File content as of revision 4:404c35f32ce3:

#include "AHRS.h"
#include "math.h"

static float eInt[3] = {0.0f, 0.0f, 0.0f}; 

// Implementation of Sebastian Madgwick's "...efficient orientation filter for... inertial/magnetic sensor arrays"
// (see http://www.x-io.co.uk/category/open-source/ for examples and more details)
// which fuses acceleration, rotation rate, and magnetic moments to produce a quaternion-based estimate of absolute
// device orientation -- which can be converted to yaw, pitch, and roll. Useful for stabilizing quadcopters, etc.
// The performance of the orientation filter is at least as good as conventional Kalman-based filtering algorithms
// but is much less computationally intensive---it can be performed on a 3.3 V Pro Mini operating at 8 MHz!

    void MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz, float deltat, float *q, float beta) {
        float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];   // short name local variable for readability
        float norm;
        float hx, hy, _2bx, _2bz;
        float s1, s2, s3, s4;
        float qDot1, qDot2, qDot3, qDot4;

        // Auxiliary variables to avoid repeated arithmetic
        float _2q1mx;
        float _2q1my;
        float _2q1mz;
        float _2q2mx;
        float _4bx;
        float _4bz;
        float _2q1 = 2.0f * q1;
        float _2q2 = 2.0f * q2;
        float _2q3 = 2.0f * q3;
        float _2q4 = 2.0f * q4;
        float _2q1q3 = 2.0f * q1 * q3;
        float _2q3q4 = 2.0f * q3 * q4;
        float q1q1 = q1 * q1;
        float q1q2 = q1 * q2;
        float q1q3 = q1 * q3;
        float q1q4 = q1 * q4;
        float q2q2 = q2 * q2;
        float q2q3 = q2 * q3;
        float q2q4 = q2 * q4;
        float q3q3 = q3 * q3;
        float q3q4 = q3 * q4;
        float q4q4 = q4 * q4;

        // Normalise accelerometer measurement
        norm = sqrt(ax * ax + ay * ay + az * az);
        if (norm == 0.0f) return; // handle NaN
        norm = 1.0f/norm;
        ax *= norm;
        ay *= norm;
        az *= norm;

        // Normalise magnetometer measurement
        norm = sqrt(mx * mx + my * my + mz * mz);
        if (norm == 0.0f) return; // handle NaN
        norm = 1.0f/norm;
        mx *= norm;
        my *= norm;
        mz *= norm;

        // Reference direction of Earth's magnetic field
        _2q1mx = 2.0f * q1 * mx;
        _2q1my = 2.0f * q1 * my;
        _2q1mz = 2.0f * q1 * mz;
        _2q2mx = 2.0f * q2 * mx;
        hx = mx * q1q1 - _2q1my * q4 + _2q1mz * q3 + mx * q2q2 + _2q2 * my * q3 + _2q2 * mz * q4 - mx * q3q3 - mx * q4q4;
        hy = _2q1mx * q4 + my * q1q1 - _2q1mz * q2 + _2q2mx * q3 - my * q2q2 + my * q3q3 + _2q3 * mz * q4 - my * q4q4;
        _2bx = sqrt(hx * hx + hy * hy);
        _2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4;
        _4bx = 2.0f * _2bx;
        _4bz = 2.0f * _2bz;

        // Gradient decent algorithm corrective step
        s1 = -_2q3 * (2.0f * q2q4 - _2q1q3 - ax) + _2q2 * (2.0f * q1q2 + _2q3q4 - ay) - _2bz * q3 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q4 + _2bz * q2) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q3 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
        s2 = _2q4 * (2.0f * q2q4 - _2q1q3 - ax) + _2q1 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q2 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + _2bz * q4 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q3 + _2bz * q1) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q4 - _4bz * q2) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
        s3 = -_2q1 * (2.0f * q2q4 - _2q1q3 - ax) + _2q4 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q3 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + (-_4bx * q3 - _2bz * q1) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q2 + _2bz * q4) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q1 - _4bz * q3) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
        s4 = _2q2 * (2.0f * q2q4 - _2q1q3 - ax) + _2q3 * (2.0f * q1q2 + _2q3q4 - ay) + (-_4bx * q4 + _2bz * q2) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q1 + _2bz * q3) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q2 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
        norm = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4);    // normalise step magnitude
        norm = 1.0f/norm;
        s1 *= norm;
        s2 *= norm;
        s3 *= norm;
        s4 *= norm;

        // Compute rate of change of quaternion
        qDot1 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - beta * s1;
        qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - beta * s2;
        qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - beta * s3;
        qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - beta * s4;

