├── IMU_Kalman-filter ├── EKF.m ├── MAIN.m └── sampledata.txt ├── README.md └── mpu9250 └── mpu9250.ino /IMU_Kalman-filter/EKF.m: -------------------------------------------------------------------------------- 1 | function [q0, q1, q2, q3] = EKF(p, q, r, B, mx, my, mz, ax, ay, az, dt, N_Q, N_R, N_P) 2 | % 3 | % 4 | global Q R 5 | global x P 6 | global firstRun 7 | 8 | %Initialize 9 | if isempty(firstRun) 10 | 11 | Q = N_Q*eye(4); 12 | 13 | R = N_R*eye(6); 14 | 15 | x = [1 0 0 0]'; 16 | P = N_P*eye(4); 17 | 18 | firstRun = 1; 19 | end 20 | 21 | %1.Predict xp and Pp 22 | %Calculate F 23 | F = Fjacob(p, q, r, dt); 24 | 25 | xp = F*x; 26 | Pp = F*P*F' + Q; 27 | 28 | %2.Correct xp and P 29 | %Calculate H 30 | H = Hjacob(x(1),x(2),x(3),x(4), B); 31 | 32 | S= (H*Pp*H' + R); 33 | K = Pp*H'*(S\eye(6)); 34 | 35 | z = [ax; 36 | ay; 37 | az; 38 | mx; 39 | my; 40 | mz]; 41 | 42 | x = xp + K*(z - H*xp); 43 | P = Pp - K*H*Pp; 44 | 45 | x_sc=(x(1)^2+x(2)^2+x(3)^2+x(4)^2)^0.5; 46 | 47 | q0 = x(1); 48 | q1 = x(2); 49 | q2 = x(3); 50 | q3 = x(4); 51 | 52 | %------------------------------ 53 | function F = Fjacob(p, q, r, dt) 54 | % 55 | % 56 | F = zeros(4); 57 | 58 | F(1,1)=1; 59 | F(1,2)= -p*dt/2; 60 | F(1,3)= -q*dt/2; 61 | F(1,4)= -r*dt/2; 62 | 63 | F(2,1)= p*dt/2; 64 | F(2,2)=1; 65 | F(2,3)= r*dt/2; 66 | F(2,4)=-q*dt/2; 67 | 68 | F(3,1)=q*dt/2; 69 | F(3,2)=-r*dt/2; 70 | F(3,3)=1; 71 | F(3,4)=p*dt/2; 72 | 73 | F(4,1)=r*dt/2; 74 | F(4,2)=p*dt/2; 75 | F(4,3)=-q*dt/2; 76 | F(4,4)=1; 77 | 78 | %------------------------------ 79 | function H = Hjacob(qt0, qt1, qt2, qt3, B) 80 | % 81 | % 82 | g=9.8; 83 | H = zeros(6,4); 84 | 85 | H(1,1) = -qt2; 86 | H(1,2) = qt3; 87 | H(1,3) = -qt0; 88 | H(1,4) = qt1; 89 | 90 | H(2,1) = qt1; 91 | H(2,2) = qt0; 92 | H(2,3) = qt3; 93 | H(2,4) = qt2; 94 | 95 | H(3,1) = qt0; 96 | H(3,2) = -qt1; 97 | H(3,3) = -qt2; 98 | H(3,4) = qt3; 99 | 100 | H(4,1) = qt0*B(1)+qt3*B(2)-qt2*B(3); 101 | H(4,2) = qt1*B(1)+qt2*B(2)+qt3*B(3); 102 | H(4,3) = -qt2*B(1)+qt1*B(2)-qt0*B(3); 103 | H(4,4) = -qt3*B(1)+qt0*B(2)+qt1*B(3); 104 | 105 | H(5,1) = -qt3*B(1)+qt0*B(2)+qt1*B(3); 106 | H(5,2) = qt2*B(1)-qt1*B(2)+qt0*B(3); 107 | H(5,3) = qt1*B(1)+qt2*B(2)+qt3*B(3); 108 | H(5,4) = -qt0*B(1)-qt3*B(2)+qt2*B(3); 109 | 110 | H(6,1) = qt2*B(1)-qt1*B(2)+qt0*B(3); 111 | H(6,2) = qt3*B(1)-qt0*B(2)-qt1*B(3); 112 | H(6,3) = qt0*B(1)+qt3*B(2)-qt2*B(3); 113 | H(6,4) = qt1*B(1)+qt2*B(2)+qt3*B(3); -------------------------------------------------------------------------------- /IMU_Kalman-filter/MAIN.m: -------------------------------------------------------------------------------- 1 | clc 2 | clear all 3 | close all 4 | 5 | %% DATA EXTRACTING 6 | fileID = fopen('sampledata.txt','r'); 7 | DATA = fscanf(fileID,'%f',[10 Inf]); % AccX_raw AccY_raw AccZ_raw