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ahrs_Madgwick.cpp
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ahrs_Madgwick.cpp
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#ifndef __AHRS_MADGWICK
#define __AHRS_MADGWICK
#include <math.h>
#include "geometry.cpp"
//фильтр ориентации Себастьяна Маджвика
class AHRSMadgwick
{
public:
//параметр фильтра "влияние акселерометра и магнетометра"
float beta;
//параметр фильтра "сила коррекции дрифта гироскопа"
float zeta;
//кватернион ориентации
Quaternion Q;
float b_x, b_z; // reference direction of flux in earth frame
float w_bx, w_by, w_bz; // estimate gyroscope biases error
AHRSMadgwick(float _beta, float _zeta): beta(_beta), zeta(_zeta)
{
Q.Ident();
b_x = 1, b_z = 0;
w_bx = 0, w_by = 0, w_bz = 0;
}
//рабочий цикл
void Update(float w_x, float w_y, float w_z, float a_x, float a_y, float a_z, float m_x, float m_y, float m_z, float deltat)
{
// local system variables
float SEq_1 = Q.W, SEq_2 = Q.X, SEq_3 = Q.Y, SEq_4 = Q.Z;
float norm; // vector norm
float SEqDot_omega_1, SEqDot_omega_2, SEqDot_omega_3, SEqDot_omega_4; // quaternion rate from gyroscopes elements
float f_1, f_2, f_3, f_4, f_5, f_6; // objective function elements
float J_11or24, J_12or23, J_13or22, J_14or21, J_32, J_33, // objective function Jacobian elements
J_41, J_42, J_43, J_44, J_51, J_52, J_53, J_54, J_61, J_62, J_63, J_64; //
float SEqHatDot_1, SEqHatDot_2, SEqHatDot_3, SEqHatDot_4; // estimated direction of the gyroscope error
float w_err_x, w_err_y, w_err_z; // estimated direction of the gyroscope error (angular)
float h_x, h_y, h_z; // computed flux in the earth frame
// axulirary variables to avoid reapeated calcualtions
float halfSEq_1 = 0.5f * SEq_1;
float halfSEq_2 = 0.5f * SEq_2;
float halfSEq_3 = 0.5f * SEq_3;
float halfSEq_4 = 0.5f * SEq_4;
float twoSEq_1 = 2.0f * SEq_1;
float twoSEq_2 = 2.0f * SEq_2;
float twoSEq_3 = 2.0f * SEq_3;
float twoSEq_4 = 2.0f * SEq_4;
float twob_x = 2.0f * b_x;
float twob_z = 2.0f * b_z;
float twob_xSEq_1 = 2.0f * b_x * SEq_1;
float twob_xSEq_2 = 2.0f * b_x * SEq_2;
float twob_xSEq_3 = 2.0f * b_x * SEq_3;
float twob_xSEq_4 = 2.0f * b_x * SEq_4;
float twob_zSEq_1 = 2.0f * b_z * SEq_1;
float twob_zSEq_2 = 2.0f * b_z * SEq_2;
float twob_zSEq_3 = 2.0f * b_z * SEq_3;
float twob_zSEq_4 = 2.0f * b_z * SEq_4;
float SEq_1SEq_2;
float SEq_1SEq_3 = SEq_1 * SEq_3;
float SEq_1SEq_4;
float SEq_2SEq_3;
float SEq_2SEq_4 = SEq_2 * SEq_4;
float SEq_3SEq_4;
