;
    let halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
    let halfex, halfey, halfez;

    // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
    if (mx === undefined || my === undefined || mz === undefined || (mx === 0 && my === 0 && mz === 0)) {
      mahonyAHRSupdateIMU(gx, gy, gz, ax, ay, az);
      return;
    }

    // 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;

      // Normalise magnetometer measurement
      recipNorm = (mx * mx + my * my + mz * mz) ** -0.5;
      mx *= recipNorm;
      my *= recipNorm;
      mz *= recipNorm;

      // Auxiliary variables to afunction repeated arithmetic
      q0q0 = q0 * q0;
      q0q1 = q0 * q1;
      q0q2 = q0 * q2;
      q0q3 = q0 * q3;
      q1q1 = q1 * q1;
      q1q2 = q1 * q2;
      q1q3 = q1 * q3;
      q2q2 = q2 * q2;
      q2q3 = q2 * q3;
      q3q3 = q3 * q3;

      // Reference direction of Earth's magnetic field
      hx = 2.0 * (mx * (0.5 - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
      hy = 2.0 * (mx * (q1q2 + q0q3) + my * (0.5 - q1q1 - q3q3) + mz * (q2q3 - q0q1));
      bx = Math.sqrt(hx * hx + hy * hy);
      bz = 2.0 * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5 - q1q1 - q2q2));

      // Estimated direction of gravity and magnetic field
      halfvx = q1q3 - q0q2;
      halfvy = q0q1 + q2q3;
      halfvz = q0q0 - 0.5 + q3q3;
      halfwx = bx * (0.5 - q2q2 - q3q3) + bz * (q1q3 - q0q2);
      halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
      halfwz = bx * (q0q2 + q1q3) + bz * (0.5 - q1q1 - q2q2);

      // Error is sum of cross product between estimated direction and measured direction of field vectors
      halfex = ay * halfvz - az * halfvy + (my * halfwz - mz * halfwy);
      halfey = az * halfvx - ax * halfvz + (mz * halfwx - mx * halfwz);
      halfez = ax * halfvy - ay * halfvx + (mx * halfwy - my * halfwx);

      // 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 mahonyAHRSupdate(gx, gy, gz, ax, ay, az, mx, my, mz, deltaTimeSec) {
    recipSampleFreq = deltaTimeSec || recipSampleFreq;
    let recipNorm;
    let q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
    let hx, hy, bx, bz;
    let halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
    let halfex, halfey, halfez;

    
    if (mx === undefined || my === undefined || mz === undefined || (mx === 0 && my === 0 && mz === 0)) {
      mahonyAHRSupdateIMU(gx, gy, gz, ax, ay, az);
      return;
    }

    
    if (ax !== 0 && ay !== 0 && az !== 0) {
      
      recipNorm = (ax * ax + ay * ay + az * az) ** -0.5;
      ax *= recipNorm;
      ay *= recipNorm;
      az *= recipNorm;

      
      recipNorm = (mx * mx + my * my + mz * mz) ** -0.5;
      mx *= recipNorm;
      my *= recipNorm;
      mz *= recipNorm;

      
      q0q0 = q0 * q0;
      q0q1 = q0 * q1;
      q0q2 = q0 * q2;
      q0q3 = q0 * q3;
      q1q1 = q1 * q1;
      q1q2 = q1 * q2;
      q1q3 = q1 * q3;
      q2q2 = q2 * q2;
      q2q3 = q2 * q3;
      q3q3 = q3 * q3;

      
      hx = 2.0 * (mx * (0.5 - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
      hy = 2.0 * (mx * (q1q2 + q0q3) + my * (0.5 - q1q1 - q3q3) + mz * (q2q3 - q0q1));
      bx = Math.sqrt(hx * hx + hy * hy);
      bz = 2.0 * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5 - q1q1 - q2q2));

      
      halfvx = q1q3 - q0q2;
      halfvy = q0q1 + q2q3;
      halfvz = q0q0 - 0.5 + q3q3;
      halfwx = bx * (0.5 - q2q2 - q3q3) + bz * (q1q3 - q0q2);
      halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
      halfwz = bx * (q0q2 + q1q3) + bz * (0.5 - q1q1 - q2q2);

