Diff: MPU9250/MPU9250.cpp

Revision:

0:17f575135219

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/MPU9250/MPU9250.cpp	Fri Sep 07 04:11:48 2018 +0000
@@ -0,0 +1,901 @@
+#include "mbed.h"
+#include "math.h"
+#include "MPU9250.h"
+
+
+MPU9250::MPU9250(PinName sda, PinName scl, RawSerial* serial_p)
+    :
+    i2c_p(new I2C(sda,scl)),
+    i2c(*i2c_p),
+    pc_p(serial_p)
+{
+    initializeValue();
+}
+
+MPU9250::~MPU9250(){}
+
+
+/*---------- public function ----------*/
+bool MPU9250::Initialize(void){
+    uint8_t whoami;
+
+    i2c.frequency(400000);                                      // use fast (400 kHz) I2C  
+    timer.start();
+
+    whoami = Whoami_MPU9250();
+    pc_p->printf("I AM 0x%x\n\r", whoami); pc_p->printf("I SHOULD BE 0x71\n\r");
+  
+    if(whoami == IAM_MPU9250){
+        resetMPU9250();                                                 // Reset registers to default in preparation for device calibration
+        calibrateMPU9250(gyroBias, accelBias);  // Calibrate gyro and accelerometers, load biases in bias registers
+        wait(1);
+
+        initMPU9250();
+        initAK8963(magCalibration);
+    
+    pc_p->printf("Accelerometer full-scale range = %f  g\n\r", 2.0f*(float)(1<<Ascale));
+    pc_p->printf("Gyroscope full-scale range = %f  deg/s\n\r", 250.0f*(float)(1<<Gscale));
+
+    if(Mscale == 0) pc_p->printf("Magnetometer resolution = 14  bits\n\r");
+    if(Mscale == 1) pc_p->printf("Magnetometer resolution = 16  bits\n\r");
+    if(Mmode == 2) pc_p->printf("Magnetometer ODR = 8 Hz\n\r");
+    if(Mmode == 6) pc_p->printf("Magnetometer ODR = 100 Hz\n\r");
+    
+        getAres();
+        getGres();
+        getMres();
+
+    pc_p->printf("mpu9250 initialized\r\n");
+    return true;
+    }else return false;
+}
+
+bool MPU9250::sensingAcGyMg(){
+    if(readByte(MPU9250_ADDRESS, INT_STATUS) & 0x01) {  // On interrupt, check if data ready interrupt
+    sensingAccel();
+        sensingGyro();   
+        sensingMag();   
+    return true;
+  }else return false;
+}
+
+
+void MPU9250::calculatePostureAngle(float degree[3]){   
+  Now = timer.read_us();
+  deltat = (float)((Now - lastUpdate)/1000000.0f); // set integration time by time elapsed since last filter update
+  lastUpdate = Now;
+    
+//  if(lastUpdate - firstUpdate > 10000000.0f) {
+//      beta = 0.04;  // decrease filter gain after stabilized
+//      zeta = 0.015; // increasey bias drift gain after stabilized
+//  }
+    
+  // Pass gyro rate as rad/s
+  MadgwickQuaternionUpdate(ax, ay, az, gx*PI/180.0f, gy*PI/180.0f, gz*PI/180.0f,  my,  mx, mz);
+  MahonyQuaternionUpdate(ax, ay, az, gx*PI/180.0f, gy*PI/180.0f, gz*PI/180.0f, my, mx, mz);   //my, mx, mzになってるけどセンサの設置上の都合だろうか
+      
+  // Define output variables from updated quaternion---these are Tait-Bryan angles, commonly used in aircraft orientation.
+  // In this coordinate system, the positive z-axis is down toward Earth. 
+  // Yaw is the angle between Sensor x-axis and Earth magnetic North (or true North if corrected for local declination, looking down on the sensor positive yaw is counterclockwise.
+  // Pitch is angle between sensor x-axis and Earth ground plane, toward the Earth is positive, up toward the sky is negative.
+  // Roll is angle between sensor y-axis and Earth ground plane, y-axis up is positive roll.
+  // These arise from the definition of the homogeneous rotation matrix constructed from quaternions.
+  // Tait-Bryan angles as well as Euler angles are non-commutative; that is, the get the correct orientation the rotations must be
+  // applied in the correct order which for this configuration is yaw, pitch, and then roll.
+  // For more see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles which has additional links.
