2 * Copyright (c) 2014, Olivier MATZ <zer0@droids-corp.org>
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3 * Copyright (c) 2011-2012, SOH Madgwick
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5 * This program is free software: you can redistribute it and/or modify
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6 * it under the terms of the GNU General Public License as published by
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7 * the Free Software Foundation, either version 3 of the License, or
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8 * (at your option) any later version.
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10 * This program is distributed in the hope that it will be useful,
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11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 * GNU General Public License for more details.
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15 * You should have received a copy of the GNU General Public License
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16 * along with this program. If not, see <http://www.gnu.org/licenses/>.
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20 //============================================================================
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22 //============================================================================
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24 // Implementation of Madgwick's IMU and AHRS algorithms.
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25 // See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
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27 // Date Author Notes
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28 // 29/09/2011 SOH Madgwick Initial release
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29 // 02/10/2011 SOH Madgwick Optimised for reduced CPU load
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30 // 19/02/2012 SOH Madgwick Magnetometer measurement is normalised
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32 //============================================================================
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34 #include "MadgwickAHRS.h"
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37 //#define sampleFreq 512.0f // sample frequency in Hz
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38 //#define sampleFreq 46.0f // sample frequency in Hz
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39 #define sampleFreq 85.0f // sample frequency in Hz
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40 #define betaDef 0.1f // 2 * proportional gain
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42 volatile float beta = betaDef; // 2 * proportional gain (Kp)
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43 volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame
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46 static float invSqrt(float x)
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48 return 1.0f / sqrtf(x);
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51 /* AHRS algorithm update */
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52 void MadgwickAHRSupdate(const struct imu_info *imu, struct quaternion *quat)
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55 float s0, s1, s2, s3;
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56 float qDot1, qDot2, qDot3, qDot4;
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58 float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz;
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59 float _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3;
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60 float q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
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61 float mx, my, mz, ax, ay, az;
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62 float q0 = quat->q0;
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63 float q1 = quat->q1;
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64 float q2 = quat->q2;
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65 float q3 = quat->q3;
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67 /* Use IMU algorithm if magnetometer measurement invalid (avoids NaN in
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68 * magnetometer normalisation) */
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69 if ((imu->mx == 0.0f) && (imu->my == 0.0f) && (imu->mz == 0.0f)) {
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70 MadgwickAHRSupdateIMU(imu, quat);
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74 /* Rate of change of quaternion from gyroscope */
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75 qDot1 = 0.5f * (-q1 * imu->gx - q2 * imu->gy - q3 * imu->gz);
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76 qDot2 = 0.5f * (q0 * imu->gx + q2 * imu->gz - q3 * imu->gy);
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77 qDot3 = 0.5f * (q0 * imu->gy - q1 * imu->gz + q3 * imu->gx);
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78 qDot4 = 0.5f * (q0 * imu->gz + q1 * imu->gy - q2 * imu->gx);
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80 /* Compute feedback only if accelerometer measurement valid (avoids NaN
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81 * in accelerometer normalisation) */
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82 if (!((imu->ax == 0.0f) && (imu->ay == 0.0f) && (imu->az == 0.0f))) {
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84 /* Normalise accelerometer measurement */
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85 recipNorm = invSqrt(imu->ax * imu->ax + imu->ay * imu->ay +
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87 ax = imu->ax * recipNorm;
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88 ay = imu->ay * recipNorm;
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89 az = imu->az * recipNorm;
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91 /* Normalise magnetometer measurement */
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92 recipNorm = invSqrt(imu->mx * imu->mx + imu->my * imu->my +
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94 mx = imu->mx * recipNorm;
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95 my = imu->my * recipNorm;
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96 mz = imu->mz * recipNorm;
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98 /* Auxiliary variables to avoid repeated arithmetic */
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99 _2q0mx = 2.0f * q0 * mx;
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100 _2q0my = 2.0f * q0 * my;
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101 _2q0mz = 2.0f * q0 * mz;
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102 _2q1mx = 2.0f * q1 * mx;
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107 _2q0q2 = 2.0f * q0 * q2;
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108 _2q2q3 = 2.0f * q2 * q3;
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120 /* Reference direction of Earth's magnetic field */