GyroX_raw GyroY_raw GyroZ_raw MagX_raw MagY_raw MagZ_raw Time(ms) 8 | N = size(DATA); 9 | Nsamples = N(2)-1; %length of DATA 10 | EulerSaved = zeros(Nsamples, 3); 11 | 12 | %% INITIALIZING 13 | g = 9.8; 14 | unit_transform_acc = 16384; 15 | unit_transform_gyro = (pi/(180*131)); 16 | unit_transform_mag=0.6; 17 | Gyro_Compen_k = 30; 18 | Mag_Compen_k = 1000; 19 | ref_mag = 30; 20 | DATA_SI = (size(DATA)); 21 | N_Q = 1; 22 | N_R = 100; 23 | N_P = 1; 24 | 25 | %% LSB to SI Unit 26 | for k = 1:Nsamples 27 | %Acc LSB -> N/m^2 28 | DATA_SI(1,k)= (g/unit_transform_acc)*DATA(1,k); 29 | DATA_SI(2,k)= (g/unit_transform_acc)*DATA(2,k); 30 | DATA_SI(3,k)= (g/unit_transform_acc)*DATA(3,k); 31 | %Gyro LSB -> deg/s -> rad/s 32 | DATA_SI(4,k)= (unit_transform_gyro)*DATA(4,k); 33 | DATA_SI(5,k)= (unit_transform_gyro)*DATA(5,k); 34 | DATA_SI(6,k)= (unit_transform_gyro)*DATA(6,k); 35 | %Mag LSB -> uT 36 | DATA_SI(7,k)= unit_transform_mag*DATA(7,k); 37 | DATA_SI(8,k)= unit_transform_mag*DATA(8,k); 38 | DATA_SI(9,k)= unit_transform_mag*DATA(9,k); 39 | %Time ms -> s 40 | DATA_SI(10,k)= DATA(10,k)/1000; 41 | end 42 | 43 | %% Gyroscope Compensation 44 | for k = 1:Gyro_Compen_k 45 | Bias_GyroX=mean(DATA_SI(4,k)); 46 | Bias_GyroY=mean(DATA_SI(5,k)); 47 | Bias_GyroZ=mean(DATA_SI(6,k)); 48 | end 49 | 50 | Bias_Gyro = [Bias_GyroX Bias_GyroY Bias_GyroZ] 51 | 52 | for k = 1:Nsamples 53 | DATA_SI(4,k)=DATA_SI(4,k)-Bias_GyroX; 54 | DATA_SI(5,k)=DATA_SI(5,k)-Bias_GyroY; 55 | DATA_SI(6,k)=DATA_SI(6,k)-Bias_GyroZ; 56 | end 57 | 58 | %% Magnetometer Compensation 59 | 60 | for k = 1:Mag_Compen_k 61 | Y(k,:) = [DATA_SI(7,k)^2+DATA_SI(8,k)^2+DATA_SI(9,k)^2]; 62 | X(k,:) = [DATA_SI(7,k) DATA_SI(8,k) DATA_SI(9,k) 1]; 63 | end 64 | 65 | N_X = [size(X)]; 66 | Xsamples = N_X(2); 67 | Bias_Mag = 0.5*((X'*X)\eye(Xsamples))*X'*Y 68 | 69 | for k = 1:Nsamples 70 | DATA_SI(7,k) = DATA_SI(7,k) - Bias_Mag(1); 71 | DATA_SI(8,k) = DATA_SI(8,k) - Bias_Mag(2); 72 | DATA_SI(9,k) = DATA_SI(9,k) - Bias_Mag(3); 73 | end 74 | 75 | %% Set Reference Magnetic vector (NORMALIZATION) 76 | M=sqrt(DATA_SI(7,ref_mag)^2+DATA_SI(8,ref_mag)^2+DATA_SI(9,ref_mag)^2); 77 | B=[DATA_SI(7,ref_mag)/M DATA_SI(8,ref_mag)/M DATA_SI(9,ref_mag)/M]; 78 | 79 | %% EKF Algorithm 80 | for k = 1:Nsamples-1 81 | %Assignment 82 | ax=DATA_SI(1,k); 83 | ay=DATA_SI(2,k); 84 | az=DATA_SI(3,k); 85 | p=DATA_SI(4,k); 86 | q=DATA_SI(5,k); 87 | r=DATA_SI(6,k); 88 | mx=DATA_SI(7,k); 89 | my=DATA_SI(8,k); 90 | mz=DATA_SI(9,k); 91 | dt=(DATA_SI(10,k+1)-DATA_SI(10,k)); 92 | %Normalization 93 | G=sqrt(ax^2+ay^2+az^2); 94 | M=sqrt(mx^2+my^2+mz^2); 95 | ax=ax/G; ay=ay/G; az=az/G; mx=mx/M; my=my/M; mz=mz/M; 96 | %MAIN EKF FUNCTION 97 | [q0, q1, q2, q3] = EKF(p, q, r, B, mx, my, mz, ax, ay, az, dt, N_Q, N_R, N_P); 98 | %Conversion to Euler