float twom_x = 2.0f * m_x;
float twom_y = 2.0f * m_y;
float twom_z = 2.0f * m_z;
// normalise the accelerometer measurement
norm = sqrt(a_x * a_x + a_y * a_y + a_z * a_z);
a_x /= norm;
a_y /= norm;
a_z /= norm;
// normalise the magnetometer measurement
norm = sqrt(m_x * m_x + m_y * m_y + m_z * m_z);
m_x /= norm;
m_y /= norm;
m_z /= norm;
// compute the objective function and Jacobian
f_1 = twoSEq_2 * SEq_4 - twoSEq_1 * SEq_3 - a_x;
f_2 = twoSEq_1 * SEq_2 + twoSEq_3 * SEq_4 - a_y;
f_3 = 1.0f - twoSEq_2 * SEq_2 - twoSEq_3 * SEq_3 - a_z;
f_4 = twob_x * (0.5f - SEq_3 * SEq_3 - SEq_4 * SEq_4) + twob_z * (SEq_2SEq_4 - SEq_1SEq_3) - m_x;
f_5 = twob_x * (SEq_2 * SEq_3 - SEq_1 * SEq_4) + twob_z * (SEq_1 * SEq_2 + SEq_3 * SEq_4) - m_y;
f_6 = twob_x * (SEq_1SEq_3 + SEq_2SEq_4) + twob_z * (0.5f - SEq_2 * SEq_2 - SEq_3 * SEq_3) - m_z;
J_11or24 = twoSEq_3; // J_11 negated in matrix multiplication
J_12or23 = 2.0f * SEq_4;
J_13or22 = twoSEq_1; // J_12 negated in matrix multiplication
J_14or21 = twoSEq_2;
J_32 = 2.0f * J_14or21; // negated in matrix multiplication
J_33 = 2.0f * J_11or24; // negated in matrix multiplication
J_41 = twob_zSEq_3; // negated in matrix multiplication
J_42 = twob_zSEq_4;
J_43 = 2.0f * twob_xSEq_3 + twob_zSEq_1; // negated in matrix multiplication
J_44 = 2.0f * twob_xSEq_4 - twob_zSEq_2; // negated in matrix multiplication
J_51 = twob_xSEq_4 - twob_zSEq_2; // negated in matrix multiplication
J_52 = twob_xSEq_3 + twob_zSEq_1;
J_53 = twob_xSEq_2 + twob_zSEq_4;
J_54 = twob_xSEq_1 - twob_zSEq_3; // negated in matrix multiplication
J_61 = twob_xSEq_3;
J_62 = twob_xSEq_4 - 2.0f * twob_zSEq_2;
J_63 = twob_xSEq_1 - 2.0f * twob_zSEq_3;
J_64 = twob_xSEq_2;
// compute the gradient (matrix multiplication)
SEqHatDot_1 = J_14or21 * f_2 - J_11or24 * f_1 - J_41 * f_4 - J_51 * f_5 + J_61 * f_6;
SEqHatDot_2 = J_12or23 * f_1 + J_13or22 * f_2 - J_32 * f_3 + J_42 * f_4 + J_52 * f_5 + J_62 * f_6;
SEqHatDot_3 = J_12or23 * f_2 - J_33 * f_3 - J_13or22 * f_1 - J_43 * f_4 + J_53 * f_5 + J_63 * f_6;
SEqHatDot_4 = J_14or21 * f_1 + J_11or24 * f_2 - J_44 * f_4 - J_54 * f_5 + J_64 * f_6;
// normalise the gradient to estimate direction of the gyroscope error
norm = sqrt(SEqHatDot_1 * SEqHatDot_1 + SEqHatDot_2 * SEqHatDot_2 + SEqHatDot_3 * SEqHatDot_3 + SEqHatDot_4 * SEqHatDot_4);
SEqHatDot_1 = SEqHatDot_1 / norm;
SEqHatDot_2 = SEqHatDot_2 / norm;
SEqHatDot_3 = SEqHatDot_3 / norm;
SEqHatDot_4 = SEqHatDot_4 / norm;
// compute angular estimated direction of the gyroscope error
