Simple example to show how to get an estimation of the attitude with a 9DOF IMU and the Kalman filter
Dependencies: L3GD20 LSM303DLHC mbed-dsp mbed
Fork of minimu-9v2 by
sensfusion9.c
- Committer:
- capriele
- Date:
- 2017-03-25
- Revision:
- 1:ba2d31e3112d
File content as of revision 1:ba2d31e3112d:
#include "sensfusion9.h" #include "math.h" #include "arm_math.h" #define M_PI_F 3.14159265358979323846f /* pi */ static inline void mat_trans(const arm_matrix_instance_f32 * pSrc, arm_matrix_instance_f32 * pDst) { arm_mat_trans_f32(pSrc, pDst); } static inline void mat_inv(const arm_matrix_instance_f32 * pSrc, arm_matrix_instance_f32 * pDst) { arm_mat_inverse_f32(pSrc, pDst); } static inline void mat_mult(const arm_matrix_instance_f32 * pSrcA, const arm_matrix_instance_f32 * pSrcB, arm_matrix_instance_f32 * pDst) { arm_mat_mult_f32(pSrcA, pSrcB, pDst); } static inline float arm_sqrt(float32_t in) { float pOut = 0; arm_status result = arm_sqrt_f32(in, &pOut); return pOut; } #define STATE_SIZE 4 #define OUTPUT_SIZE 6 static float Q_VARIANCE = 0.01f; static float R_VARIANCE_ACC = 25.0f; static float R_VARIANCE_MAG = 50.0f; // The covariance matrix static float P[STATE_SIZE][STATE_SIZE] = {{0}}; static float R[OUTPUT_SIZE] = {0}; static arm_matrix_instance_f32 Pm = {STATE_SIZE, STATE_SIZE, (float *)P}; // The state update matrix static float A[STATE_SIZE][STATE_SIZE]; static arm_matrix_instance_f32 Am = {STATE_SIZE, STATE_SIZE, (float *)A}; // linearized dynamics for covariance update; // Temporary matrices for the covariance updates static float tmpNN1d[STATE_SIZE][STATE_SIZE]; static arm_matrix_instance_f32 tmpNN1m = { STATE_SIZE, STATE_SIZE, (float *)tmpNN1d}; static float tmpNN2d[STATE_SIZE][STATE_SIZE]; static arm_matrix_instance_f32 tmpNN2m = { STATE_SIZE, STATE_SIZE, (float *)tmpNN2d}; // quaternion of sensor frame relative to auxiliary frame static float q0 = 1.0f; static float q1 = 0.0f; static float q2 = 0.0f; static float q3 = 0.0f; // Unit vector in the estimated gravity direction static float gravX, gravY, gravZ; // The acc in Z for static position (g) // Set on first update, assuming we are in a static position since the sensors were just calibrates. // This value will be better the more level the copter is at calibration time static float baseZacc = 1.0; static bool isInit; static bool isCalibrated = false; static void sensfusion9UpdateQImpl(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float dt); static float sensfusion9GetAccZ(const float ax, const float ay, const float az); static void estimatedGravityDirection(float* gx, float* gy, float* gz); // TODO: Make math util file static float invSqrt(float x); void sensfusion9Init() { if(isInit) return; for(int