mpu.cpp

#include "mpu.h"
#include <Arduino.h>
#include <Wire.h>

//===================================================================================================================
//====== Set of useful function to access acceleration. gyroscope, magnetometer, and temperature data
//===================================================================================================================

// Wire.h read and write protocols
void MPU::writeByte(uint8_t address, uint8_t subAddress, uint8_t data)
{
    Wire.beginTransmission(address);  // Initialize the Tx buffer
    Wire.write(subAddress);           // Put slave register address in Tx buffer
    Wire.write(data);                 // Put data in Tx buffer
    Wire.endTransmission();           // Send the Tx buffer
}

uint8_t MPU::readByte(uint8_t address, uint8_t subAddress)
{
    uint8_t data; // `data` will store the register data
    Wire.beginTransmission(address);         // Initialize the Tx buffer
    Wire.write(subAddress);                   // Put slave register address in Tx buffer
    Wire.endTransmission(false);             // Send the Tx buffer, but send a restart to keep connection alive
    Wire.requestFrom(address, (uint8_t) 1);  // Read one byte from slave register address
    data = Wire.read();                      // Fill Rx buffer with result
    return data;                             // Return data read from slave register
}

void MPU::readBytes(uint8_t address, uint8_t subAddress, uint8_t count, uint8_t * dest)
{
    Wire.beginTransmission(address);   // Initialize the Tx buffer
    Wire.write(subAddress);            // Put slave register address in Tx buffer
    Wire.endTransmission(false);       // Send the Tx buffer, but send a restart to keep connection alive
    uint8_t i = 0;
    Wire.requestFrom(address, count);  // Read bytes from slave register address
    while (Wire.available()) {
        dest[i++] = Wire.read();
    }         // Put read results in the Rx buffer
}

void MPU::getMres() {
    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.*4912./8190.; // Proper scale to return milliGauss
        break;
        case MFS_16BITS:
        mRes = 10.*4912./32760.0; // Proper scale to return milliGauss
        break;
    }
}

void MPU::getGres() {
    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 MPU::getAres() {
    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 MPU::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)rawData[0] << 8) | rawData[1] ;  // Turn the MSB and LSB into a signed 16-bit value
    destination[1] = ((int16_t)rawData[2] << 8) | rawData[3] ;
    destination[2] = ((int16_t)rawData[4] << 8) | rawData[5] ;
}


void MPU::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)rawData[0] << 8) | rawData[1] ;  // Turn the MSB and LSB into a signed 16-bit value
    destination[1] = ((int16_t)rawData[2] << 8) | rawData[3] ;
    destination[2] = ((int16_t)rawData[4] << 8) | rawData[5] ;
}

void MPU::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)rawData[1] << 8) | rawData[0] ;  // Turn the MSB and LSB into a signed 16-bit value
            destination[1] = ((int16_t)rawData[3] << 8) | rawData[2] ;  // Data stored as little Endian
            destination[2] = ((int16_t)rawData[5] << 8) | rawData[4] ;
        }
    }
}

int16_t MPU::readTempData()
{
    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)rawData[0] << 8) | rawData[1] ;  // Turn the MSB and LSB into a 16-bit value
}

void MPU::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
    delay(10);
    writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x0F); // Enter Fuse ROM access mode
    delay(10);
    readBytes(AK8963_ADDRESS, AK8963_ASAX, 3, &rawData[0]);  // Read the x-, y-, and z-axis calibration values
    destination[0] =  (float)(rawData[0] - 128)/256. + 1.;   // Return x-axis sensitivity adjustment values, etc.
    destination[1] =  (float)(rawData[1] - 128)/256. + 1.;
    destination[2] =  (float)(rawData[2] - 128)/256. + 1.;
    writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00); // Power down magnetometer
    delay(10);
    // 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
    delay(10);
}


void MPU::initMPU9250()
{
    // wake up device
    writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00); // Clear sleep mode bit (6), enable all sensors
    delay(100); // Wait for all registers to reset

    // get stable time source
    writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x01);  // Auto select clock source to be PLL gyroscope reference if ready else
    delay(200);

