
// 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 & 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!

#include "quaternionFilters.h"

// These are the free parameters in the Mahony filter and fusion scheme, Kp
// for proportional feedback, Ki for integral
#define Kp 2.0f * 5.0f
#define Ki 0.0f

static float GyroMeasError = PI * (40.0f / 180.0f);
// gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
// static float GyroMeasDrift = PI * (0.0f  / 180.0f);
// There is a tradeoff in the beta parameter between accuracy and response
// speed. In the original Madgwick study, beta of 0.041 (corresponding to
// GyroMeasError of 2.7 degrees/s) was found to give optimal accuracy.
// However, with this value, the LSM9SD0 response time is about 10 seconds
// to a stable initial quaternion. Subsequent changes also require a
// longish lag time to a stable output, not fast enough for a quadcopter or
// robot car! By increasing beta (GyroMeasError) by about a factor of
// fifteen, the response time constant is reduced to ~2 sec. I haven't
// noticed any reduction in solution accuracy. This is essentially the I
// coefficient in a PID control sense; the bigger the feedback coefficient,
// the faster the solution converges, usually at the expense of accuracy.
// In any case, this is the free parameter in the Madgwick filtering and
// fusion scheme.
static float beta_ = sqrt(3.0f / 4.0f) * GyroMeasError;  // Compute beta
// Compute zeta, the other free parameter in the Madgwick scheme usually
// set to a small or zero value
// static float zeta = sqrt(3.0f / 4.0f) * GyroMeasDrift;

// Vector to hold integral error for Mahony method
static float eInt[3] = {0.0f, 0.0f, 0.0f};
// Vector to hold quaternion
static float q[4] = {1.0f, 0.0f, 0.0f, 0.0f};

void MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy,
                              float gz, float mx, float my, float mz,
                              float deltat) {
    // short name local variable for readability
    float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];
    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) {
    // short name local variable for readability
    float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];
    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;
}

const float* getQ() {
    return q;
}