+  translateQuaternionToDeg(q);
+    calibrateDegree();  
+    degree[0] = roll;
+    degree[1] = pitch;
+    degree[2] = yaw;
+}
+
+
+float MPU9250::calculateYawByMg(){
+    transformCoordinateFromCompassToMPU();
+    lpmag[0] = LPGAIN_MAG *lpmag[0] + (1 - LPGAIN_MAG)*mx;
+    lpmag[1] = LPGAIN_MAG *lpmag[1] + (1 - LPGAIN_MAG)*my;
+    lpmag[2] = LPGAIN_MAG *lpmag[2] + (1 - LPGAIN_MAG)*mz;
+    
+    float radroll = PI/180.0f * roll;
+    float radpitch = PI/180.0f * pitch;
+
+    return 180.0f/PI * atan2(lpmag[2]*sin(radpitch) - lpmag[1]*cos(radpitch),
+                                         lpmag[0]*cos(radroll) - lpmag[1]*sin(radroll)*sin(radpitch) + lpmag[2]*sin(radroll)*cos(radpitch));
+}
+
+
+// Accelerometer and gyroscope self test; check calibration wrt factory settings
+void MPU9250::MPU9250SelfTest(float * destination) // Should return percent deviation from factory trim values, +/- 14 or less deviation is a pass
+{
+    uint8_t rawData[6] = {0, 0, 0, 0, 0, 0};
+    uint8_t selfTest[6];
+    int16_t gAvg[3], aAvg[3], aSTAvg[3], gSTAvg[3];
+    float factoryTrim[6];
+    uint8_t FS = 0;
+   
+    writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x00); // Set gyro sample rate to 1 kHz
+    writeByte(MPU9250_ADDRESS, CONFIG, 0x02); // Set gyro sample rate to 1 kHz and DLPF to 92 Hz
+    writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 1<<FS); // Set full scale range for the gyro to 250 dps
+    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, 0x02); // Set accelerometer rate to 1 kHz and bandwidth to 92 Hz
+    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 1<<FS); // Set full scale range for the accelerometer to 2 g
+
+    for( int ii = 0; ii < 200; ii++) { // get average current values of gyro and acclerometer
+        readBytes(MPU9250_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]); // Read the six raw data registers into data array
+        aAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ; // Turn the MSB and LSB into a signed 16-bit value
+    aAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
+        aAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
+        
+        readBytes(MPU9250_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]); // Read the six raw data registers sequentially into data array
+        gAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ; // Turn the MSB and LSB into a signed 16-bit value
+        gAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
+        gAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
+    }
+  
+    for (int ii =0; ii < 3; ii++) { // Get average of 200 values and store as average current readings
+        aAvg[ii] /= 200;
+        gAvg[ii] /= 200;
+    }
+  
+    // Configure the accelerometer for self-test
+    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0xE0); // Enable self test on all three axes and set accelerometer range to +/- 2 g
+    writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 0xE0); // Enable self test on all three axes and set gyro range to +/- 250 degrees/s
+    //delay(55); // Delay a while to let the device stabilize
+
+    for( int ii = 0; ii < 200; ii++) { // get average self-test values of gyro and acclerometer
+        readBytes(MPU9250_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]); // Read the six raw data registers into data array
+        aSTAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ; // Turn the MSB and LSB into a signed 16-bit value
+        aSTAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
+        aSTAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
+        
+        readBytes(MPU9250_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]); // Read the six raw data registers sequentially into data array
+        gSTAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ; // Turn the MSB and LSB into a signed 16-bit value
+        gSTAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
+        gSTAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
+    }
+  
+    for (int ii =0; ii < 3; ii++) { // Get average of 200 values and store as average self-test readings
+        aSTAvg[ii] /= 200;
+        gSTAvg[ii] /= 200;
+    }
+  
+ // Configure the gyro and accelerometer for normal operation
+    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0x00);
+    writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 0x00);
+    //delay(45); // Delay a while to let the device stabilize
+   
+  // Retrieve accelerometer and gyro factory Self-Test Code from USR_Reg
+    selfTest[0] = readByte(MPU9250_ADDRESS, SELF_TEST_X_ACCEL); // X-axis accel self-test results
+    selfTest[1] = readByte(MPU9250_ADDRESS, SELF_TEST_Y_ACCEL); // Y-axis accel self-test results
+    selfTest[2] = readByte(MPU9250_ADDRESS, SELF_TEST_Z_ACCEL); // Z-axis accel self-test results
+    selfTest[3] = readByte(MPU9250_ADDRESS, SELF_TEST_X_GYRO); // X-axis gyro self-test results
+    selfTest[4] = readByte(MPU9250_ADDRESS, SELF_TEST_Y_GYRO); // Y-axis gyro self-test results
+    selfTest[5] = readByte(MPU9250_ADDRESS, SELF_TEST_Z_GYRO); // Z-axis gyro self-test results
+
+    // Retrieve factory self-test value from self-test code reads
+    factoryTrim[0] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[0] - 1.0) )); // FT[Xa] factory trim calculation
+    factoryTrim[1] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[1] - 1.0) )); // FT[Ya] factory trim calculation
+    factoryTrim[2] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[2] - 1.0) )); // FT[Za] factory trim calculation
+    factoryTrim[3] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[3] - 1.0) )); // FT[Xg] factory trim calculation
+    factoryTrim[4] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[4] - 1.0) )); // FT[Yg] factory trim calculation
+    factoryTrim[5] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[5] - 1.0) )); // FT[Zg] factory trim calculation
+ 
+    // Report results as a ratio of (STR - FT)/FT; the change from Factory Trim of the Self-Test Response
+    // To get percent, must multiply by 100
+    for (int i = 0; i < 3; i++) {
+        destination[i] = 100.0*((float)(aSTAvg[i] - aAvg[i]))/factoryTrim[i]; // Report percent differences
+        destination[i+3] = 100.0*((float)(gSTAvg[i] - gAvg[i]))/factoryTrim[i+3]; // Report percent differences
+    } 
+}
+
+void MPU9250::pickupAccel(float accel[3]){
+    sensingAccel();
+    accel[0] = ax;
+    accel[1] = ay;
+    accel[2] = az;
+}
+
+void MPU9250::pickupGyro(float gyro[3]){
+    sensingGyro();
+    gyro[0] = gx;
+    gyro[1] = gy;
+    gyro[2] = gz;
+}
+
+void MPU9250::pickupMag(float mag[3]){
+    sensingMag();
+    mag[0] = mx;
+    mag[1] = my;
+    mag[2] = mz;
+}
+
+float MPU9250::pickupTemp(void){
+    sensingTemp();
+    return temperature;
+}
+
+void MPU9250::displayAccel(void){
+    pc_p->printf("ax = %f", 1000*ax); 
+  pc_p->printf(" ay = %f", 1000*ay); 
+  pc_p->printf(" az = %f  mg\n\r", 1000*az); 
+}
+
+void MPU9250::displayGyro(void){
+  pc_p->printf("gx = %f", gx); 
