#include "MPU6050.h"


const float MPU6050::PI = 3.14159265358979323846f;
const float MPU6050::GyroMeasError = PI * (60.0f / 180.0f);     // gyroscope measurement error in rads/s (start at 60 deg/s), then reduce after ~10 s to 3
const float MPU6050::beta = sqrt(3.0f / 4.0f) * GyroMeasError;  // compute beta
const float MPU6050::GyroMeasDrift = PI * (1.0f / 180.0f);      // gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
const float MPU6050::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

MPU6050::MPU6050(SoftwareI2C *iic, PinName ad0pin)
	{
		i2c = iic;
		ad0 = new DigitalOut(ad0pin);

		*ad0 = true;
		q[0] = 1.0f;

		gScale = GFS_250DPS;
		aScale = AFS_2G;

		for(int i = 0 ; i < 3; i++)
		{
			q[i+1] = 0.0f;
			gyroBias[i] = 0.0f;
			accelBias[i] = 0.0f;
		}

		lastUpdate = 0;
		firstUpdate = 0;
	}

	void MPU6050::create(SoftwareI2C *iic, PinName ad0pin)
	{
		i2c = iic;
		ad0 = new DigitalOut(ad0pin);

		*ad0 = 1;

		q[0] = 1.0f;

		gScale = GFS_250DPS;
		aScale = AFS_2G;

		for(int i = 0 ; i < 3; i++)
		{
			q[i+1] = 0.0f;
			gyroBias[i] = 0.0f;
			accelBias[i] = 0.0f;
		}

		lastUpdate = 0;
		firstUpdate = 0;
		dt = -1;
	}

  void MPU6050::writeByte(uint8_t address, uint8_t subAddress, uint8_t data)
  {
		*ad0 = 0;
    uint8_t data_write[2];
    data_write[0] = subAddress;
    data_write[1] = data;
    i2c->write(address, data_write, 2);
		*ad0 = 1;
  }

  uint8_t MPU6050::readByte(uint8_t address, uint8_t subAddress)
  {
		*ad0 = 0;
    uint8_t data[1]; // data will store the register data
    uint8_t data_write[1];
    data_write[0] = subAddress;
    i2c->write(address, data_write, 1); // no stop
    i2c->read(address, data, 1);
		*ad0 = 1;
    return data[0];
  }

  void MPU6050::readBytes(uint8_t address, uint8_t subAddress, uint8_t count, uint8_t * dest)
  {
		*ad0 = 0;
    uint8_t data[14];
    uint8_t data_write[1];
    data_write[0] = subAddress;
    i2c->write(address, data_write, 1); // no stop
    i2c->read(address, data, count);
    for(int i = 0; i < count; i++)
		{
      dest[i] = data[i];
    }
		*ad0 = 1;
  }

  void MPU6050::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 MPU6050::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 MPU6050::readAccelData(int16_t * destination)
  {
    uint8_t rawData[6];  // x/y/z accel register data stored here
    readBytes(MPU6050_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 MPU6050::readGyroData(int16_t * destination)
  {
    uint8_t rawData[6];  // x/y/z gyro register data stored here
    readBytes(MPU6050_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]) ;
  }

  int16_t MPU6050::readTempData()
  {
    uint8_t rawData[2];  // x/y/z gyro register data stored here
    readBytes(MPU6050_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
  }

  void MPU6050::init()
  {
    // Initialize MPU6050 device
    // wake up device
    writeByte(MPU6050_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(MPU6050_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(MPU6050_ADDRESS, CONFIG, 0x03);

    // Set sample rate = gyroscope output rate/(1 + SMPLRT_DIV)
    writeByte(MPU6050_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(MPU6050_ADDRESS, GYRO_CONFIG);
    writeByte(MPU6050_ADDRESS, GYRO_CONFIG, c & ~0xE0); // Clear self-test bits [7:5]
    writeByte(MPU6050_ADDRESS, GYRO_CONFIG, c & ~0x18); // Clear AFS bits [4:3]
    writeByte(MPU6050_ADDRESS, GYRO_CONFIG, c | gScale << 3); // Set full scale range for the gyro

    // Set accelerometer configuration
    c =  readByte(MPU6050_ADDRESS, ACCEL_CONFIG);
    writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, c & ~0xE0); // Clear self-test bits [7:5]
    writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, c & ~0x18); // Clear AFS bits [4:3]
    writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, c | aScale << 3); // Set full scale range for the accelerometer