        // Integrate to yield quaternion
        q1 += qDot1 * deltat;
        q2 += qDot2 * deltat;
        q3 += qDot3 * deltat;
        q4 += qDot4 * deltat;
        norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);    // normalise quaternion
        norm = 1.0f/norm;
        q[0] = q1 * norm;
        q[1] = q2 * norm;
        q[2] = q3 * norm;
        q[3] = q4 * norm;

}



// Similar to Madgwick scheme but uses proportional and integral filtering on the error between estimated reference vectors and
// measured ones.
    void MahonyQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz, float deltat, float *q) {
        float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];   // short name local variable for readability
        float norm;
        float hx, hy, bx, bz;
        float vx, vy, vz, wx, wy, wz;
        float ex, ey, ez;
        float pa, pb, pc;

        // Auxiliary variables to avoid repeated arithmetic
        float q1q1 = q1 * q1;
        float q1q2 = q1 * q2;
        float q1q3 = q1 * q3;
        float q1q4 = q1 * q4;
        float q2q2 = q2 * q2;
        float q2q3 = q2 * q3;
        float q2q4 = q2 * q4;
        float q3q3 = q3 * q3;
        float q3q4 = q3 * q4;
        float q4q4 = q4 * q4;

        // Normalise accelerometer measurement
        norm = sqrt(ax * ax + ay * ay + az * az);
        if (norm == 0.0f) return; // handle NaN
        norm = 1.0f / norm;        // use reciprocal for division
        ax *= norm;
        ay *= norm;
        az *= norm;

        // Normalise magnetometer measurement
        norm = sqrt(mx * mx + my * my + mz * mz);
        if (norm == 0.0f) return; // handle NaN
        norm = 1.0f / norm;        // use reciprocal for division
        mx *= norm;
        my *= norm;
        mz *= norm;

        // Reference direction of Earth's magnetic field
        hx = 2.0f * mx * (0.5f - q3q3 - q4q4) + 2.0f * my * (q2q3 - q1q4) + 2.0f * mz * (q2q4 + q1q3);
        hy = 2.0f * mx * (q2q3 + q1q4) + 2.0f * my * (0.5f - q2q2 - q4q4) + 2.0f * mz * (q3q4 - q1q2);
        bx = sqrt((hx * hx) + (hy * hy));
        bz = 2.0f * mx * (q2q4 - q1q3) + 2.0f * my * (q3q4 + q1q2) + 2.0f * mz * (0.5f - q2q2 - q3q3);

        // Estimated direction of gravity and magnetic field
        vx = 2.0f * (q2q4 - q1q3);
        vy = 2.0f * (q1q2 + q3q4);
        vz = q1q1 - q2q2 - q3q3 + q4q4;
        wx = 2.0f * bx * (0.5f - q3q3 - q4q4) + 2.0f * bz * (q2q4 - q1q3);
        wy = 2.0f * bx * (q2q3 - q1q4) + 2.0f * bz * (q1q2 + q3q4);
        wz = 2.0f * bx * (q1q3 + q2q4) + 2.0f * bz * (0.5f - q2q2 - q3q3);

        // Error is cross product between estimated direction and measured direction of gravity
        ex = (ay * vz - az * vy) + (my * wz - mz * wy);
        ey = (az * vx - ax * vz) + (mz * wx - mx * wz);
        ez = (ax * vy - ay * vx) + (mx * wy - my * wx);
        if (Ki > 0.0f) {
            eInt[0] += ex;      // accumulate integral error
            eInt[1] += ey;
            eInt[2] += ez;
        } else {
            eInt[0] = 0.0f;     // prevent integral wind up
            eInt[1] = 0.0f;
            eInt[2] = 0.0f;
        }

        // Apply feedback terms
        gx = gx + Kp * ex + Ki * eInt[0];
        gy = gy + Kp * ey + Ki * eInt[1];
        gz = gz + Kp * ez + Ki * eInt[2];

        // Integrate rate of change of quaternion
        pa = q2;
        pb = q3;
        pc = q4;
        q1 = q1 + (-q2 * gx - q3 * gy - q4 * gz) * (0.5f * deltat);
        q2 = pa + (q1 * gx + pb * gz - pc * gy) * (0.5f * deltat);
        q3 = pb + (q1 * gy - pa * gz + pc * gx) * (0.5f * deltat);
        q4 = pc + (q1 * gz + pa * gy - pb * gx) * (0.5f * deltat);

        // Normalise quaternion
        norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
        norm = 1.0f / norm;
        q[0] = q1 * norm;
        q[1] = q2 * norm;
        q[2] = q3 * norm;
        q[3] = q4 * norm;

    }