+  pc_p->printf(" gy = %f", gy); 
+  pc_p->printf(" gz = %f  deg/s\n\r", gz); 
+}
+
+void MPU9250::displayMag(void){
+  pc_p->printf("mx = %f,", mx); 
+  pc_p->printf(" my = %f,", my); 
+  pc_p->printf(" mz = %f  mG\n\r", mz); 
+}
+
+void MPU9250::displayQuaternion(void){
+  pc_p->printf("q0 = %f\n\r", q[0]);
+  pc_p->printf("q1 = %f\n\r", q[1]);
+  pc_p->printf("q2 = %f\n\r", q[2]);
+  pc_p->printf("q3 = %f\n\r", q[3]);
+}
+
+void MPU9250::displayAngle(void){
+    //pc_p->printf("$%d %d %d;",(int)(yaw*100),(int)(pitch*100),(int)(roll*100));
+    pc_p->printf("Roll: %f\tPitch: %f\tYaw: %f\n\r",  roll,   pitch,   yaw);
+}
+
+void MPU9250::displayTemperature(void){
+    pc_p->printf(" temperature = %f  C\n\r", temperature);
+}
+
+void MPU9250::setMagBias(float bias_x, float bias_y, float bias_z){
+    magbias[0] = bias_x;
+    magbias[1] = bias_y;
+    magbias[2] = bias_z;
+}
+
+/*---------- private function ----------*/
+
+void MPU9250::writeByte(uint8_t address, uint8_t subAddress, uint8_t data)
+{
+    char data_write[2];
+    
+    data_write[0] = subAddress;
+  data_write[1] = data;
+  i2c.write(address, data_write, 2, 0);
+}
+
+char MPU9250::readByte(uint8_t address, uint8_t subAddress)
+{
+    char data[1]; // `data` will store the register data     
+    char data_write[1];
+    
+    data_write[0] = subAddress;
+    i2c.write(address, data_write, 1, 1); // no stop
+    i2c.read(address, data, 1, 0); 
+    return data[0]; 
+}
+
+void MPU9250::readBytes(uint8_t address, uint8_t subAddress, uint8_t count, uint8_t * dest)
+{     
+    char data[14];
+    char data_write[1];
+    
+    data_write[0] = subAddress;
+    i2c.write(address, data_write, 1, 1); // no stop
+    i2c.read(address, data, count, 0); 
+    for(int ii = 0; ii < count; ii++) {
+        dest[ii] = data[ii];
+  }
+} 
+
+void MPU9250::initializeValue(void){
+    Ascale = AFS_2G;     // AFS_2G, AFS_4G, AFS_8G, AFS_16G
+    Gscale = GFS_250DPS; // GFS_250DPS, GFS_500DPS, GFS_1000DPS, GFS_2000DPS
+    Mscale = MFS_16BITS; // MFS_14BITS or MFS_16BITS, 14-bit or 16-bit magnetometer resolution
+    Mmode = 0x06;        // Either 8 Hz 0x02) or 100 Hz (0x06) magnetometer data ODR  
+
+    GyroMeasError = PI * (60.0f / 180.0f);
+    beta = sqrt(3.0f / 4.0f) * GyroMeasError;  // compute beta
+    GyroMeasDrift = PI * (1.0f / 180.0f);      // gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
+    zeta = sqrt(3.0f / 4.0f) * GyroMeasDrift;  // compute zeta, the other free parameter in the Madgwick scheme usually set to a small or zero value
+
+    deltat = 0.0f;                             // integration interval for both filter schemes
+    lastUpdate = 0, firstUpdate = 0, Now = 0;    // used to calculate integration interval                               // used to calculate integration interval
+
+    for(int i=0; i<3; i++){
+        magCalibration[i] = 0;
+        gyroBias[i] = 0;
+        accelBias[i] = 0;
+        magbias[i] = 0;
+
+        eInt[i] = 0.0f; 
+    
+        lpmag[i] = 0.0f;
+    }
+
+    q[0] = 1.0f;
+    q[1] = 0.0f;
+    q[2] = 0.0f;
+    q[3] = 0.0f;
+}
+
+void MPU9250::initMPU9250(void)
+{  
+    // Initialize MPU9250 device
+    // wake up device
+    writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00); // Clear sleep mode bit (6), enable all sensors 
+    wait(0.1); // Delay 100 ms for PLL to get established on x-axis gyro; should check for PLL ready interrupt  
+
+    // get stable time source
+    writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x01);  // Set clock source to be PLL with x-axis gyroscope reference, bits 2:0 = 001
+
+    // Configure Gyro and Accelerometer
+    // Disable FSYNC and set accelerometer and gyro bandwidth to 44 and 42 Hz, respectively; 
+    // DLPF_CFG = bits 2:0 = 010; this sets the sample rate at 1 kHz for both
+    // Maximum delay is 4.9 ms which is just over a 200 Hz maximum rate
+    writeByte(MPU9250_ADDRESS, CONFIG, 0x03);  
+
+    // Set sample rate = gyroscope output rate/(1 + SMPLRT_DIV)
+    writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x04);  // Use a 200 Hz rate; the same rate set in CONFIG above
+ 
+    // Set gyroscope full scale range
+    // Range selects FS_SEL and AFS_SEL are 0 - 3, so 2-bit values are left-shifted into positions 4:3
+    uint8_t c = readByte(MPU9250_ADDRESS, GYRO_CONFIG); // get current GYRO_CONFIG register value
+    // c = c & ~0xE0; // Clear self-test bits [7:5] 
+    c = c & ~0x02; // Clear Fchoice bits [1:0] 
+    c = c & ~0x18; // Clear AFS bits [4:3]
+    c = c | Gscale << 3; // Set full scale range for the gyro
+    // c =| 0x00; // Set Fchoice for the gyro to 11 by writing its inverse to bits 1:0 of GYRO_CONFIG
+    writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c ); // Write new GYRO_CONFIG value to register
+
+    // Set accelerometer full-scale range configuration
+    c = readByte(MPU9250_ADDRESS, ACCEL_CONFIG); // get current ACCEL_CONFIG register value
+    // c = c & ~0xE0; // Clear self-test bits [7:5] 
+    c = c & ~0x18;  // Clear AFS bits [4:3]
+    c = c | Ascale << 3; // Set full scale range for the accelerometer 
+    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c); // Write new ACCEL_CONFIG register value
+
+    // Set accelerometer sample rate configuration
+    // It is possible to get a 4 kHz sample rate from the accelerometer by choosing 1 for
+    // accel_fchoice_b bit [3]; in this case the bandwidth is 1.13 kHz
+    c = readByte(MPU9250_ADDRESS, ACCEL_CONFIG2); // get current ACCEL_CONFIG2 register value
+    c = c & ~0x0F; // Clear accel_fchoice_b (bit 3) and A_DLPFG (bits [2:0])  
+    c = c | 0x03;  // Set accelerometer rate to 1 kHz and bandwidth to 41 Hz
+    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, c); // Write new ACCEL_CONFIG2 register value
+
+    // The accelerometer, gyro, and thermometer are set to 1 kHz sample rates, 
+    // but all these rates are further reduced by a factor of 5 to 200 Hz because of the SMPLRT_DIV setting
+
+    // Configure Interrupts and Bypass Enable
+    // Set interrupt pin active high, push-pull, and clear on read of INT_STATUS, enable I2C_BYPASS_EN so additional chips 
+    // can join the I2C bus and all can be controlled by the Arduino as master
+    writeByte(MPU9250_ADDRESS, INT_PIN_CFG, 0x22);    
+    writeByte(MPU9250_ADDRESS, INT_ENABLE, 0x01);  // Enable data ready (bit 0) interrupt
+}
+
+void MPU9250::initAK8963(float * destination)
+{
+    // First extract the factory calibration for each magnetometer axis
+    uint8_t rawData[3];  // x/y/z gyro calibration data stored here
+
+    writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00); // Power down magnetometer  
+    wait(0.01);
+    
+    writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x0F); // Enter Fuse ROM access mode
+    wait(0.01);
+  
+    readBytes(AK8963_ADDRESS, AK8963_ASAX, 3, &rawData[0]);  // Read the x-, y-, and z-axis calibration values
+    destination[0] =  (float)(rawData[0] - 128)/256.0f + 1.0f;   // Return x-axis sensitivity adjustment values, etc.