    // Configure Gyro and Thermometer
    // Disable FSYNC and set thermometer and gyro bandwidth to 41 and 42 Hz, respectively;
    // minimum delay time for this setting is 5.9 ms, which means sensor fusion update rates cannot
    // be higher than 1 / 0.0059 = 170 Hz
    // DLPF_CFG = bits 2:0 = 011; this limits the sample rate to 1000 Hz for both
    // With the MPU9250, it is possible to get gyro sample rates of 32 kHz (!), 8 kHz, or 1 kHz
    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; a rate consistent with the filter update rate
    // determined inset 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);
    //  writeRegister(GYRO_CONFIG, c & ~0xE0); // Clear self-test bits [7:5]
    writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c & ~0x02); // Clear Fchoice bits [1:0]
    writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c & ~0x18); // Clear AFS bits [4:3]
    writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c | Gscale << 3); // Set full scale range for the gyro
    // writeRegister(GYRO_CONFIG, c | 0x00); // Set Fchoice for the gyro to 11 by writing its inverse to bits 1:0 of GYRO_CONFIG

    // Set accelerometer full-scale range configuration
    c = readByte(MPU9250_ADDRESS, ACCEL_CONFIG);
    //  writeRegister(ACCEL_CONFIG, c & ~0xE0); // Clear self-test bits [7:5]
    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c & ~0x18); // Clear AFS bits [4:3]
    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c | Ascale << 3); // Set full scale range for the accelerometer

    // 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);
    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, c & ~0x0F); // Clear accel_fchoice_b (bit 3) and A_DLPFG (bits [2:0])
    writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, c | 0x03); // Set accelerometer rate to 1 kHz and bandwidth to 41 Hz

    // 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, hold interrupt pin level HIGH until interrupt cleared,
    // clear on read of INT_STATUS, and 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
    delay(100);
}


// 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 MPU::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};

    // reset device
    writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x80); // Write a one to bit 7 reset bit; toggle reset device
    delay(100);

    // get stable time source; Auto select clock source to be PLL gyroscope reference if ready
    // else use the internal oscillator, bits 2:0 = 001
    writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x01);
    writeByte(MPU9250_ADDRESS, PWR_MGMT_2, 0x00);
    delay(200);

    // 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
    delay(15);

    // Configure MPU6050 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-9150)
    delay(40); // accumulate 40 samples in 40 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]);

    // Output scaled gyro biases for display in the main program
    dest1[0] = (float) gyro_bias[0]/(float) gyrosensitivity;
    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.

    int32_t accel_bias_reg[3] = {0, 0, 0}; // A place to hold the factory accelerometer trim biases
    readBytes(MPU9250_ADDRESS, XA_OFFSET_H, 2, &data[0]); // Read factory accelerometer trim values
    accel_bias_reg[0] = (int32_t) (((int16_t)data[0] << 8) | data[1]);
    readBytes(MPU9250_ADDRESS, YA_OFFSET_H, 2, &data[0]);
    accel_bias_reg[1] = (int32_t) (((int16_t)data[0] << 8) | data[1]);
    readBytes(MPU9250_ADDRESS, ZA_OFFSET_H, 2, &data[0]);
    accel_bias_reg[2] = (int32_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 display 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;


}

// Accelerometer and gyroscope self test; check calibration wrt factory settings
void MPU::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(25);  // 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(25);  // 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
    }

}



// 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 MPU::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;

}



// Similar to Madgwick scheme but uses proportional and integral filtering on the error between estimated reference vectors and
// measured ones.
void MPU::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 MPU::magcalMPU9250(float * dest1, float * dest2)
{
    uint16_t ii = 0, sample_count = 0;
    int32_t mag_bias[3] = {0, 0, 0}, mag_scale[3] = {0, 0, 0};
    int16_t mag_max[3] = {0x8000, 0x8000, 0x8000}, mag_min[3] = {0x7FFF, 0x7FFF, 0x7FFF}, mag_temp[3] = {0, 0, 0};

    if (VERBOSE) Serial.println("Mag Calibration: Wave device in a figure eight until done!");

    sample_count = 128;
    for(ii = 0; ii < sample_count; ii++) {
        readMagData(mag_temp);  // Read the mag data
        for (int jj = 0; jj < 3; jj++) {
            if(mag_temp[jj] > mag_max[jj]) mag_max[jj] = mag_temp[jj];
            if(mag_temp[jj] < mag_min[jj]) mag_min[jj] = mag_temp[jj];
        }
        delay(135);  // at 8 Hz ODR, new mag data is available every 125 ms
    }

