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annotate src/compass_calib.c @ 282:7d9edd3b8c86

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Make a more compact COMPASS calibration code (<7KB), and add more tests.
author jDG
date Fri, 22 May 2015 14:50:40 +0200
parents a4bff632e97b
children ca4556fb60b9
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1 //////////////////////////////////////////////////////////////////////////////
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2 /// compass_calib.c
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3 /// Calibrate hard-iron for magnetic compass measurements.
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4 /// Copyright (c) 2012-2015, JD Gascuel, HeinrichsWeikamp, all right reserved.
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5 //////////////////////////////////////////////////////////////////////////////
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6 // 2015-05-22 [jDG] Make a smaller calibration code (15.6 --> 6.7 KB).
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7
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8 #include "compass.h"
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9
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10 //////////////////////////////////////////////////////////////////////////////
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11 // mH: Put compass data into bank 8 (stack) and bank 9 (variables)
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12 #ifndef UNIX
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13 # pragma udata overlay bank8=0x800
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14 static char C_STACK[256]; // Overlay C-code data stack here.
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15 # define RESET_C_STACK \
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16 _asm \
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17 LFSR 1, 0x800 \
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18 LFSR 2, 0x800 \
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19 _endasm
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20 # pragma udata overlay bank9_compass
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21 #else
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22 # define RESET_C_STACK
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23 #endif
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24
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25 //////////////////////////////////////////////////////////////////////////////
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26
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27 static unsigned short int compass_N;
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28
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29 static float Su, Sv, Sw; // First order moments.
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30 static float Suu, Svv, Sww, Suv, Suw, Svw; // Second order moments.
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31 static float Saa; // Suu + Svv + Sww
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32 static float Saau; // Suuu + Svvu + Swwu // Third order moment.
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33 static float Saav; // Suuv + Svvv + Swwv
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34 static float Saaw; // Suuw + Svvw + Swww
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35 static float yu, yv, yw; // temp solution vector.
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36 static float uc, vc, wc; // temp sphere's center.
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37
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38 //////////////////////////////////////////////////////////////////////////////
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39
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40 void compass_reset_calibration()
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41 {
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42 RESET_C_STACK;
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43
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44 compass_N = 0;
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45 Su = Sv = Sw = 0.0;
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46 Suu = Svv = Sww = Suv = Suw = Svw = 0.0;
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47 Saau = Saav = Saaw = 0.0;
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48 compass_CX_f = compass_CY_f = compass_CZ_f = 0;
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49 }
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50
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51 //////////////////////////////////////////////////////////////////////////////
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52
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53 void compass_add_calibration()
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54 {
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55 RESET_C_STACK;
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56
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57 // Get filtered/calibrated magnetic direction:
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58 yu = (compass_DX_f - compass_CX_f) / 32768.0f;
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59 yv = (compass_DY_f - compass_CY_f) / 32768.0f;
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60 yw = (compass_DZ_f - compass_CZ_f) / 32768.0f;
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61
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62 // Add to all moments:
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63 compass_N++;
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64
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65 Su += yu;
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66 Sv += yv;
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67 Sw += yw;
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68
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69 Suu += yu*yu;
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70 Suv += yu*yv;
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71 Suw += yu*yw;
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72 Svv += yv*yv;
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73 Svw += yv*yw;
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74 Sww += yw*yw;
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75
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76 Saa = yu*yu + yv*yv + yw*yw;
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77 Saau += yu * Saa;
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78 Saav += yv * Saa;
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79 Saaw += yw * Saa;
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80 }
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81
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82 //////////////////////////////////////////////////////////////////////////////
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83
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84 static float compass_discriminent(PARAMETER char column)
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85 {
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86 // Basic symetric matrix:
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87 OVERLAY float a = Suu, d = Suv, g = Suw;
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88 OVERLAY float b = Suv, e = Svv, h = Svw;
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89 OVERLAY float c = Suw, f = Svw, i = Sww;
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90
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91 // Substitute a column, if asked to:
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92 if( column==1 ) { a = yu; b = yv; c = yw; }
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93 if( column==2 ) { d = yu; e = yv; f = yw; }
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94 if( column==3 ) { g = yu; h = yv; i = yw; }
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95
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96 // Do the math:
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97 return a * (e * i - f * h)
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98 - b * (d * i - f * g)
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99 + c * (d * h - e * g);
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100 }
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101
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102 //////////////////////////////////////////////////////////////////////////////
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103
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104 static float compass_dotc(PARAMETER float u, float v, float w)
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105 {
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106 return u*uc + v*vc + w*wc;
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107 }
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108
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109 //////////////////////////////////////////////////////////////////////////////
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110
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111 void compass_solve_calibration()
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112 {
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113 OVERLAY float delta;
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114 RESET_C_STACK;
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115
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116 //---- Compute center of measured magnetic directions --------------------
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117 uc = Su/compass_N;
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118 vc = Sv/compass_N;
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119 wc = Sw/compass_N;
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120
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121 //---- Normalize partial sums --------------------------------------------
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122 //
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123 // We measured the (u, v, w) values, and need the centered (x, y, z) ones
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124 // around the sphere center's (uc, vc, wc) as:
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125 // uc = Su / N; The mean value
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126 // x = u - uc; The differnce to the mean.