+    destination[1] =  (float)(rawData[1] - 128)/256.0f + 1.0f;  
+    destination[2] =  (float)(rawData[2] - 128)/256.0f + 1.0f; 
+    writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00); // Power down magnetometer  
+    wait(0.01);
+
+    // Configure the magnetometer for continuous read and highest resolution
+    // set Mscale bit 4 to 1 (0) to enable 16 (14) bit resolution in CNTL register,
+    // and enable continuous mode data acquisition Mmode (bits [3:0]), 0010 for 8 Hz and 0110 for 100 Hz sample rates
+    writeByte(AK8963_ADDRESS, AK8963_CNTL, Mscale << 4 | Mmode); // Set magnetometer data resolution and sample ODR
+    wait(0.01);
+}
+
+void MPU9250::resetMPU9250(void)
+{
+    // reset device
+    writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x80); // Write a one to bit 7 reset bit; toggle reset device
+    wait(0.1);
+}
+
+// Function which accumulates gyro and accelerometer data after device initialization. It calculates the average
+// of the at-rest readings and then loads the resulting offsets into accelerometer and gyro bias registers.
+void MPU9250::calibrateMPU9250(float * dest1, float * dest2)
+{  
+    uint8_t data[12]; // data array to hold accelerometer and gyro x, y, z, data
+    uint16_t ii, packet_count, fifo_count;
+    int32_t gyro_bias[3] = {0, 0, 0}, accel_bias[3] = {0, 0, 0};
+    int32_t accel_bias_reg[3] = {0, 0, 0}; // A place to hold the factory accelerometer trim biases
+  
+    // reset device, reset all registers, clear gyro and accelerometer bias registers
+    writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x80); // Write a one to bit 7 reset bit; toggle reset device
+    wait(0.1);  
+   
+    // get stable time source
+    // Set clock source to be PLL with x-axis gyroscope reference, bits 2:0 = 001
+    writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x01);  
+    writeByte(MPU9250_ADDRESS, PWR_MGMT_2, 0x00); 
+    wait(0.2);
+
+    // Configure device for bias calculation
+    writeByte(MPU9250_ADDRESS, INT_ENABLE, 0x00);   // Disable all interrupts
+    writeByte(MPU9250_ADDRESS, FIFO_EN, 0x00);      // Disable FIFO
+    writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00);   // Turn on internal clock source
+    writeByte(MPU9250_ADDRESS, I2C_MST_CTRL, 0x00); // Disable I2C master
+    writeByte(MPU9250_ADDRESS, USER_CTRL, 0x00);    // Disable FIFO and I2C master modes
+    writeByte(MPU9250_ADDRESS, USER_CTRL, 0x0C);    // Reset FIFO and DMP
+    wait(0.015);
+  
+    // Configure MPU9250 gyro and accelerometer for bias calculation
+    writeByte(MPU9250_ADDRESS, CONFIG, 0x01);      // Set low-pass filter to 188 Hz
+    writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x00);  // Set sample rate to 1 kHz
+    writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 0x00);  // Set gyro full-scale to 250 degrees per second, maximum sensitivity
+    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0x00); // Set accelerometer full-scale to 2 g, maximum sensitivity
+
+    uint16_t gyrosensitivity  = 131;   // = 131 LSB/degrees/sec
+    uint16_t accelsensitivity = 16384;  // = 16384 LSB/g
+
+    // Configure FIFO to capture accelerometer and gyro data for bias calculation
+    writeByte(MPU9250_ADDRESS, USER_CTRL, 0x40);   // Enable FIFO  
+    writeByte(MPU9250_ADDRESS, FIFO_EN, 0x78);     // Enable gyro and accelerometer sensors for FIFO (max size 512 bytes in MPU-9250)
+    wait(0.04); // accumulate 40 samples in 80 milliseconds = 480 bytes
+
+    // At end of sample accumulation, turn off FIFO sensor read
+    writeByte(MPU9250_ADDRESS, FIFO_EN, 0x00);        // Disable gyro and accelerometer sensors for FIFO
+    readBytes(MPU9250_ADDRESS, FIFO_COUNTH, 2, &data[0]); // read FIFO sample count
+    fifo_count = ((uint16_t)data[0] << 8) | data[1];
+    packet_count = fifo_count/12;// How many sets of full gyro and accelerometer data for averaging
+
+    for (ii = 0; ii < packet_count; ii++) {
+        int16_t accel_temp[3] = {0, 0, 0}, gyro_temp[3] = {0, 0, 0};
+        readBytes(MPU9250_ADDRESS, FIFO_R_W, 12, &data[0]); // read data for averaging
+        accel_temp[0] = (int16_t) (((int16_t)data[0] << 8) | data[1]  ) ;  // Form signed 16-bit integer for each sample in FIFO
+        accel_temp[1] = (int16_t) (((int16_t)data[2] << 8) | data[3]  ) ;
+        accel_temp[2] = (int16_t) (((int16_t)data[4] << 8) | data[5]  ) ;    
+        gyro_temp[0]  = (int16_t) (((int16_t)data[6] << 8) | data[7]  ) ;
+        gyro_temp[1]  = (int16_t) (((int16_t)data[8] << 8) | data[9]  ) ;
+        gyro_temp[2]  = (int16_t) (((int16_t)data[10] << 8) | data[11]) ;
+    