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121 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
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122 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
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123 _2bx = sqrt(hx * hx + hy * hy);
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124 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
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125 _4bx = 2.0f * _2bx;
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126 _4bz = 2.0f * _2bz;
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128 /* Gradient decent algorithm corrective step */
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129 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);
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130 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);
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131 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);
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132 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);
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134 /* normalize step magnitude */
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135 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3);
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141 /* Apply feedback step */
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142 qDot1 -= beta * s0;
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143 qDot2 -= beta * s1;
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144 qDot3 -= beta * s2;
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145 qDot4 -= beta * s3;
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148 /* Integrate rate of change of quaternion to yield quaternion */
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149 q0 += qDot1 * (1.0f / sampleFreq);
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150 q1 += qDot2 * (1.0f / sampleFreq);
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151 q2 += qDot3 * (1.0f / sampleFreq);
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152 q3 += qDot4 * (1.0f / sampleFreq);
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154 /* Normalise quaternion */
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155 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
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156 quat->q0 = q0 * recipNorm;
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157 quat->q1 = q1 * recipNorm;
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158 quat->q2 = q2 * recipNorm;
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159 quat->q3 = q3 * recipNorm;
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162 /* IMU algorithm update (does not take magneto in account) */
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163 void MadgwickAHRSupdateIMU(const struct imu_info *imu, struct quaternion *quat)
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166 float s0, s1, s2, s3;
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167 float qDot1, qDot2, qDot3, qDot4;
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168 float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
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170 float q0 = quat->q0;
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171 float q1 = quat->q1;
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172 float q2 = quat->q2;
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173 float q3 = quat->q3;
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175 /* Rate of change of quaternion from gyroscope */
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176 qDot1 = 0.5f * (-q1 * imu->gx - q2 * imu->gy - q3 * imu->gz);
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177 qDot2 = 0.5f * (q0 * imu->gx + q2 * imu->gz - q3 * imu->gy);
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178 qDot3 = 0.5f * (q0 * imu->gy - q1 * imu->gz + q3 * imu->gx);
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179 qDot4 = 0.5f * (q0 * imu->gz + q1 * imu->gy - q2 * imu->gx);
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182 /* Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation) */
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183 if(!((imu->ax == 0.0f) && (imu->ay == 0.0f) && (imu->az == 0.0f))) {
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185 /* Normalise accelerometer measurement */
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186 recipNorm = invSqrt(imu->ax * imu->ax + imu->ay * imu->ay + imu->az * imu->az);
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187 ax = imu->ax * recipNorm;
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188 ay = imu->ay * recipNorm;
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189 az = imu->az * recipNorm;
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191 /* Auxiliary variables to avoid repeated arithmetic */
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206 /* Gradient decent algorithm corrective step */
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207 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
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208 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
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209 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
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210 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
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211 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); /* normalise step magnitude */
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218 /* Apply feedback step */
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219 qDot1 -= beta * s0;
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220 qDot2 -= beta * s1;
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221 qDot3 -= beta * s2;
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222 qDot4 -= beta * s3;
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225 /* Integrate rate of change of quaternion to yield quaternion */
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226 q0 += qDot1 * (1.0f / sampleFreq);
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227 q1 += qDot2 * (1.0f / sampleFreq);
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228 q2 += qDot3 * (1.0f / sampleFreq);
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229 q3 += qDot4 * (1.0f / sampleFreq);
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231 /* Normalise quaternion */
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232 recipNorm = invSqrt(q0 * q0 + q1 * q1 +
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233 q2 * q2 + q3 * q3);
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234 quat->q0 = q0 * recipNorm;
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235 quat->q1 = q1 * recipNorm;
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236 quat->q2 = q2 * recipNorm;
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237 quat->q3 = q3 * recipNorm;
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