w_err_x = twoSEq_1 * SEqHatDot_2 - twoSEq_2 * SEqHatDot_1 - twoSEq_3 * SEqHatDot_4 + twoSEq_4 * SEqHatDot_3;
w_err_y = twoSEq_1 * SEqHatDot_3 + twoSEq_2 * SEqHatDot_4 - twoSEq_3 * SEqHatDot_1 - twoSEq_4 * SEqHatDot_2;
w_err_z = twoSEq_1 * SEqHatDot_4 - twoSEq_2 * SEqHatDot_3 + twoSEq_3 * SEqHatDot_2 - twoSEq_4 * SEqHatDot_1;
// compute and remove the gyroscope baises
w_bx += w_err_x * deltat * zeta;
w_by += w_err_y * deltat * zeta;
w_bz += w_err_z * deltat * zeta;
w_x -= w_bx;
w_y -= w_by;
w_z -= w_bz;
// compute the quaternion rate measured by gyroscopes
SEqDot_omega_1 = -halfSEq_2 * w_x - halfSEq_3 * w_y - halfSEq_4 * w_z;
SEqDot_omega_2 = halfSEq_1 * w_x + halfSEq_3 * w_z - halfSEq_4 * w_y;
SEqDot_omega_3 = halfSEq_1 * w_y - halfSEq_2 * w_z + halfSEq_4 * w_x;
SEqDot_omega_4 = halfSEq_1 * w_z + halfSEq_2 * w_y - halfSEq_3 * w_x;
// compute then integrate the estimated quaternion rate
SEq_1 += (SEqDot_omega_1 - (beta * SEqHatDot_1)) * deltat;
SEq_2 += (SEqDot_omega_2 - (beta * SEqHatDot_2)) * deltat;
SEq_3 += (SEqDot_omega_3 - (beta * SEqHatDot_3)) * deltat;
SEq_4 += (SEqDot_omega_4 - (beta * SEqHatDot_4)) * deltat;
// normalise quaternion
norm = sqrt(SEq_1 * SEq_1 + SEq_2 * SEq_2 + SEq_3 * SEq_3 + SEq_4 * SEq_4);
SEq_1 /= norm;
SEq_2 /= norm;
SEq_3 /= norm;
SEq_4 /= norm;
// compute flux in the earth frame
SEq_1SEq_2 = SEq_1 * SEq_2; // recompute axulirary variables
SEq_1SEq_3 = SEq_1 * SEq_3;
SEq_1SEq_4 = SEq_1 * SEq_4;
SEq_3SEq_4 = SEq_3 * SEq_4;
SEq_2SEq_3 = SEq_2 * SEq_3;
SEq_2SEq_4 = SEq_2 * SEq_4;
h_x = twom_x * (0.5f - SEq_3 * SEq_3 - SEq_4 * SEq_4) + twom_y * (SEq_2SEq_3 - SEq_1SEq_4) + twom_z * (SEq_2SEq_4 + SEq_1SEq_3);
h_y = twom_x * (SEq_2SEq_3 + SEq_1SEq_4) + twom_y * (0.5f - SEq_2 * SEq_2 - SEq_4 * SEq_4) + twom_z * (SEq_3SEq_4 - SEq_1SEq_2);
h_z = twom_x * (SEq_2SEq_4 - SEq_1SEq_3) + twom_y * (SEq_3SEq_4 + SEq_1SEq_2) + twom_z * (0.5f - SEq_2 * SEq_2 - SEq_3 * SEq_3);
// normalise the flux vector to have only components in the x and z
b_x = sqrt((h_x * h_x) + (h_y * h_y));
b_z = h_z;
Q.Set(SEq_2, SEq_3, SEq_4, SEq_1);
}
void UpdateGA(float w_x, float w_y, float w_z, float a_x, float a_y, float a_z, float deltat)
{
// Local system variables
float SEq_1 = Q.W, SEq_2 = Q.X, SEq_3 = Q.Y, SEq_4 = Q.Z;
float norm; // vector norm
float SEqDot_omega_1, SEqDot_omega_2, SEqDot_omega_3, SEqDot_omega_4; // quaternion derrivative from gyroscopes elements
float f_1, f_2, f_3; // objective function elements