+        accel_bias[0] += (int32_t) accel_temp[0]; // Sum individual signed 16-bit biases to get accumulated signed 32-bit biases
+        accel_bias[1] += (int32_t) accel_temp[1];
+        accel_bias[2] += (int32_t) accel_temp[2];
+        gyro_bias[0]  += (int32_t) gyro_temp[0];
+        gyro_bias[1]  += (int32_t) gyro_temp[1];
+        gyro_bias[2]  += (int32_t) gyro_temp[2];
+            
+    }
+    accel_bias[0] /= (int32_t) packet_count; // Normalize sums to get average count biases
+    accel_bias[1] /= (int32_t) packet_count;
+    accel_bias[2] /= (int32_t) packet_count;
+    gyro_bias[0]  /= (int32_t) packet_count;
+    gyro_bias[1]  /= (int32_t) packet_count;
+    gyro_bias[2]  /= (int32_t) packet_count;
+    
+  if(accel_bias[2] > 0L) {accel_bias[2] -= (int32_t) accelsensitivity;}  // Remove gravity from the z-axis accelerometer bias calculation
+  else {accel_bias[2] += (int32_t) accelsensitivity;}
+ 
+    // Construct the gyro biases for push to the hardware gyro bias registers, which are reset to zero upon device startup
+    data[0] = (-gyro_bias[0]/4  >> 8) & 0xFF; // Divide by 4 to get 32.9 LSB per deg/s to conform to expected bias input format
+    data[1] = (-gyro_bias[0]/4)       & 0xFF; // Biases are additive, so change sign on calculated average gyro biases
+    data[2] = (-gyro_bias[1]/4  >> 8) & 0xFF;
+    data[3] = (-gyro_bias[1]/4)       & 0xFF;
+    data[4] = (-gyro_bias[2]/4  >> 8) & 0xFF;
+    data[5] = (-gyro_bias[2]/4)       & 0xFF;
+
+    /// Push gyro biases to hardware registers
+/*  
+    writeByte(MPU9250_ADDRESS, XG_OFFSET_H, data[0]);
+    writeByte(MPU9250_ADDRESS, XG_OFFSET_L, data[1]);
+    writeByte(MPU9250_ADDRESS, YG_OFFSET_H, data[2]);
+    writeByte(MPU9250_ADDRESS, YG_OFFSET_L, data[3]);
+    writeByte(MPU9250_ADDRESS, ZG_OFFSET_H, data[4]);
+    writeByte(MPU9250_ADDRESS, ZG_OFFSET_L, data[5]);
+*/
+    dest1[0] = (float) gyro_bias[0]/(float) gyrosensitivity; // construct gyro bias in deg/s for later manual subtraction
+    dest1[1] = (float) gyro_bias[1]/(float) gyrosensitivity;
+    dest1[2] = (float) gyro_bias[2]/(float) gyrosensitivity;
+
+    // Construct the accelerometer biases for push to the hardware accelerometer bias registers. These registers contain
+    // factory trim values which must be added to the calculated accelerometer biases; on boot up these registers will hold
+    // non-zero values. In addition, bit 0 of the lower byte must be preserved since it is used for temperature
+    // compensation calculations. Accelerometer bias registers expect bias input as 2048 LSB per g, so that
+    // the accelerometer biases calculated above must be divided by 8.
+
+    readBytes(MPU9250_ADDRESS, XA_OFFSET_H, 2, &data[0]); // Read factory accelerometer trim values
+    accel_bias_reg[0] = (int16_t) ((int16_t)data[0] << 8) | data[1];
+    readBytes(MPU9250_ADDRESS, YA_OFFSET_H, 2, &data[0]);
+    accel_bias_reg[1] = (int16_t) ((int16_t)data[0] << 8) | data[1];
+    readBytes(MPU9250_ADDRESS, ZA_OFFSET_H, 2, &data[0]);
+    accel_bias_reg[2] = (int16_t) ((int16_t)data[0] << 8) | data[1];
+  
+    uint32_t mask = 1uL; // Define mask for temperature compensation bit 0 of lower byte of accelerometer bias registers
+    uint8_t mask_bit[3] = {0, 0, 0}; // Define array to hold mask bit for each accelerometer bias axis
+  
+    for(ii = 0; ii < 3; ii++) {
+        if(accel_bias_reg[ii] & mask) mask_bit[ii] = 0x01; // If temperature compensation bit is set, record that fact in mask_bit
+    }
+
+  // Construct total accelerometer bias, including calculated average accelerometer bias from above
+    accel_bias_reg[0] -= (accel_bias[0]/8); // Subtract calculated averaged accelerometer bias scaled to 2048 LSB/g (16 g full scale)
+    accel_bias_reg[1] -= (accel_bias[1]/8);
+    accel_bias_reg[2] -= (accel_bias[2]/8);
+ 
+    data[0] = (accel_bias_reg[0] >> 8) & 0xFF;
+    data[1] = (accel_bias_reg[0])      & 0xFF;
+    data[1] = data[1] | mask_bit[0]; // preserve temperature compensation bit when writing back to accelerometer bias registers
+    data[2] = (accel_bias_reg[1] >> 8) & 0xFF;
+    data[3] = (accel_bias_reg[1])      & 0xFF;
+    data[3] = data[3] | mask_bit[1]; // preserve temperature compensation bit when writing back to accelerometer bias registers
+    data[4] = (accel_bias_reg[2] >> 8) & 0xFF;
+    data[5] = (accel_bias_reg[2])      & 0xFF;
+    data[5] = data[5] | mask_bit[2]; // preserve temperature compensation bit when writing back to accelerometer bias registers
+
+// Apparently this is not working for the acceleration biases in the MPU-9250
+// Are we handling the temperature correction bit properly?