angle 99 | phi = atan2( 2*(q2*q3 + q0*q1), 1 - 2*(q1^2 + q2^2) ); 100 | theta = -asin( 2*(q1*q3 - q0*q2) ); 101 | psi = atan2( 2*(q1*q2 + q0*q3), 1 - 2*(q2^2 + q3^2) ); 102 | EulerSaved(k, :) = [ phi theta psi ]; 103 | end 104 | 105 | %% Plot 106 | %Radian to Degree 107 | PhiSaved = EulerSaved(:, 1) * 180/pi; 108 | ThetaSaved = EulerSaved(:, 2) * 180/pi; 109 | PsiSaved = EulerSaved(:, 3) * 180/pi; 110 | x = [0 0]; 111 | y = [-1000,1000]; 112 | 113 | figure() 114 | P1=plot(DATA_SI(10,:), PhiSaved, 'r'); 115 | hold on 116 | P2=plot(DATA_SI(10,:), ThetaSaved, 'b'); 117 | P3=plot(DATA_SI(10,:), PsiSaved, 'g'); 118 | refline([0 0]) 119 | title('Euler Angle (degree)') 120 | Timeline_1 = line('XData',x,'YData',y); 121 | TimeValue_1= xlabel(''); 122 | legend([P1 P2 P3],{'Phi', 'Theta', 'Psi'},'Location','northwest','AutoUpdate','off'); 123 | axis([0 DATA_SI(10,Nsamples) -300 300]) 124 | 125 | figure() 126 | subplot(1,3,1) 127 | plot(DATA_SI(10,:),DATA_SI(1,:),'r',DATA_SI(10,:),DATA_SI(2,:),'g',DATA_SI(10,:),DATA_SI(3,:),'b'); 128 | refline([0 0]) 129 | title('Acceleration (m/s^2)'); 130 | Timeline_2 = line('XData',x,'YData',y); 131 | TimeValue_2= xlabel(''); 132 | legend({'AccX', 'AccY', 'AccZ'},'Location','northwest','AutoUpdate','off'); 133 | axis([0 DATA_SI(10,Nsamples) -20 20]) 134 | 135 | subplot(1,3,2) 136 | plot(DATA_SI(10,:),DATA_SI(4,:),'r',DATA_SI(10,:),DATA_SI(5,:),'g',DATA_SI(10,:),DATA_SI(6,:),'b'); 137 | refline([0 0]) 138 | title('Angular velocity (rad/s)') 139 | Timeline_3 = line('XData',x,'YData',y); 140 | TimeValue_3= xlabel(''); 141 | legend({'GyroX', 'GyroY', 'GyroZ'},'Location','northwest','AutoUpdate','off'); 142 | axis([0 DATA_SI(10,Nsamples) -3 3]) 143 | 144 | subplot(1,3,3) 145 | plot(DATA_SI(10,:),DATA_SI(7,:),'r',DATA_SI(10,:),DATA_SI(8,:),'g',DATA_SI(10,:),DATA_SI(9,:),'b'); 146 | refline([0 0]) 147 | title('Magnetic flux density (uT)') 148 | Timeline_4 = line('XData',x,'YData',y); 149 | TimeValue_4= xlabel(''); 150 | legend({'MagX', 'MagY', 'MagZ'},'Location','northwest','AutoUpdate','off'); 151 | axis([0 DATA_SI(10,Nsamples) -40 40]) 152 | 153 | %% Graphical Plot & Dynamic Plot 154 | %set IMU Object's vertex 155 | Cuboid_1=[-2,-3,-0.5]; 156 | Cuboid_2=[2,-3,-0.5]; 157 | Cuboid_3=[2,3,-0.5]; 158 | Cuboid_4=[-2,3,-0.5]; 159 | Cuboid_5=[-2,-3,0.5]; 160 | Cuboid_6=[2,-3,0.5]; 161 | Cuboid_7=[2,3,0.5]; 162 | Cuboid_8=[-2,3,0.5]; 163 | Cuboid=[Cuboid_1; Cuboid_2; Cuboid_3; Cuboid_4; Cuboid_5; Cuboid_6; Cuboid_7; Cuboid_8]; 164 | % ? 