    // 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(MPU6050_ADDRESS, INT_PIN_CFG, 0x22);
    writeByte(MPU6050_ADDRESS, INT_ENABLE, 0x01);  // Enable data ready (bit 0) interrupt
  }

  void MPU6050::reset() {
    // reset device
    writeByte(MPU6050_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 MPU6050::calibrate(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, reset all registers, clear gyro and accelerometer bias registers
    writeByte(MPU6050_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(MPU6050_ADDRESS, PWR_MGMT_1, 0x01);
    writeByte(MPU6050_ADDRESS, PWR_MGMT_2, 0x00);
    wait(0.2);

    // Configure device for bias calculation
    writeByte(MPU6050_ADDRESS, INT_ENABLE, 0x00);   // Disable all interrupts
    writeByte(MPU6050_ADDRESS, FIFO_EN, 0x00);      // Disable FIFO
    writeByte(MPU6050_ADDRESS, PWR_MGMT_1, 0x00);   // Turn on internal clock source
    writeByte(MPU6050_ADDRESS, I2C_MST_CTRL, 0x00); // Disable I2C master
    writeByte(MPU6050_ADDRESS, USER_CTRL, 0x00);    // Disable FIFO and I2C master modes
    writeByte(MPU6050_ADDRESS, USER_CTRL, 0x0C);    // Reset FIFO and DMP
    wait(0.015);

    // Configure MPU6050 gyro and accelerometer for bias calculation
    writeByte(MPU6050_ADDRESS, CONFIG, 0x01);      // Set low-pass filter to 188 Hz
    writeByte(MPU6050_ADDRESS, SMPLRT_DIV, 0x00);  // Set sample rate to 1 kHz
    writeByte(MPU6050_ADDRESS, GYRO_CONFIG, 0x00);  // Set gyro full-scale to 250 degrees per second, maximum sensitivity
    writeByte(MPU6050_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(MPU6050_ADDRESS, USER_CTRL, 0x40);   // Enable FIFO
    writeByte(MPU6050_ADDRESS, FIFO_EN, 0x78);     // Enable gyro and accelerometer sensors for FIFO  (max size 1024 bytes in MPU-6050)
    wait(0.08); // accumulate 80 samples in 80 milliseconds = 960 bytes

    // At end of sample accumulation, turn off FIFO sensor read
    writeByte(MPU6050_ADDRESS, FIFO_EN, 0x00);        // Disable gyro and accelerometer sensors for FIFO
    readBytes(MPU6050_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(MPU6050_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(MPU6050_ADDRESS, XG_OFFS_USRH, data[0]);
    writeByte(MPU6050_ADDRESS, XG_OFFS_USRL, data[1]);
    writeByte(MPU6050_ADDRESS, YG_OFFS_USRH, data[2]);
    writeByte(MPU6050_ADDRESS, YG_OFFS_USRL, data[3]);
    writeByte(MPU6050_ADDRESS, ZG_OFFS_USRH, data[4]);
    writeByte(MPU6050_ADDRESS, ZG_OFFS_USRL, 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.

    int32_t accel_bias_reg[3] = {
      0, 0, 0    }; // A place to hold the factory accelerometer trim biases
    readBytes(MPU6050_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(MPU6050_ADDRESS, YA_OFFSET_H, 2, &data[0]);
    accel_bias_reg[1] = (int16_t) ((int16_t)data[0] << 8) | data[1];
    readBytes(MPU6050_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

    // Push accelerometer biases to hardware registers
    //  writeByte(MPU6050_ADDRESS, XA_OFFSET_H, data[0]);
    //  writeByte(MPU6050_ADDRESS, XA_OFFSET_L_TC, data[1]);
    //  writeByte(MPU6050_ADDRESS, YA_OFFSET_H, data[2]);
    //  writeByte(MPU6050_ADDRESS, YA_OFFSET_L_TC, data[3]);
    //  writeByte(MPU6050_ADDRESS, ZA_OFFSET_H, data[4]);
    //  writeByte(MPU6050_ADDRESS, ZA_OFFSET_L_TC, 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;
  }


  // Accelerometer and gyroscope self test; check calibration wrt factory settings
  void MPU6050::selfTest(float * destination) // Should return percent deviation from factory trim values, +/- 14 or less deviation is a pass
  {
    uint8_t rawData[4] = {
      0, 0, 0, 0    };
    uint8_t selfTest[6];
    float factoryTrim[6];