+// Push accelerometer biases to hardware registers
+/*
+    writeByte(MPU9250_ADDRESS, XA_OFFSET_H, data[0]);
+    writeByte(MPU9250_ADDRESS, XA_OFFSET_L, data[1]);
+    writeByte(MPU9250_ADDRESS, YA_OFFSET_H, data[2]);
+    writeByte(MPU9250_ADDRESS, YA_OFFSET_L, data[3]);
+    writeByte(MPU9250_ADDRESS, ZA_OFFSET_H, data[4]);
+    writeByte(MPU9250_ADDRESS, ZA_OFFSET_L, data[5]);
+*/
+// Output scaled accelerometer biases for manual subtraction in the main program
+    dest2[0] = (float)accel_bias[0]/(float)accelsensitivity; 
+    dest2[1] = (float)accel_bias[1]/(float)accelsensitivity;
+    dest2[2] = (float)accel_bias[2]/(float)accelsensitivity;
+}
+
+void MPU9250::getMres(void)
+{
+    switch (Mscale)
+    {
+        // Possible magnetometer scales (and their register bit settings) are:
+        // 14 bit resolution (0) and 16 bit resolution (1)
+        case MFS_14BITS:
+                mRes = 10.0*4219.0/8190.0; // Proper scale to return milliGauss
+                break;
+        case MFS_16BITS:
+                mRes = 10.0*4219.0/32760.0; // Proper scale to return milliGauss
+                break;
+  }
+}
+
+void MPU9250::getGres(void) {
+    switch (Gscale)
+    {
+        // Possible gyro scales (and their register bit settings) are:
+        // 250 DPS (00), 500 DPS (01), 1000 DPS (10), and 2000 DPS  (11). 
+        // Here's a bit of an algorith to calculate DPS/(ADC tick) based on that 2-bit value:
+        case GFS_250DPS:
+                gRes = 250.0/32768.0;
+                break;
+        case GFS_500DPS:
+                gRes = 500.0/32768.0;
+                break;
+        case GFS_1000DPS:
+                gRes = 1000.0/32768.0;
+                break;
+        case GFS_2000DPS:
+                gRes = 2000.0/32768.0;
+                break;
+  }
+}
+
+
+void MPU9250::getAres(void) 
+{
+    switch (Ascale)
+    {
+        // Possible accelerometer scales (and their register bit settings) are:
+        // 2 Gs (00), 4 Gs (01), 8 Gs (10), and 16 Gs  (11). 
+        // Here's a bit of an algorith to calculate DPS/(ADC tick) based on that 2-bit value:
+        case AFS_2G:
+                aRes = 2.0/32768.0;
+                break;
+        case AFS_4G:
+                aRes = 4.0/32768.0;
+                break;
+        case AFS_8G:
+                aRes = 8.0/32768.0;
+                break;
+        case AFS_16G:
+                aRes = 16.0/32768.0;
+                break;
+  }
+}
+
+void MPU9250::readAccelData(int16_t * destination)
+{
+    uint8_t rawData[6];  // x/y/z accel register data stored here
+  
+    readBytes(MPU9250_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]);  // Read the six raw data registers into data array
+    destination[0] = (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ;  // Turn the MSB and LSB into a signed 16-bit value
+    destination[1] = (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;  
+    destination[2] = (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ; 
+}
+
+void MPU9250::readGyroData(int16_t * destination)
+{
+    uint8_t rawData[6];  // x/y/z gyro register data stored here
+  
+    readBytes(MPU9250_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]);  // Read the six raw data registers sequentially into data array
+    destination[0] = (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ;  // Turn the MSB and LSB into a signed 16-bit value
+    destination[1] = (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;  
+    destination[2] = (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ; 
+}
+
+void MPU9250::readMagData(int16_t * destination)
+{
+    uint8_t rawData[7];  // x/y/z gyro register data, ST2 register stored here, must read ST2 at end of data acquisition
+  
+    if(readByte(AK8963_ADDRESS, AK8963_ST1) & 0x01) { // wait for magnetometer data ready bit to be set
+        readBytes(AK8963_ADDRESS, AK8963_XOUT_L, 7, &rawData[0]);  // Read the six raw data and ST2 registers sequentially into data array
+        uint8_t c = rawData[6]; // End data read by reading ST2 register
+        if(!(c & 0x08)) { // Check if magnetic sensor overflow set, if not then report data
+            destination[0] = (int16_t)(((int16_t)rawData[1] << 8) | rawData[0]);  // Turn the MSB and LSB into a signed 16-bit value
+            destination[1] = (int16_t)(((int16_t)rawData[3] << 8) | rawData[2]) ;  // Data stored as little Endian
+            destination[2] = (int16_t)(((int16_t)rawData[5] << 8) | rawData[4]) ; 
+        }
+    }
+}
+
+int16_t MPU9250::readTempData(void)
+{
+  uint8_t rawData[2];  // x/y/z gyro register data stored here
+  
+  readBytes(MPU9250_ADDRESS, TEMP_OUT_H, 2, &rawData[0]);  // Read the two raw data registers sequentially into data array 
+  
+  return (int16_t)(((int16_t)rawData[0]) << 8 | rawData[1]) ;  // Turn the MSB and LSB into a 16-bit value
+}
+
+uint8_t MPU9250::Whoami_MPU9250(void){
+    return readByte(MPU9250_ADDRESS, WHO_AM_I_MPU9250);