      
      halfex = ay * halfvz - az * halfvy + (my * halfwz - mz * halfwy);
      halfey = az * halfvx - ax * halfvz + (mz * halfwx - mx * halfwz);
      halfez = ax * halfvy - ay * halfvx + (mx * halfwy - my * halfwx);

      
      if (twoKi > 0.0) {
        integralFBx += twoKi * halfex * recipSampleFreq; 
        integralFBy += twoKi * halfey * recipSampleFreq;
        integralFBz += twoKi * halfez * recipSampleFreq;
        gx += integralFBx; 
        gy += integralFBy;
        gz += integralFBz;
      } else {
        integralFBx = 0.0; 
        integralFBy = 0.0;
        integralFBz = 0.0;
      }

      
      gx += twoKp * halfex;
      gy += twoKp * halfey;
      gz += twoKp * halfez;
    }

    
    gx *= 0.5 * recipSampleFreq; 
    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;

    
    recipNorm = (q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3) ** -0.5;
    q0 *= recipNorm;
    q1 *= recipNorm;
    q2 *= recipNorm;
    q3 *= recipNorm;
  }
function mahonyAHRSupdate ( gx , gy , gz , ax , ay , az , mx , my , mz , deltaTimeSec ) { recipSampleFreq = deltaTimeSec || recipSampleFreq ; let recipNorm ; let q0q0 , q0q1 , q0q2 , q0q3 , q1q1 , q1q2 , q1q3 , q2q2 , q2q3 , q3q3 ; let hx , hy , bx , bz ; let halfvx , halfvy , halfvz , halfwx , halfwy , halfwz ; let halfex , halfey , halfez ; // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation) if ( mx === undefined || my === undefined || mz === undefined || ( mx === 0 && my === 0 && mz === 0 ) ) { mahonyAHRSupdateIMU ( gx , gy , gz , ax , ay , az ) ; return ; } // 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 ; // Normalise magnetometer measurement recipNorm = ( mx * mx + my * my + mz * mz ) ** - 0.5 ; mx *= recipNorm ; my *= recipNorm ; mz *= recipNorm ; // Auxiliary variables to afunction repeated arithmetic q0q0 = q0 * q0 ; q0q1 = q0 * q1 ; q0q2 = q0 * q2 ; q0q3 = q0 * q3 ; q1q1 = q1 * q1 ; q1q2 = q1 * q2 ; q1q3 = q1 * q3 ; q2q2 = q2 * q2 ; q2q3 = q2 * q3 ; q3q3 = q3 * q3 ; // Reference direction of Earth's magnetic field hx = 2.0 * ( mx * ( 0.5 - q2q2 - q3q3 ) + my * ( q1q2 - q0q3 ) + mz * ( q1q3 + q0q2 ) ) ; hy = 2.0 * ( mx * ( q1q2 + q0q3 ) + my * ( 0.5 - q1q1 - q3q3 ) + mz * ( q2q3 - q0q1 ) ) ; bx = Math . sqrt ( hx * hx + hy * hy ) ; bz = 2.0 * ( mx * ( q1q3 - q0q2 ) + my * ( q2q3 + q0q1 ) + mz * ( 0.5 - q1q1 - q2q2 ) ) ; // Estimated direction of gravity and magnetic field halfvx = q1q3 - q0q2 ; halfvy = q0q1 + q2q3 ; halfvz = q0q0 - 0.5 + q3q3 ; halfwx = bx * ( 0.5 - q2q2 - q3q3 ) + bz * ( q1q3 - q0q2 ) ; halfwy = bx * ( q1q2 - q0q3 ) + bz * ( q0q1 + q2q3 ) ; halfwz = bx * ( q0q2 + q1q3 ) + bz * ( 0.5 - q1q1 - q2q2 ) ; // Error is sum of cross product between estimated direction and measured direction of field vectors halfex = ay * halfvz - az * halfvy + ( my * halfwz - mz * halfwy ) ; halfey = az * halfvx - ax * halfvz + ( mz * halfwx - mx * halfwz ) ; halfez = ax * halfvy - ay * halfvx + ( mx * halfwy - my * halfwx ) ; // 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 ; }
--------------------------------------------------------------------------------------------------- AHRS algorithm update
--------------------------------------------------------------------------------------------------- AHRS algorithm update