i = 0; i < STATE_SIZE; ++i) P[i][i] = Q_VARIANCE; R[0] = R_VARIANCE_ACC; R[1] = R_VARIANCE_ACC; R[2] = R_VARIANCE_ACC; R[3] = R_VARIANCE_MAG; R[4] = R_VARIANCE_MAG; R[5] = R_VARIANCE_MAG; isInit = true; } bool sensfusion9Test(void) { return isInit; } void sensfusion9UpdateQ(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float dt) { //Cambio gli assi del magnetometro perchè rispetto a quelli del gyro/acc sono diversi: //In particolare: //Mx = (Gy = Ay) //My = (Gx = Ax) //-Mz = (Gz = Az) sensfusion9UpdateQImpl(gx, gy, gz, ax, ay, az, mx, my, mz, dt); estimatedGravityDirection(&gravX, &gravY, &gravZ); if (!isCalibrated) { baseZacc = sensfusion9GetAccZ(ax, ay, az); isCalibrated = true; } } /* static void sensfusion9UpdateQImpl(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float dt) { float recipNorm; gx = gx * M_PI_F / 180.0f; gy = gy * M_PI_F / 180.0f; gz = gz * M_PI_F / 180.0f; // 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; A[0][0] = 1.0f; A[0][1] = gz*dt; A[0][2] = -gy*dt; A[1][0] = -gz*dt; A[1][1] = 1.0f; A[1][2] = gx*dt; A[2][0] = gy*dt; A[2][1] = -gx*dt; A[2][2] = 1.0f; float q[4][1]; arm_matrix_instance_f32 qm = {4, 1, (float *)q}; q[0][0] = q0; q[1][0] = q1; q[2][0] = q2; q[3][0] = q3; float W[4][4]; arm_matrix_instance_f32 Wm = {4, 4, (float *)W}; W[0][0] = 0.0f; W[0][1] = -gx; W[0][2] = -gy; W[0][3] = -gz; W[1][0] = gx; W[1][1] = 0.0f; W[1][2] = gz; W[1][3] = -gy; W[2][0] = gy; W[2][1] = -gz; W[2][2] = 0.0f; W[2][3] = gx; W[3][0] = gz; W[3][1] = gy; W[3][2] = -gx; W[3][3] = 0.0f; //Aggiorno lo stato con runge kutta 4 float m1[4][1]; float m2[4][1]; float m3[4][1]; float x1[4][1]; float x2[4][1]; arm_matrix_instance_f32 m1m = {4, 1, (float *)m1}; arm_matrix_instance_f32 m2m = {4, 1, (float *)m2}; arm_matrix_instance_f32 m3m = {4, 1, (float *)m3}; arm_matrix_instance_f32 x1m = {4, 1, (float *)x1}; arm_matrix_instance_f32 x2m = {4, 1, (float *)x2}; //Primo step mat_mult(&Wm, &qm, &m1m); for(int i = 0; i < 4; ++i){ x1[i][0] = q[i][0] + 0.5f*m1[i][0]*dt; } //Secondo step mat_mult(&Wm, &x1m, &m2m); for(int i = 0; i < 4; ++i){ x2[i][0] = q[i][0] + 0.5f*(m1[i][0] + m2[i][0])*dt/4.0f; } //Terzo step mat_mult(&Wm, &x2m, &m3m); for(int i = 0; i < 4; ++i){ q[i][0] = q[i][0] + 0.5f*(m1[i][0] + m2[i][0] + 4.0f*m3[i][0])*(dt/6.0f); } //Normalizzo la stima dei quaternioni recipNorm = invSqrt(q[0][0]*q[0][0] + q[1][0]*q[1][0] + q[2][0]*q[2][0] + q[3][0]*q[3][0]); for(int i = 0; i < 4; ++i){ q[i][0] *= recipNorm; } q0 = q[0][0]; q1 = q[1][0]; q2 = q[2][0]; q3 = q[3][0]; //Matrice di rotazione float QuaternionDCM[3][3]; arm_matrix_instance_f32 QuaternionDCMm = {3, 3, (float *)QuaternionDCM}; QuaternionDCM[0][0] = 2*q0*q0-1+2*q1*q1; QuaternionDCM[0][1] = 