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- void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
- float recipNorm;
- float s0, s1, s2, s3;
- float qDot1, qDot2, qDot3, qDot4;
- float hx, hy;
- float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
- // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
- if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
- MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az);
- return;
- }
- // Rate of change of quaternion from gyroscope
- qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
- qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
- qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
- qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
- // 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 = invSqrt(ax * ax + ay * ay + az * az);
- ax *= recipNorm;
- ay *= recipNorm;
- az *= recipNorm;
- // Normalise magnetometer measurement
- recipNorm = invSqrt(mx * mx + my * my + mz * mz);
- mx *= recipNorm;
- my *= recipNorm;
- mz *= recipNorm;
- // Auxiliary variables to avoid repeated arithmetic
- _2q0mx = 2.0f * q0 * mx;
- _2q0my = 2.0f * q0 * my;
- _2q0mz = 2.0f * q0 * mz;
- _2q1mx = 2.0f * q1 * mx;
- _2q0 = 2.0f * q0;
- _2q1 = 2.0f * q1;
- _2q2 = 2.0f * q2;
- _2q3 = 2.0f * q3;
- _2q0q2 = 2.0f * q0 * q2;
- _2q2q3 = 2.0f * q2 * q3;
- 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 = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
- hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
- _2bx = sqrt(hx * hx + hy * hy);
- _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
- _4bx = 2.0f * _2bx;
- _4bz = 2.0f * _2bz;
- // Gradient decent algorithm corrective step
- s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q3 + _2bz * q1) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
- s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q2 + _2bz * q0) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q3 - _4bz * q1) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
- s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q1 + _2bz * q3) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q0 - _4bz * q2) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
- s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q0 + _2bz * q2) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
- recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
- s0 *= recipNorm;
- s1 *= recipNorm;
- s2 *= recipNorm;
- s3 *= recipNorm;
- // Apply feedback step
- qDot1 -= beta * s0;
- qDot2 -= beta * s1;
- qDot3 -= beta * s2;
- qDot4 -= beta * s3;
- }
- // Integrate rate of change of quaternion to yield quaternion
- q0 += qDot1 * (1.0f / sampleFreq);
- q1 += qDot2 * (1.0f / sampleFreq);
- q2 += qDot3 * (1.0f / sampleFreq);
- q3 += qDot4 * (1.0f / sampleFreq);
- // Normalise quaternion
- recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
- q0 *= recipNorm;
- q1 *= recipNorm;
- q2 *= recipNorm;
- q3 *= recipNorm;
- }
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