165 | fac = [1 2 6 5;2 3 7 6;3 4 8 7;4 1 5 8;1 2 3 4;5 6 7 8]; 166 | %Plot Object 167 | figure() 168 | view(3) 169 | Obejct_IMU = patch('Faces', fac, 'Vertices', [0, 0, 0]); 170 | Obejct_IMU.FaceColor = 'g'; 171 | axis([-5 5 -5 5 -5 5]) 172 | title('IMU state') 173 | Realtime = xlabel(' '); 174 | %Animate 175 | for k=1:Nsamples-1 176 | %Rotation matrix for vertex 177 | Rz = [cosd(PsiSaved(k)) -sind(PsiSaved(k)) 0; sind(PsiSaved(k)) cosd(PsiSaved(k)) 0; 0 0 1]; 178 | Ry = [cosd(ThetaSaved(k)) 0 sind(ThetaSaved(k)); 0 1 0; -sind(ThetaSaved(k)) 0 cosd(ThetaSaved(k))]; 179 | Rx = [1 0 0; 0 cosd(PhiSaved(k)) -sind(PhiSaved(k)); 0 sind(PhiSaved(k)) cosd(PhiSaved(k))]; 180 | dt=(DATA_SI(10,k+1)-DATA_SI(10,k)); 181 | for j=1:8 182 | %Rotated vertex 183 | Result_1(j,:,k) = Rx*Ry*Rz*Cuboid(j,:)'; 184 | end 185 | %Display realtime object and time 186 | set(Obejct_IMU, 'Vertices', Result_1(:,:,k)) 187 | set(Realtime, 'String', sprintf('time = %.2f [s]', DATA_SI(10, k))) 188 | %Display realtime sensor values 189 | set(TimeValue_1, 'String', sprintf('Phi: %.2f Theta: %.2f Psi: %.2f', PhiSaved(k), ThetaSaved(k), PsiSaved(k))); 190 | set(TimeValue_2, 'String', sprintf('X: %.2f Y: %.2f Z: %.2f', DATA_SI(1,k), DATA_SI(2,k), DATA_SI(3,k))); 191 | set(TimeValue_3, 'String', sprintf('X: %.2f Y: %.2f Z: %.2f', DATA_SI(4,k), DATA_SI(5,k), DATA_SI(6,k))); 192 | set(TimeValue_4, 'String', sprintf('X: %.2f Y: %.2f Z: %.2f', DATA_SI(7,k), DATA_SI(8,k), DATA_SI(9,k))); 193 | %Display timeline 194 | set(Timeline_1, 'XData', [DATA_SI(10, k) DATA_SI(10, k)]); 195 | set(Timeline_2, 'XData', [DATA_SI(10, k) DATA_SI(10, k)]); 196 | set(Timeline_3, 'XData', [DATA_SI(10, k) DATA_SI(10, k)]); 197 | set(Timeline_4, 'XData', [DATA_SI(10, k) DATA_SI(10, k)]); 198 | % pause(dt) 199 | drawnow 200 | end -------------------------------------------------------------------------------- /IMU_Kalman-filter/sampledata.txt: 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-47 -42 -22 -32 -25 68285 1378 | 536 2756 17116 42 -86 -4 -23 -33 -24 68333 1379 | 544 2708 17172 -976 -104 56 -22 -34 -24 68379 1380 | 644 2596 17144 314 -71 -19 -22 -33 -26 68427 1381 | 608 2708 17044 863 -36 -49 -20 -33 -23 68475 1382 | 552 2884 17076 640 -16 -31 -22 -30 -23 68523 -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # IMU_Kalman-filter_MATLAB 2 | Attitude estimation and animated plot using MATLAB Extended Kalman Filter with MPU9250 (9-Axis IMU) 3 | 4 | This is a Kalman filter algorithm for 9-Axis IMU sensors. (Accelerometer, Gyroscope, Magnetometer) 5 | 6 | You can see graphically animated IMU sensor with data. 7 | 8 | 9 | 10 | # Demonstration 11 | 12 | https://youtu.be/NHTlb84UMCk 13 | 14 | 15 | # Features 16 | 1. Animated plot 17 | 2. Timeline 18 | 3. Hard-iron bias compensation 19 | 4. Angular velocity bias compensation 20 | 5. EKF based on quarternion dynamics 21 | 22 | # Description 23 | MAIN : Main code 24 | 25 | EKF : Main EKF function 26 | 27 | sampledata : sampledata I used 28 | 29 | mpu9250: If you use mpu9250 and arduino, you can get your sampledata by uploading this file to your arduino. I edited this code from http://arduinolearning.com/code/arduino-mpu-9250-example.php 30 | 31 | 32 | # How to use 33 | **1. Get data from IMU sensor.