2*(q1*q2+q0*q3); QuaternionDCM[0][2] = 2*(q1*q3-q0*q2); QuaternionDCM[1][0] = 2*(q1*q2-q0*q3); QuaternionDCM[1][1] = 2*q0*q0-1+2*q2*q2; QuaternionDCM[1][2] = 2*(q2*q3+q0*q1); QuaternionDCM[2][0] = 2*(q1*q3+q0*q2); QuaternionDCM[2][1] = 2*(q2*q3-q0*q1); QuaternionDCM[2][2] = 2*q0*q0-1+2*q3*q3; //Gravity Reference float G[3][1]; float Gr[3][1]; arm_matrix_instance_f32 Gm = {3, 1, (float *)G}; arm_matrix_instance_f32 Grm = {3, 1, (float *)Gr}; G[0][0] = 0; G[1][0] = 0; G[2][0] = 1; mat_mult(&QuaternionDCMm, &Gm, &Grm); //Magnetic field Reference float M[3][1]; float Mr[3][1]; arm_matrix_instance_f32 Mm = {3, 1, (float *)M}; arm_matrix_instance_f32 Mrm = {3, 1, (float *)Mr}; float hx = mx*q0*q0 + 2.0f*mz*q0*q2 - 2.0f*my*q0*q3 + mx*q1*q1 + 2.0f*my*q1*q2 + 2.0f*mz*q1*q3 - mx*q2*q2 - mx*q3*q3; float hy = my*q0*q0 - 2.0f*mz*q0*q1 + 2.0f*mx*q0*q3 - my*q1*q1 + 2.0f*mx*q1*q2 + my*q2*q2 + 2.0f*mz*q2*q3 - my*q3*q3; float hz = mz*q0*q0 + 2.0f*my*q0*q1 - 2.0f*mx*q0*q2 - mz*q1*q1 + 2.0f*mx*q1*q3 - mz*q2*q1 + 2.0f*my*q2*q3 + mz*q3*q3; M[0][0] = arm_sqrt(hx*hx + hy*hy); M[1][0] = 0; M[2][0] = hz; mat_mult(&QuaternionDCMm, &Mm, &Mrm); // Aggiorno la Covarianza float P0[STATE_SIZE][STATE_SIZE]; arm_matrix_instance_f32 P0m = {STATE_SIZE, STATE_SIZE, (float *)P0}; mat_mult(&Am, &Pm, &tmpNN1m); // A P mat_trans(&Am, &tmpNN2m); // A' mat_mult(&tmpNN1m, &tmpNN2m, &P0m); // A P A' for(int i = 0; i < STATE_SIZE; ++i){ P0[i][i] += Q_VARIANCE; } // Calcolo il guadagno float K[STATE_SIZE][OUTPUT_SIZE]; arm_matrix_instance_f32 Km = {STATE_SIZE, OUTPUT_SIZE, (float *)K}; float h[OUTPUT_SIZE][STATE_SIZE]; arm_matrix_instance_f32 Hm = {OUTPUT_SIZE, STATE_SIZE, (float *)h}; float hT[STATE_SIZE][OUTPUT_SIZE]; arm_matrix_instance_f32 HTm = {STATE_SIZE, OUTPUT_SIZE, (float *)hT}; float P0hT[STATE_SIZE][OUTPUT_SIZE]; arm_matrix_instance_f32 P0HTm = {STATE_SIZE, OUTPUT_SIZE, (float *)P0hT}; float hP0hT[OUTPUT_SIZE][OUTPUT_SIZE]; arm_matrix_instance_f32 HP0HTm = {OUTPUT_SIZE, OUTPUT_SIZE, (float *)hP0hT}; float hP0hT_inv[OUTPUT_SIZE][OUTPUT_SIZE]; arm_matrix_instance_f32 HP0HT_INVm = {OUTPUT_SIZE, OUTPUT_SIZE, (float *)hP0hT_inv}; //Accelerometer h[0][0] = 0; h[0][1] = -Gr[2][0]; h[0][2] = Gr[1][0]; h[1][0] = Gr[2][0]; h[1][1] = 0; h[1][2] = -Gr[0][0]; h[2][0] = -Gr[1][0]; h[2][1] = Gr[0][0]; h[2][2] = 0; //Magnetometer h[3][0] = 0; h[3][1] = -Mr[2][0]; h[3][2] = Mr[1][0]; h[4][0] = Mr[2][0]; h[4][1] = 0; h[4][2] = -Mr[0][0]; h[5][0] = -Mr[1][0]; h[5][1] = Mr[0][0]; h[5][2] = 0; // ====== INNOVATION COVARIANCE ====== mat_trans(&Hm, &HTm); mat_mult(&P0m, &HTm, &P0HTm); // P0*H' mat_mult(&Hm, &P0HTm, &HP0HTm); // H*P0*H' for (int i = 0; i < OUTPUT_SIZE; ++i) { // Add the element of HPH' to the above