+}
+
+uint8_t MPU9250::Whoami_AK8963(void){
+    return readByte(WHO_AM_I_AK8963, WHO_AM_I_AK8963);
+}
+
+void MPU9250::sensingAccel(void){
+    readAccelData(accelCount);
+    ax = (float)accelCount[0]*aRes - accelBias[0];
+    ay = (float)accelCount[1]*aRes - accelBias[1];   
+    az = (float)accelCount[2]*aRes - accelBias[2];
+}
+
+void MPU9250::sensingGyro(void){
+    readGyroData(gyroCount);
+    gx = (float)gyroCount[0]*gRes - gyroBias[0];
+    gy = (float)gyroCount[1]*gRes - gyroBias[1];  
+    gz = (float)gyroCount[2]*gRes - gyroBias[2];   
+}
+
+void MPU9250::sensingMag(void){
+    readMagData(magCount);
+    mx = (float)magCount[0]*mRes*magCalibration[0] - magbias[0];
+    my = (float)magCount[1]*mRes*magCalibration[1] - magbias[1];  
+    mz = (float)magCount[2]*mRes*magCalibration[2] - magbias[2];
+}
+
+void MPU9250::sensingTemp(void){
+    tempCount = readTempData();
+  temperature = ((float) tempCount) / 333.87f + 21.0f; // Temperature in degrees Centigrade
+}
+
+// Implementation of Sebastian Madgwick's "...efficient orientation filter for... inertial/magnetic sensor arrays"
+// (see http://www.x-io.co.uk/category/open-source/ for examples and more details)
+// which fuses acceleration, rotation rate, and magnetic moments to produce a quaternion-based estimate of absolute
+// device orientation -- which can be converted to yaw, pitch, and roll. Useful for stabilizing quadcopters, etc.
+// The performance of the orientation filter is at least as good as conventional Kalman-based filtering algorithms
+// but is much less computationally intensive---it can be performed on a 3.3 V Pro Mini operating at 8 MHz!
+void MPU9250::MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz)
+{
+    float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];   // short name local variable for readability
+    float norm;
+    float hx, hy, _2bx, _2bz;
+    float s1, s2, s3, s4;
+    float qDot1, qDot2, qDot3, qDot4;
+
+    // Auxiliary variables to avoid repeated arithmetic
+    float _2q1mx;
+    float _2q1my;
+    float _2q1mz;
+    float _2q2mx;
+    float _4bx;
+    float _4bz;
+    float _2q1 = 2.0f * q1;
+    float _2q2 = 2.0f * q2;
+    float _2q3 = 2.0f * q3;
+    float _2q4 = 2.0f * q4;
+    float _2q1q3 = 2.0f * q1 * q3;
+    float _2q3q4 = 2.0f * q3 * q4;
+    float q1q1 = q1 * q1;
+    float q1q2 = q1 * q2;
+    float q1q3 = q1 * q3;
+    float q1q4 = q1 * q4;
+    float q2q2 = q2 * q2;
+    float q2q3 = q2 * q3;
+    float q2q4 = q2 * q4;
+    float q3q3 = q3 * q3;
+    float q3q4 = q3 * q4;
+    float q4q4 = q4 * q4;
+
+    // Normalise accelerometer measurement
+    norm = sqrt(ax * ax + ay * ay + az * az);
+    if (norm == 0.0f) return; // handle NaN
+    norm = 1.0f/norm;
+    ax *= norm;
+    ay *= norm;
+    az *= norm;
+
+    // Normalise magnetometer measurement
+    norm = sqrt(mx * mx + my * my + mz * mz);
+    if (norm == 0.0f) return; // handle NaN
+    norm = 1.0f/norm;
+    mx *= norm;
+    my *= norm;
+    mz *= norm;
+
+    // Reference direction of Earth's magnetic field
+    _2q1mx = 2.0f * q1 * mx;
+    _2q1my = 2.0f * q1 * my;
+    _2q1mz = 2.0f * q1 * mz;
+    _2q2mx = 2.0f * q2 * mx;
+    hx = mx * q1q1 - _2q1my * q4 + _2q1mz * q3 + mx * q2q2 + _2q2 * my * q3 + _2q2 * mz * q4 - mx * q3q3 - mx * q4q4;
+    hy = _2q1mx * q4 + my * q1q1 - _2q1mz * q2 + _2q2mx * q3 - my * q2q2 + my * q3q3 + _2q3 * mz * q4 - my * q4q4;
+    _2bx = sqrt(hx * hx + hy * hy);
+    _2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4;
+    _4bx = 2.0f * _2bx;
+    _4bz = 2.0f * _2bz;
+
+    // Gradient decent algorithm corrective step
+    s1 = -_2q3 * (2.0f * q2q4 - _2q1q3 - ax) + _2q2 * (2.0f * q1q2 + _2q3q4 - ay) - _2bz * q3 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q4 + _2bz * q2) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q3 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
+    s2 = _2q4 * (2.0f * q2q4 - _2q1q3 - ax) + _2q1 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q2 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + _2bz * q4 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q3 + _2bz * q1) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q4 - _4bz * q2) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
+    s3 = -_2q1 * (2.0f * q2q4 - _2q1q3 - ax) + _2q4 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q3 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + (-_4bx * q3 - _2bz * q1) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q2 + _2bz * q4) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q1 - _4bz * q3) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
+    s4 = _2q2 * (2.0f * q2q4 - _2q1q3 - ax) + _2q3 * (2.0f * q1q2 + _2q3q4 - ay) + (-_4bx * q4 + _2bz * q2) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q1 + _2bz * q3) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q2 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