** 34 | 35 | You should stay put IMU sensor for the first 2~3 seconds(until Gyro_Compen_k, It's for gyro compensation), then rotate it. 36 | 37 | I recommend you to rotate it several times, different directions. (It's good for magnetometer compensation.) 38 | 39 | **2. The data must look like this ↓** 40 | 41 | 42 | 'AccX AccY AccZ GyroX GyroY GyroZ MagX MagY MagZ time' (for k=1) 43 | 44 | 'AccX AccY AccZ GyroX GyroY GyroZ MagX MagY MagZ time' (for k=2) 45 | 46 | . 47 | 48 | . 49 | 50 | . 51 | 52 | (time: IMU running time in ms) 53 | 54 | If you use arduino, you can copy from serial monitor, and paste it at sampledata.txt 55 | 56 | **3. Edit Initializing variables.** 57 | 58 | unit_transform_acc : Converting constant for LSB to N/m^2 (I call the raw data's unit as LSB, It could be wrong. The important thing is that you should convert raw data units to SI units.) 59 | 60 | unit_transform_gyro : Converting constant for LSB to rad/s 61 | 62 | Gyro_Compen_k : 1\~k'th data will be used for gyro compensation. I recommend 30 63 | 64 | Mag_Compen_k : 1\~k'th data will be used for magnetometer compensation. I recommend Nsamples 65 | 66 | ref_mag : ref_mag'th data will be reference for psi. I recommend below 30 67 | 68 | N_Q : N_Q * unit_matrix for Q matrix 69 | 70 | N_R : N_R * unit_matrix for R matrix 71 | 72 | N_P : N_P * unit_matrix for P matrix 73 | 74 | **4. Run** 75 | 76 | If the code is slow, you can comment out the 'Graphical Plot & Dynamic Plot'. you will see only graph. 77 | 78 | # Reference 79 | https://github.com/pronenewbits/Arduino_AHRS_System 80 | 81 | http://arduinolearning.com/code/arduino-mpu-9250-example.php 82 | 83 | MPU-9250 Datasheet & Register map 84 | 85 | 칼만 필터는 어렵지 않아 with MATLAB Examples - 김성필 (Steady seller about Kalman filter written in Korean) 86 | 87 | 88 | # Closing 89 | If you have better idea or find error, please let me know. 90 | 91 | But, I'm not good at english, so I will be grateful if you explain it easily. 92 | -------------------------------------------------------------------------------- /mpu9250/mpu9250.ino: -------------------------------------------------------------------------------- 1 | #include 2 | 3 | #define MPU9250_ADDRESS 0x68 4 | #define MAG_ADDRESS 0x0C 5 | 6 | #define GYRO_FULL_SCALE_250_DPS 0x00 7 | #define GYRO_FULL_SCALE_500_DPS 0x08 8 | #define GYRO_FULL_SCALE_1000_DPS 0x10 9 | #define GYRO_FULL_SCALE_2000_DPS 0x18 10 | 11 | #define ACC_FULL_SCALE_2_G 0x00 12 | #define ACC_FULL_SCALE_4_G 0x08 13 | #define ACC_FULL_SCALE_8_G 0x10 14 | #define ACC_FULL_SCALE_16_G 0x18 15 | 16 | 17 | //Funcion auxiliar