hP0hT[i][i] += R[i]; } mat_inv(&HP0HTm, &HP0HT_INVm); // (H*P0*H' + R)^(-1) mat_mult(&P0HTm, &HP0HT_INVm, &Km); // K = P0*H'*(H*P0*H' + R)^(-1) //Aggiorno la P mat_mult(&Km, &Hm, &tmpNN1m); // KH for (int i = 0; i < STATE_SIZE; ++i) { tmpNN1d[i][i] -= 1.0f; for (int j = 0; j < STATE_SIZE; ++j) { tmpNN1d[i][j] *= -1.0f; } } // -(KH - I) mat_mult(&tmpNN1m, &P0m, &Pm); // -(KH - I)*P0 float Error[OUTPUT_SIZE][1]; arm_matrix_instance_f32 Errorm = {STATE_SIZE, 1, (float *)Error}; float ae[STATE_SIZE][1]; arm_matrix_instance_f32 aem = {STATE_SIZE, 1, (float *)ae}; Error[0][0] = ax - Gr[0][0]; Error[1][0] = ay - Gr[1][0]; Error[2][0] = az - Gr[2][0]; Error[3][0] = mx - Mr[0][0]; Error[4][0] = my - Mr[1][0]; Error[5][0] = mz - Mr[2][0]; mat_mult(&Km, &Errorm, &aem); // K*error(k) float qe0 = 1; float qe1 = ae[0][0]/2; float qe2 = ae[1][0]/2; float qe3 = ae[2][0]/2; float q0tmp = q0; float q1tmp = q1; float q2tmp = q2; float q3tmp = q3; q0 = q0tmp*qe0 - q1tmp*qe1 - q2tmp*qe2 - q3tmp*qe3; q1 = q0tmp*qe1 + q1tmp*qe0 + q2tmp*qe3 - q3tmp*qe2; q2 = q0tmp*qe2 + q2tmp*qe0 - q1tmp*qe3 + q3tmp*qe1; q3 = q0tmp*qe3 + q1tmp*qe2 - q2tmp*qe1 + q3tmp*qe0; // Normalise quaternion recipNorm = invSqrt(q0*q0 + q1*q1 + q2*q2 + q3*q3); q0 *= recipNorm; q1 *= recipNorm; q2 *= recipNorm; q3 *= recipNorm; } */ static void sensfusion9UpdateQImpl(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float dt) { float recipNorm; gx = gx * M_PI_F / 180.0f; gy = gy * M_PI_F / 180.0f; gz = gz * M_PI_F / 180.0f; // 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; //Converto il vettore intensità campo magnetico //float h1 = mx*q1 + my*q2 + mz*q3; //float h2 = mx*q0 - my*q3 + mz*q2; //float h3 = mx*q3 + my*q0 - mz*q1; //float h4 = -mx*q2 + my*q1 + mz*q0; //float n2 = q0*h2 + q1*h1 + q2*h4 - q3*h3; //float n3 = q0*h3 - q1*h4 + q2*h1 + q3*h2; //float n4 = q0*h4 + q1*h3 - q2*h2 + q3*h1; //float b2 = arm_sqrt(n2*n2 + n3*n3); //float b4 = n4; //float b2 = mx; //float b4 = mz; float hx = mx*q0*q0 + 2.0f*mz*q0*q2 - 2.0f*my*q0*q3 + mx*q1*q1 + 2.0f*my*q1*q2 + 2.0f*mz*q1*q3 - mx*q2*q2 - mx*q3*q3; float hy = my*q0*q0 - 2.0f*mz*q0*q1 + 2.0f*mx*q0*q3 - my*q1*q1 + 2.0f*mx*q1*q2 + my*q2*q2 + 2.0f*mz*q2*q3 - my*q3*q3; float hz = mz*q0*q0 + 2.0f*my*q0*q1 - 2.0f*mx*q0*q2 - mz*q1*q1 + 2.0f*mx*q1*q3 - mz*q2*q1 + 2.0f*my*q2*q3 + mz*q3*q3; float b2 = arm_sqrt(hx*hx + hy*hy); float b4 = hz; A[0][0] = 1.0f; A[0][1] = -gx*dt*0.5f; A[0][2] = -gy*dt*0.5f; A[0][3] = -gz*dt*0.5f; A[1][0] = gx*dt*0.5f; A[1][1] = 1.0f; A[1][2] = gz*dt*0.5f; A[1][3] = -gy*dt*0.5f; A[2][0] = gy*dt*0.5f; A[2][1] = -gz*dt*0.5f; A[2][2] = 1.0f; A[2][3] = gx*dt*0.5f; A[3][0] = gz*dt*0.5f; A[3][1] = gy*dt*0.5f; A[3][2] = -gx*dt*0.5f; A[3][3] = 1.0f; // Aggiorno la