+    norm = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4);    // normalise step magnitude
+    norm = 1.0f/norm;
+    s1 *= norm;
+    s2 *= norm;
+    s3 *= norm;
+    s4 *= norm;
+
+    // Compute rate of change of quaternion
+    qDot1 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - beta * s1;
+    qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - beta * s2;
+    qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - beta * s3;
+    qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - beta * s4;
+
+    // Integrate to yield quaternion
+    q1 += qDot1 * deltat;
+    q2 += qDot2 * deltat;
+    q3 += qDot3 * deltat;
+    q4 += qDot4 * deltat;
+    norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);    // normalise quaternion
+    norm = 1.0f/norm;
+    q[0] = q1 * norm;
+    q[1] = q2 * norm;
+    q[2] = q3 * norm;
+    q[3] = q4 * norm;
+
+}
+
+void MPU9250::MahonyQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz)
+{
+    float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];   // short name local variable for readability
+    float norm;
+    float hx, hy, bx, bz;
+    float vx, vy, vz, wx, wy, wz;
+    float ex, ey, ez;
+    float pa, pb, pc;
+
+    // Auxiliary variables to avoid repeated arithmetic
+    float q1q1 = q1 * q1;
+    float q1q2 = q1 * q2;
+    float q1q3 = q1 * q3;
+    float q1q4 = q1 * q4;
+    float q2q2 = q2 * q2;
+    float q2q3 = q2 * q3;
+    float q2q4 = q2 * q4;
+    float q3q3 = q3 * q3;
+    float q3q4 = q3 * q4;
+    float q4q4 = q4 * q4;   
+
+    // Normalise accelerometer measurement
+    norm = sqrt(ax * ax + ay * ay + az * az);
+    if (norm == 0.0f) return; // handle NaN
+    norm = 1.0f / norm;        // use reciprocal for division
+    ax *= norm;
+    ay *= norm;
+    az *= norm;
+
+    // Normalise magnetometer measurement
+    norm = sqrt(mx * mx + my * my + mz * mz);
+    if (norm == 0.0f) return; // handle NaN
+    norm = 1.0f / norm;        // use reciprocal for division
+    mx *= norm;
+    my *= norm;
+    mz *= norm;
+
+    // Reference direction of Earth's magnetic field
+    hx = 2.0f * mx * (0.5f - q3q3 - q4q4) + 2.0f * my * (q2q3 - q1q4) + 2.0f * mz * (q2q4 + q1q3);
+    hy = 2.0f * mx * (q2q3 + q1q4) + 2.0f * my * (0.5f - q2q2 - q4q4) + 2.0f * mz * (q3q4 - q1q2);
+    bx = sqrt((hx * hx) + (hy * hy));
+    bz = 2.0f * mx * (q2q4 - q1q3) + 2.0f * my * (q3q4 + q1q2) + 2.0f * mz * (0.5f - q2q2 - q3q3);
+
+    // Estimated direction of gravity and magnetic field
+    vx = 2.0f * (q2q4 - q1q3);
+    vy = 2.0f * (q1q2 + q3q4);
+    vz = q1q1 - q2q2 - q3q3 + q4q4;
+    wx = 2.0f * bx * (0.5f - q3q3 - q4q4) + 2.0f * bz * (q2q4 - q1q3);
+    wy = 2.0f * bx * (q2q3 - q1q4) + 2.0f * bz * (q1q2 + q3q4);
+    wz = 2.0f * bx * (q1q3 + q2q4) + 2.0f * bz * (0.5f - q2q2 - q3q3);  
+
+    // Error is cross product between estimated direction and measured direction of gravity
+    ex = (ay * vz - az * vy) + (my * wz - mz * wy);
+    ey = (az * vx - ax * vz) + (mz * wx - mx * wz);
+    ez = (ax * vy - ay * vx) + (mx * wy - my * wx);
+    if (Ki > 0.0f){
+        eInt[0] += ex;      // accumulate integral error
+        eInt[1] += ey;
+        eInt[2] += ez;
+
+    }else{
+        eInt[0] = 0.0f;     // prevent integral wind up
+        eInt[1] = 0.0f;
+        eInt[2] = 0.0f;
+    }
+
+  // Apply feedback terms
+    gx = gx + Kp * ex + Ki * eInt[0];
+    gy = gy + Kp * ey + Ki * eInt[1];
+    gz = gz + Kp * ez + Ki * eInt[2];
+
+    // Integrate rate of change of quaternion
+    pa = q2;
+    pb = q3;
+    pc = q4;
+    q1 = q1 + (-q2 * gx - q3 * gy - q4 * gz) * (0.5f * deltat);
+    q2 = pa + (q1 * gx + pb * gz - pc * gy) * (0.5f * deltat);
+    q3 = pb + (q1 * gy - pa * gz + pc * gx) * (0.5f * deltat);
+    q4 = pc + (q1 * gz + pa * gy - pb * gx) * (0.5f * deltat);
+
+    // Normalise quaternion
+    norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
+    norm = 1.0f / norm;
+    q[0] = q1 * norm;
+    q[1] = q2 * norm;
+    q[2] = q3 * norm;
+    q[3] = q4 * norm;
+
+}
+
+void MPU9250::translateQuaternionToDeg(float quaternion[4]){
+  yaw   = atan2(2.0f * (quaternion[1] * quaternion[2] + quaternion[0] * quaternion[3]), quaternion[0] * quaternion[0] + quaternion[1] * quaternion[1] - quaternion[2] * quaternion[2] - quaternion[3] * quaternion[3]);   
+  roll = -asin(2.0f * (quaternion[1] * quaternion[3] - quaternion[0] * quaternion[2]));
+  pitch  = atan2(2.0f * (quaternion[0] * quaternion[1] + quaternion[2] * quaternion[3]), quaternion[0] * quaternion[0] - quaternion[1] * quaternion[1] - quaternion[2] * quaternion[2] + quaternion[3] * quaternion[3]);
+}
+
+void MPU9250::calibrateDegree(void){
+    pitch *= 180.0f / PI;
+  yaw   *= 180.0f / PI; 
+  yaw   -= DECLINATION;
+  roll  *= 180.0f / PI; 
+}
+
+void MPU9250::transformCoordinateFromCompassToMPU(){
+    float buf = mx;
+    mx = my;
+    my = buf;
+    mz = -mz;
+}
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