float J_11or24, J_12or23, J_13or22, J_14or21, J_32, J_33; // objective function Jacobian elements
float SEqHatDot_1, SEqHatDot_2, SEqHatDot_3, SEqHatDot_4; // estimated direction of the gyroscope error
// Axulirary variables to avoid reapeated calcualtions
float halfSEq_1 = 0.5f * SEq_1;
float halfSEq_2 = 0.5f * SEq_2;
float halfSEq_3 = 0.5f * SEq_3;
float halfSEq_4 = 0.5f * SEq_4;
float twoSEq_1 = 2.0f * SEq_1;
float twoSEq_2 = 2.0f * SEq_2;
float twoSEq_3 = 2.0f * SEq_3;
// Normalise the accelerometer measurement
norm = sqrt(a_x * a_x + a_y * a_y + a_z * a_z);
a_x /= norm;
a_y /= norm;
a_z /= norm;
// Compute the objective function and Jacobian
f_1 = twoSEq_2 * SEq_4 - twoSEq_1 * SEq_3 - a_x;
f_2 = twoSEq_1 * SEq_2 + twoSEq_3 * SEq_4 - a_y;
f_3 = 1.0f - twoSEq_2 * SEq_2 - twoSEq_3 * SEq_3 - a_z;
J_11or24 = twoSEq_3; // J_11 negated in matrix multiplication
J_12or23 = 2.0f * SEq_4;
J_13or22 = twoSEq_1; // J_12 negated in matrix multiplication
J_14or21 = twoSEq_2;
J_32 = 2.0f * J_14or21; // negated in matrix multiplication
J_33 = 2.0f * J_11or24; // negated in matrix multiplication
// Compute the gradient (matrix multiplication)
SEqHatDot_1 = J_14or21 * f_2 - J_11or24 * f_1;
SEqHatDot_2 = J_12or23 * f_1 + J_13or22 * f_2 - J_32 * f_3;
SEqHatDot_3 = J_12or23 * f_2 - J_33 * f_3 - J_13or22 * f_1;
SEqHatDot_4 = J_14or21 * f_1 + J_11or24 * f_2;
// Normalise the gradient
norm = sqrt(SEqHatDot_1 * SEqHatDot_1 + SEqHatDot_2 * SEqHatDot_2 + SEqHatDot_3 * SEqHatDot_3 + SEqHatDot_4 * SEqHatDot_4);
SEqHatDot_1 /= norm;
SEqHatDot_2 /= norm;
SEqHatDot_3 /= norm;
SEqHatDot_4 /= norm;
// Compute the quaternion derrivative measured by gyroscopes
SEqDot_omega_1 = -halfSEq_2 * w_x - halfSEq_3 * w_y - halfSEq_4 * w_z;
SEqDot_omega_2 = halfSEq_1 * w_x + halfSEq_3 * w_z - halfSEq_4 * w_y;
SEqDot_omega_3 = halfSEq_1 * w_y - halfSEq_2 * w_z + halfSEq_4 * w_x;
SEqDot_omega_4 = halfSEq_1 * w_z + halfSEq_2 * w_y - halfSEq_3 * w_x;
// Compute then integrate the estimated quaternion derrivative
SEq_1 += (SEqDot_omega_1 - (beta * SEqHatDot_1)) * deltat;
SEq_2 += (SEqDot_omega_2 - (beta * SEqHatDot_2)) * deltat;
SEq_3 += (SEqDot_omega_3 - (beta * SEqHatDot_3)) * deltat;
SEq_4 += (SEqDot_omega_4 - (beta * SEqHatDot_4)) * deltat;
// Normalise quaternion
norm = sqrt(SEq_1 * SEq_1 + SEq_2 * SEq_2 + SEq_3 * SEq_3 + SEq_4 * SEq_4);
SEq_1 /= norm;
SEq_2 /= norm;
SEq_3 /= norm;
SEq_4 /= norm;
Q.Set(SEq_2, SEq_3, SEq_4, SEq_1);
}
};
#endif /*__AHRS_MADGWICK*/