Covarianza float P0[STATE_SIZE][STATE_SIZE]; arm_matrix_instance_f32 P0m = {STATE_SIZE, STATE_SIZE, (float *)P0}; mat_mult(&Am, &Pm, &tmpNN1m); // A P mat_trans(&Am, &tmpNN2m); // A' mat_mult(&tmpNN1m, &tmpNN2m, &P0m); // A P A' for(int i = 0; i < STATE_SIZE; ++i){ P0[i][i] += Q_VARIANCE; } // Calcolo il guadagno float K[STATE_SIZE][OUTPUT_SIZE]; arm_matrix_instance_f32 Km = {STATE_SIZE, OUTPUT_SIZE, (float *)K}; float h[OUTPUT_SIZE][STATE_SIZE]; arm_matrix_instance_f32 Hm = {OUTPUT_SIZE, STATE_SIZE, (float *)h}; float hT[STATE_SIZE][OUTPUT_SIZE]; arm_matrix_instance_f32 HTm = {STATE_SIZE, OUTPUT_SIZE, (float *)hT}; float P0hT[STATE_SIZE][OUTPUT_SIZE]; arm_matrix_instance_f32 P0HTm = {STATE_SIZE, OUTPUT_SIZE, (float *)P0hT}; float hP0hT[OUTPUT_SIZE][OUTPUT_SIZE]; arm_matrix_instance_f32 HP0HTm = {OUTPUT_SIZE, OUTPUT_SIZE, (float *)hP0hT}; float hP0hT_inv[OUTPUT_SIZE][OUTPUT_SIZE]; arm_matrix_instance_f32 HP0HT_INVm = {OUTPUT_SIZE, OUTPUT_SIZE, (float *)hP0hT_inv}; //Accelerometer h[0][0] = -2.0f*q2; h[0][1] = 2.0f*q3; h[0][2] = -2.0f*q0; h[0][3] = 2.0f*q1; h[1][0] = 2.0f*q1; h[1][1] = 2.0f*q0; h[1][2] = 2.0f*q3; h[1][3] = 2.0f*q2; h[2][0] = 4.0f*q0; h[2][1] = 0.0f; h[2][2] = 0.0f; h[2][3] = 4.0f*q3; //h[2][0] = 2.0f*q0; //h[2][1] = -2.0f*q1; //h[2][2] = -2.0f*q2; //h[2][3] = 2.0f*q3; //Magnetometer h[3][0] = 4.0f*b2*q0 - 2.0f*b4*q2; h[3][1] = 4.0f*b2*q1 + 2.0f*b4*q3; h[3][2] = -2.0f*b4*q0; h[3][3] = 2.0f*b4*q1; h[4][0] = 2.0f*b4*q1 - 2.0f*b2*q3; h[4][1] = 2.0f*b2*q2 + 2.0f*b4*q0; h[4][2] = 2.0f*b2*q1 + 2.0f*b4*q3; h[4][3] = 2.0f*b4*q2 - 2.0f*b2*q0; h[5][0] = 2.0f*b2*q2 + 4.0f*b4*q0; h[5][1] = 2.0f*b2*q3; h[5][2] = 2.0f*b2*q0; h[5][3] = 2.0f*b2*q1 + 4.0f*b4*q3; //h[3][0] = -2.0f*b4*q2; //h[3][1] = 2.0f*b4*q3; //h[3][2] = -4.0f*b2*q2 - 2.0f*b4*q0; //h[3][3] = -4.0f*b2*q3 + 2.0f*b4*q1; //h[4][0] = -2.0f*b2*q3 + 2.0f*b4*q1; //h[4][1] = 2.0f*b2*q2 + 2.0f*b4*q0; //h[4][2] = 2.0f*b2*q1 + 2.0f*b4*q3; //h[4][3] = -2.0f*b2*q0 + 2.0f*b4*q2; //h[5][0] = 2.0f*b2*q2; //h[5][1] = 2.0f*b2*q3 - 4.0f*b4*q1; //h[5][2] = 2.0f*b2*q0 - 4.0f*b4*q2; //h[5][3] = 2.0f*b2*q1; // ====== INNOVATION COVARIANCE ====== mat_trans(&Hm, &HTm); mat_mult(&P0m, &HTm, &P0HTm); // P0*H' mat_mult(&Hm, &P0HTm, &HP0HTm); // H*P0*H' for (int i = 0; i < OUTPUT_SIZE; ++i) { // Add the element of HPH' to the above hP0hT[i][i] += R[i]; } mat_inv(&HP0HTm, &HP0HT_INVm); // (H*P0*H' + R)^(-1) mat_mult(&P0HTm, &HP0HT_INVm, &Km); // K = P0*H'*(H*P0*H' + R)^(-1) //Aggiorno Stato float State[STATE_SIZE][1]; arm_matrix_instance_f32 Statem = {STATE_SIZE, 1, (float *)State}; float StateTMP[STATE_SIZE][1]; arm_matrix_instance_f32 StateTMPm = {STATE_SIZE, 1, (float *)StateTMP}; float Error[OUTPUT_SIZE][1]; arm_matrix_instance_f32 