    // Get hard iron correction
    mag_bias[0]  = (mag_max[0] + mag_min[0])/2;  // get average x mag bias in counts
    mag_bias[1]  = (mag_max[1] + mag_min[1])/2;  // get average y mag bias in counts
    mag_bias[2]  = (mag_max[2] + mag_min[2])/2;  // get average z mag bias in counts

    dest1[0] = (float) mag_bias[0]*mRes*magCalibration[0];  // save mag biases in G for main program
    dest1[1] = (float) mag_bias[1]*mRes*magCalibration[1];
    dest1[2] = (float) mag_bias[2]*mRes*magCalibration[2];

    // Get soft iron correction estimate
    mag_scale[0]  = (mag_max[0] - mag_min[0])/2;  // get average x axis max chord length in counts
    mag_scale[1]  = (mag_max[1] - mag_min[1])/2;  // get average y axis max chord length in counts
    mag_scale[2]  = (mag_max[2] - mag_min[2])/2;  // get average z axis max chord length in counts

    float avg_rad = mag_scale[0] + mag_scale[1] + mag_scale[2];
    avg_rad /= 3.0;

    dest2[0] = avg_rad/((float)mag_scale[0]);
    dest2[1] = avg_rad/((float)mag_scale[1]);
    dest2[2] = avg_rad/((float)mag_scale[2]);

    if (VERBOSE) Serial.println("Mag Calibration done!");
}


void MPU::setupMPU() {
    // lcd.begin(16,2);
    Wire.begin();
    //  TWBR = 12;  // 400 kbit/sec I2C speed
    if (VERBOSE) Serial.begin(115200);


    // Set up the interrupt pin, its set as active high, push-pull
    pinMode(intPin, INPUT);
    digitalWrite(intPin, LOW);
    pinMode(myLed, OUTPUT);
    digitalWrite(myLed, HIGH);

    #if LCD_ON
    // Print startup message
    lcd.clear();
    lcd.print("Think");
    lcd.setCursor(5,1);
    lcd.print("different.");
    #endif

    // Start device display with ID of sensor
    if (VERBOSE) {
        Serial.println("MPU9250");
        Serial.println("9-DOF 16-bit");
        Serial.println("motion sensor");
        Serial.println("60 ug LSB");
    }
    delay(800);


    // Read the WHO_AM_I register, this is a good test of communication
    byte c = readByte(MPU9250_ADDRESS, WHO_AM_I_MPU9250);  // Read WHO_AM_I register for MPU-9250

    if (VERBOSE) {
        Serial.print("MPU9250 ");
        Serial.print("I AM ");
        Serial.print(c, HEX);
        Serial.print(" I should be ");
        Serial.println(0x71, HEX);
    }
    delay(800);



    if (c == 0x71) // WHO_AM_I should always be 0x68
    {
        if (VERBOSE) Serial.println("MPU9250 is online...");

        MPU9250SelfTest(SelfTest); // Start by performing self test and reporting values
        if (VERBOSE) {
            Serial.print("x-axis self test: acceleration trim within : "); Serial.print(SelfTest[0],1); Serial.println("% of factory value");
            Serial.print("y-axis self test: acceleration trim within : "); Serial.print(SelfTest[1],1); Serial.println("% of factory value");
            Serial.print("z-axis self test: acceleration trim within : "); Serial.print(SelfTest[2],1); Serial.println("% of factory value");
            Serial.print("x-axis self test: gyration trim within : "); Serial.print(SelfTest[3],1); Serial.println("% of factory value");
            Serial.print("y-axis self test: gyration trim within : "); Serial.print(SelfTest[4],1); Serial.println("% of factory value");
            Serial.print("z-axis self test: gyration trim within : "); Serial.print(SelfTest[5],1); Serial.println("% of factory value");
        }

        calibrateMPU9250(gyroBias, accelBias); // Calibrate gyro and accelerometers, load biases in bias registers

        if (VERBOSE) {
            Serial.println("MPU9250 bias");

            Serial.println(" x   y   z  ");


            Serial.print((int)(1000*accelBias[0]));
            Serial.print((int)(1000*accelBias[1]));
            Serial.print((int)(1000*accelBias[2]));
            Serial.print("mg");

            Serial.print(gyroBias[0], 1);
            Serial.print(gyroBias[1], 1);
            Serial.print(gyroBias[2], 1);
            Serial.println("o/s");

        }
        delay(1000);

        initMPU9250();

        if (VERBOSE) Serial.println("MPU9250 initialized for active data mode...."); // Initialize device for active mode read of acclerometer, gyroscope, and temperature