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127 //
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128 // So:
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129 // x**2 = (u - uc)**2 = u**2 - 2u*uc + uc**2
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130 //
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131 // We need the Sxx sum of 2nd orders:
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132 // Sxx = Suu - 2 uc Su + N*uc*(Su/N) = Suu - uc Su
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133 Suu -= Su*uc;
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134 Svv -= Sv*vc;
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135 Sww -= Sw*wc;
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136
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137 // (u - uc)(v - vc) = uv - u vc - v uc + uc vc
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138 // Sxy = Suv - Su vc - Sv uc + N uc vc
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139 // = Suv - Su vc - N vc uc + N uc vc
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140 // = Suv - Su vc
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141 Suv -= Su*vc;
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142 Suw -= Su*wc;
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143 Svw -= Sv*wc;
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144
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145 // (u + um)**3 = u**3 + 3 u**2 um + 3 u um**2 + um**3
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146 // Sxxx = Suuu + 3 um Suu + 3 um**2 Su + N.um**3
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147 // Su = 0, um = Sx/N:
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148 // Suuu = Sxxx - 3 Sx*Suu/N - N.(Sx/N)**3
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149 // = Sxxx - 3 Sx*Suu/N - Sx**3/N**2
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150
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151 // (u + um)**2 (v + vm) = (u**2 + 2 u um + um**2)(v + vm)
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152 // Sxxy = Suuv + vm Suu + 2 um (Suv + vm Su) + um**2 (Sv + N.vm)
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153 //
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154 // Su = 0, Sv = 0, vm = Sy/N:
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155 // Sxxy = Suuv + vm Suu + 2 um Suv + N um**2 vm
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156 //
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157 // Suuv = Sxxy - (Sy/N) Suu - 2 (Sx/N) Suv - (Sx/N)**2 Sy
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158 // = Sxxy - Suu*Sy/N - 2 Suv*Sx/N - Sx*Sx*Sy/N/N
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159 // = Sxxy - (Suu + Sx*Sx/N)*Sy/N - 2 Suv*Sx/N
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160 Saa = Suu + Svv + Sww;
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161 yu = Saau - Saa*uc - compass_dotc(Su*uc + 2*Suu, Sv*uc + 2*Suv, Sw*uc + 2*Suw);
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162 yv = Saav - Saa*vc - compass_dotc(Su*vc + 2*Suv, Sv*vc + 2*Svv, Sw*vc + 2*Svw);
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163 yw = Saaw - Saa*wc - compass_dotc(Su*wc + 2*Suw, Sv*wc + 2*Svw, Sw*wc + 2*Sww);
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164
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165 //---- Solve the system --------------------------------------------------
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166 // uc Suu + vc Suv + wc Suw = (Suuu + Svvu + Swwu) / 2
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167 // uc Suv + vc Svv + wc Svw = (Suuv + Svvv + Swwv) / 2
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168 // uc Suw + vc Svw + wc Sww = (Suuw + Svvw + Swww) / 2
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169 // Note this is symetric, with a positiv diagonal, hence
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170 // discriminent is always not null.
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171 delta = 0.5f / compass_discriminent(0);
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172
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173 // So computed new center, with offsetted values:
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174 uc += compass_discriminent(1) * delta;
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175 vc += compass_discriminent(2) * delta;
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176 wc += compass_discriminent(3) * delta;
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177
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178 // Add correction due to already applyed calibration:
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179 compass_CX_f += (short)(32768 * uc);
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180 compass_CY_f += (short)(32768 * vc);
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181 compass_CZ_f += (short)(32768 * wc);
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182 }