Errorm = {STATE_SIZE, 1, (float *)Error}; float ErrorTMP[OUTPUT_SIZE][1]; arm_matrix_instance_f32 ErrorTMPm = {STATE_SIZE, 1, (float *)ErrorTMP}; State[0][0] = q0; State[1][0] = q1; State[2][0] = q2; State[3][0] = q3; mat_mult(&Am, &Statem, &StateTMPm); // A*x(k) Error[0][0] = ax - 2.0f*(q1*q3 - q0*q2); Error[1][0] = ay - 2.0f*(q0*q1 + q2*q3); Error[2][0] = az - 2.0f*(q0*q0 + q3*q3 - 0.5f); Error[3][0] = mx - 2.0f*(b2*(q0*q0 + q1*q1 - 0.5f) - b4*(q0*q2 - q1*q3)); Error[4][0] = my - 2.0f*(b4*(q0*q1 + q2*q3) - b2*(q0*q3 - q1*q2)); Error[5][0] = mz - 2.0f*(b4*(q0*q0 + q3*q3 - 0.5f) + b2*(q0*q2 + q1*q3)); mat_mult(&Km, &Errorm, &ErrorTMPm); // K*error(k) q0 = StateTMP[0][0] + ErrorTMP[0][0]; q1 = StateTMP[1][0] + ErrorTMP[1][0]; q2 = StateTMP[2][0] + ErrorTMP[2][0]; q3 = StateTMP[3][0] + ErrorTMP[3][0]; //Aggiorno la P mat_mult(&Km, &Hm, &tmpNN1m); // KH for (int i = 0; i < STATE_SIZE; ++i) { tmpNN1d[i][i] -= 1.0f; for (int j = 0; j < STATE_SIZE; ++j) { tmpNN1d[i][j] *= -1.0f; } } // -(KH - I) mat_mult(&tmpNN1m, &P0m, &Pm); // -(KH - I)*P0 // Normalise quaternion recipNorm = invSqrt(q0*q0 + q1*q1 + q2*q2 + q3*q3); q0 *= recipNorm; q1 *= recipNorm; q2 *= recipNorm; q3 *= recipNorm; } void sensfusion9GetEulerRPY(float* roll, float* pitch, float* yaw) { float gx = gravX; float gy = gravY; float gz = gravZ; if (gx > 1) gx = 1; if (gx < -1) gx = -1; *yaw = atan2f(2.0f*(q0*q3 + q1*q2), q0*q0 + q1*q1 - q2*q2 - q3*q3) * 180.0f / M_PI_F; *pitch = asinf(gx) * 180.0f / M_PI_F; //Pitch seems to be inverted *roll = atan2f(gy, gz) * 180.0f / M_PI_F; } void sensfusion9GetQuaternion(float* Q0, float* Q1, float* Q2, float* Q3) { *Q0 = q0; *Q1 = q1; *Q2 = q2; *Q3 = q3; } float sensfusion9GetAccZWithoutGravity(const float ax, const float ay, const float az) { return sensfusion9GetAccZ(ax, ay, az) - baseZacc; } float sensfusion9GetInvThrustCompensationForTilt() { // Return the z component of the estimated gravity direction // (0, 0, 1) dot G return gravZ; } //--------------------------------------------------------------------------------------------------- // Fast inverse square-root // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root float invSqrt(float x) { float halfx = 0.5f * x; float y = x; long i = *(long*)&y; i = 0x5f3759df - (i>>1); y = *(float*)&i; y = y * (1.5f - (halfx * y * y)); return y; } static float sensfusion9GetAccZ(const float ax, const float ay, const float az) { // return vertical acceleration // (A dot G) / |G|, (|G| = 1) -> (A dot G) return (ax * gravX + ay * gravY + az * gravZ); } static void estimatedGravityDirection(float* gx, float* gy, float* gz) { *gx = 2 * (q1 * q3 - q0 * q2); *gy = 2 * (q0 * q1 + q2 * q3); *gz = q0 * q0 - q1 * q1 - q2 * q2 + q3 * q3; }