        // Read the WHO_AM_I register of the magnetometer, this is a good test of communication
        byte d = readByte(AK8963_ADDRESS, WHO_AM_I_AK8963);  // Read WHO_AM_I register for AK8963

        if (VERBOSE) {
            Serial.print("AK8963 ");
            Serial.print("I AM ");
            Serial.print(d, HEX);
            Serial.print(" I should be ");
            Serial.println(0x48, HEX);
        }
        delay(1000);

        // Get magnetometer calibration from AK8963 ROM
        initAK8963(magCalibration);
        if (VERBOSE) Serial.println("AK8963 initialized for active data mode...."); // Initialize device for active mode read of magnetometer
        getMres();

        #if LCD_ON
        lcd.clear();
        lcd.print("Wave in figure-");
        lcd.setCursor(0,1);
        lcd.print("eight motion");
        #endif
        magcalMPU9250(magBias,magScale);
        #if LCD_ON
        lcd.clear();
        lcd.print("Done.");
        #endif
        delay(500);


        if(VERBOSE) {
            //  Serial.println("Calibration values: ");
            Serial.print("X-Axis sensitivity adjustment value "); Serial.println(magCalibration[0], 2);
            Serial.print("Y-Axis sensitivity adjustment value "); Serial.println(magCalibration[1], 2);
            Serial.print("Z-Axis sensitivity adjustment value "); Serial.println(magCalibration[2], 2);

            Serial.println("AK8963");
            Serial.println("ASAX ");
            Serial.println(magCalibration[0], 2);
            Serial.println("ASAY ");
            Serial.println(magCalibration[1], 2);
            Serial.println("ASAZ ");
            Serial.println(magCalibration[2], 2);
        }
        delay(1000);
    }
    else
    {
        Serial.print("Could not connect to MPU9250: 0x");
        Serial.println(c, HEX);

        #if LCD_ON
        lcd.clear();
        lcd.print("NO CONNECTION :(");
        #endif

        while(1); // Loop forever if communication doesn't happen
    }
}

void MPU::updateMPU()
{
    // If intPin goes high, all data registers have new data
    if (readByte(MPU9250_ADDRESS, INT_STATUS) & 0x01) {  // On interrupt, check if data ready interrupt
        readAccelData(accelCount);  // Read the x/y/z adc values
        getAres();

        // Now we'll calculate the accleration value into actual g's
        ax = (float)accelCount[0]*aRes; // - accelBias[0];  // get actual g value, this depends on scale being set
        ay = (float)accelCount[1]*aRes; // - accelBias[1];
        az = (float)accelCount[2]*aRes; // - accelBias[2];

        readGyroData(gyroCount);  // Read the x/y/z adc values
        getGres();

        // Calculate the gyro value into actual degrees per second
        gx = (float)gyroCount[0]*gRes;  // get actual gyro value, this depends on scale being set
        gy = (float)gyroCount[1]*gRes;
        gz = (float)gyroCount[2]*gRes;

        readMagData(magCount);  // Read the x/y/z adc values
        getMres();
        //    magbias[0] = +470.;  // User environmental x-axis correction in milliGauss, should be automatically calculated
        //    magbias[1] = +120.;  // User environmental x-axis correction in milliGauss
        //    magbias[2] = +125.;  // User environmental x-axis correction in milliGauss

        // Calculate the magnetometer values in milliGauss
        // Include factory calibration per data sheet and user environmental corrections
        mx = (float)magCount[0]*mRes*magCalibration[0] - magBias[0];  // get actual magnetometer value, this depends on scale being set
        my = (float)magCount[1]*mRes*magCalibration[1] - magBias[1];
        mz = (float)magCount[2]*mRes*magCalibration[2] - magBias[2];
    }

    Now = micros();
    deltat = ((Now - lastUpdate)/1000000.0f); // set integration time by time elapsed since last filter update
    lastUpdate = Now;

    sum += deltat; // sum2wsaXZ for averaging filter update rate
    sumCount++;