lectura 18 | void I2Cread(uint8_t Address, uint8_t Register, uint8_t Nbytes, uint8_t* Data) 19 | { 20 | Wire.beginTransmission(Address); 21 | Wire.write(Register); 22 | Wire.endTransmission(); 23 | 24 | Wire.requestFrom(Address, Nbytes); 25 | uint8_t index = 0; 26 | while (Wire.available()) 27 | Data[index++] = Wire.read(); 28 | } 29 | 30 | 31 | // Funcion auxiliar de escritura 32 | void I2CwriteByte(uint8_t Address, uint8_t Register, uint8_t Data) 33 | { 34 | Wire.beginTransmission(Address); 35 | Wire.write(Register); 36 | Wire.write(Data); 37 | Wire.endTransmission(); 38 | } 39 | 40 | 41 | void setup() 42 | { 43 | Wire.begin(); 44 | Serial.begin(9600); 45 | 46 | // Configurar acelerometro 47 | I2CwriteByte(MPU9250_ADDRESS, 28, ACC_FULL_SCALE_16_G); 48 | // Configurar giroscopio 49 | I2CwriteByte(MPU9250_ADDRESS, 27, GYRO_FULL_SCALE_2000_DPS); 50 | // Configurar magnetometro 51 | I2CwriteByte(MPU9250_ADDRESS, 0x37, 0x02); 52 | I2CwriteByte(MAG_ADDRESS, 0x0A, 0x01); 53 | } 54 | 55 | 56 | void loop() 57 | { 58 | unsigned long millisTime = millis(); 59 | // --- Lectura acelerometro y giroscopio --- 60 | uint8_t Buf[14]; 61 | I2Cread(MPU9250_ADDRESS, 0x3B, 14, Buf); 62 | 63 | // Convertir registros acelerometro 64 | int16_t ax = -(Buf[0] << 8 | Buf[1]); 65 | int16_t ay = -(Buf[2] << 8 | Buf[3]); 66 | int16_t az = Buf[4] << 8 | Buf[5]; 67 | 68 | // Convertir registros giroscopio 69 | int16_t gx = -(Buf[8] << 8 | Buf[9]); 70 | int16_t gy = -(Buf[10] << 8 | Buf[11]); 71 | int16_t gz = Buf[12] << 8 | Buf[13]; 72 | 73 | 74 | 75 | // --- Lectura del magnetometro --- 76 | uint8_t ST1; 77 | I2CwriteByte(MAG_ADDRESS,0x0A,0x01); 78 | do 79 | { 80 | I2Cread(MAG_ADDRESS, 0x02, 1, &ST1); 81 | } while (!(ST1 & 0x01)); 82 | 83 | uint8_t Mag[7]; 84 | I2Cread(MAG_ADDRESS, 0x03, 7, Mag); 85 | 86 | 87 | // Convertir registros magnetometro 88 | int16_t mx = -(Mag[3] << 8 | Mag[2]); 89 | int16_t my = -(Mag[1] << 8 | Mag[0]); 90 | int16_t mz = -(Mag[5] << 8 | Mag[4]); 91 | 92 | 93 | // --- Mostrar valores --- 94 | 95 | // Acelerometro 96 | Serial.print(ax, DEC); 97 | Serial.print("\t"); 98 | Serial.print(ay, DEC); 99 | Serial.print("\t"); 100 | Serial.print(az, DEC); 101 | Serial.print("\t"); 102 | 103 | // Giroscopio 104 | Serial.print(gx, DEC); 105 | Serial.print("\t"); 106 | Serial.print(gy, DEC); 107 | Serial.print("\t"); 108 | Serial.print(gz, DEC); 109 | Serial.print("\t"); 110 | 111 | 112 | // Magnetometro 113 | Serial.print(mx, DEC); 114 | Serial.print("\t"); 115 | Serial.print(my, DEC); 116 | Serial.print("\t"); 117 | Serial.print(mz, DEC); 118 | Serial.print("\t"); 119 | 120 | // Fin medicion 121 | Serial.println(millisTime); 122 | 123 | delay(5); 124 | } 125 | --------------------------------------------------------------------------------