    // Sensors x (y)-axis of the accelerometer is aligned with the y (x)-axis of the magnetometer;
    // the magnetometer z-axis (+ down) is opposite to z-axis (+ up) of accelerometer and gyro!
    // We have to make some allowance for this orientationmismatch in feeding the output to the quaternion filter.
    // For the MPU-9250, we have chosen a magnetic rotation that keeps the sensor forward along the x-axis just like
    // in the LSM9DS0 sensor. This rotation can be modified to allow any convenient orientation convention.
    // This is ok by aircraft orientation standards!
    // 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);


    if (VERBOSE) {
        delt_t = millis() - count;
        if (delt_t > 500) {
            tempCount = readTempData();  // Read the adc values
            temperature = ((float) tempCount) / 333.87 + 21.0; // Temperature in degrees Centigrade
            // Print temperature in degrees Centigrade
            Serial.print("Temperature is ");  Serial.print(temperature, 1);  Serial.println(" degrees C"); // Print T values to tenths of s degree C

            count = millis();
            digitalWrite(myLed, !digitalRead(myLed));  // toggle led
        }
    }
    // Serial print and/or display at 0.5 s rate independent of data rates
    delt_t = millis() - count;
    if (delt_t > 100) { // update LCD_ON independent of read rate
        if (VERBOSE) {
            Serial.print("ax = "); Serial.print((int)1000*ax);
            Serial.print(" ay = "); Serial.print((int)1000*ay);
            Serial.print(" az = "); Serial.print((int)1000*az); Serial.println(" mg");
            Serial.print("gx = "); Serial.print( gx, 2);
            Serial.print(" gy = "); Serial.print( gy, 2);
            Serial.print(" gz = "); Serial.print( gz, 2); Serial.println(" deg/s");
            Serial.print("mx = "); Serial.print( (int)mx );
            Serial.print(" my = "); Serial.print( (int)my );
            Serial.print(" mz = "); Serial.print( (int)mz ); Serial.println(" mG");

            Serial.print("q0 = "); Serial.print(q[0]);
            Serial.print(" qx = "); Serial.print(q[1]);
            Serial.print(" qy = "); Serial.print(q[2]);
            Serial.print(" qz = "); Serial.println(q[3]);
        }

        // 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.
        yaw   = atan2(2.0f * (q[1] * q[2] + q[0] * q[3]), q[0] * q[0] + q[1] * q[1] - q[2] * q[2] - q[3] * q[3]);
        pitch = -asin(2.0f * (q[1] * q[3] - q[0] * q[2]));
        roll  = atan2(2.0f * (q[0] * q[1] + q[2] * q[3]), q[0] * q[0] - q[1] * q[1] - q[2] * q[2] + q[3] * q[3]);
        pitch *= 180.0f / PI;
        yaw   *= 180.0f / PI;
        yaw   += 180.0f;
        yaw   += 12.0;          // Declination at Lancaster, CA
        roll  *= 180.0f / PI;

        if (VERBOSE) {
            Serial.print("Yaw, Pitch, Roll: ");
            Serial.print(yaw+180, 2);
            Serial.print(" ");
            Serial.print(pitch, 2);
            Serial.print(" ");
            Serial.println(roll, 2);
        }

        #if LCD_ON
        lcd.clear();
        lcd.print("Yaw  Pitch  Roll");
        lcd.setCursor(0,1);
        lcd.print((int)(yaw+180));
        lcd.setCursor(5,1);
        lcd.print((int)pitch);
        lcd.setCursor(12, 1);
        lcd.print((int)roll);
        #endif

        // display tone whose frequency maps to the yaw
        // tone(9, (int)yaw+500);

        //
        // With these settings the filter is updating at a ~145 Hz rate using the Madgwick scheme and
        // >200 Hz using the Mahony scheme even though the display refreshes at only 2 Hz.
        // The filter update rate is determined mostly by the mathematical steps in the respective algorithms,
        // the processor speed (8 MHz for the 3.3V Pro Mini), and the magnetometer ODR:
        // an ODR of 10 Hz for the magnetometer produce the above rates, maximum magnetometer ODR of 100 Hz produces
        // filter update rates of 36 - 145 and ~38 Hz for the Madgwick and Mahony schemes, respectively.
        // This is presumably because the magnetometer read takes longer than the gyro or accelerometer reads.
        // This filter update rate should be fast enough to maintain accurate platform orientation for
        // stabilization control of a fast-moving robot or quadcopter. Compare to the update rate of 200 Hz
        // produced by the on-board Digital Motion Processor of Invensense's MPU6050 6 DoF and MPU9150 9DoF sensors.
        // The 3.3 V 8 MHz Pro Mini is doing pretty well!
        //    display.setCursor(0, 40);
        if (VERBOSE) {
            Serial.println("rt: ");
            Serial.println((float) sumCount / sum, 2);
            Serial.println(" Hz");
        }
        //    display.display();

        count = millis();
        sumCount = 0;
        sum = 0;
    }
}

MPU::MPU() {
}

float MPU::getYaw() {
    return yaw;
}