    // Configure the accelerometer for self-test
    writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, 0xF0); // Enable self test on all three axes and set accelerometer range to +/- 8 g
    writeByte(MPU6050_ADDRESS, GYRO_CONFIG,  0xE0); // Enable self test on all three axes and set gyro range to +/- 250 degrees/s
    wait(0.25);  // Delay a while to let the device execute the self-test
    rawData[0] = readByte(MPU6050_ADDRESS, SELF_TEST_X); // X-axis self-test results
    rawData[1] = readByte(MPU6050_ADDRESS, SELF_TEST_Y); // Y-axis self-test results
    rawData[2] = readByte(MPU6050_ADDRESS, SELF_TEST_Z); // Z-axis self-test results
    rawData[3] = readByte(MPU6050_ADDRESS, SELF_TEST_A); // Mixed-axis self-test results
    // Extract the acceleration test results first
    selfTest[0] = (rawData[0] >> 3) | (rawData[3] & 0x30) >> 4 ; // XA_TEST result is a five-bit unsigned integer
    selfTest[1] = (rawData[1] >> 3) | (rawData[3] & 0x0C) >> 4 ; // YA_TEST result is a five-bit unsigned integer
    selfTest[2] = (rawData[2] >> 3) | (rawData[3] & 0x03) >> 4 ; // ZA_TEST result is a five-bit unsigned integer
    // Extract the gyration test results first
    selfTest[3] = rawData[0]  & 0x1F ; // XG_TEST result is a five-bit unsigned integer
    selfTest[4] = rawData[1]  & 0x1F ; // YG_TEST result is a five-bit unsigned integer
    selfTest[5] = rawData[2]  & 0x1F ; // ZG_TEST result is a five-bit unsigned integer
    // Process results to allow final comparison with factory set values
    factoryTrim[0] = (4096.0f*0.34f)*(pow( (0.92f/0.34f) , ((selfTest[0] - 1.0f)/30.0f))); // FT[Xa] factory trim calculation
    factoryTrim[1] = (4096.0f*0.34f)*(pow( (0.92f/0.34f) , ((selfTest[1] - 1.0f)/30.0f))); // FT[Ya] factory trim calculation
    factoryTrim[2] = (4096.0f*0.34f)*(pow( (0.92f/0.34f) , ((selfTest[2] - 1.0f)/30.0f))); // FT[Za] factory trim calculation
    factoryTrim[3] =  ( 25.0f*131.0f)*(pow( 1.046f , (selfTest[3] - 1.0f) ));             // FT[Xg] factory trim calculation
    factoryTrim[4] =  (-25.0f*131.0f)*(pow( 1.046f , (selfTest[4] - 1.0f) ));             // FT[Yg] factory trim calculation
    factoryTrim[5] =  ( 25.0f*131.0f)*(pow( 1.046f , (selfTest[5] - 1.0f) ));             // FT[Zg] factory trim calculation

    //  Output self-test results and factory trim calculation if desired
    //  Serial.println(selfTest[0]); Serial.println(selfTest[1]); Serial.println(selfTest[2]);
    //  Serial.println(selfTest[3]); Serial.println(selfTest[4]); Serial.println(selfTest[5]);
    //  Serial.println(factoryTrim[0]); Serial.println(factoryTrim[1]); Serial.println(factoryTrim[2]);
    //  Serial.println(factoryTrim[3]); Serial.println(factoryTrim[4]); Serial.println(factoryTrim[5]);

    // Report results as a ratio of (STR - FT)/FT; the change from Factory Trim of the Self-Test Response
    // To get to percent, must multiply by 100 and subtract result from 100
    for (int i = 0; i < 6; i++) {
      destination[i] = 100.0f + 100.0f*(selfTest[i] - factoryTrim[i])/factoryTrim[i]; // Report percent differences
    }

  }


	void MPU6050::updateDt()
	{
		long tmp = millis();
		if(dt < 0) dt = 0.01f;
		else
		{
			dt = ((float)(tmp - lastUpdate)) / 1000.0f;
			if(dt == 0.0f)
				dt = 0.01f;
		}

		lastUpdate = tmp;
	}

  // 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 and rotation rate to produce a quaternion-based estimate of relative
  // 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 MPU6050::updateQuaternion(float gx, float gy, float gz, float ax, float ay, float az) {
		float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];         // short name local variable for readability
		float norm;                                               // vector norm
		float f1, f2, f3;                                         // objective funcyion elements
		float J_11or24, J_12or23, J_13or22, J_14or21, J_32, J_33; // objective function Jacobian elements
		float qDot1, qDot2, qDot3, qDot4;
		float hatDot1, hatDot2, hatDot3, hatDot4;
		float gerrx, gerry, gerrz, gbiasx, gbiasy, gbiasz;  // gyro bias error

		// Auxiliary variables to avoid repeated arithmetic
		float _halfq1 = 0.5f * q1;
		float _halfq2 = 0.5f * q2;
		float _halfq3 = 0.5f * q3;
		float _halfq4 = 0.5f * q4;
		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;

		// 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;

		// Compute the objective function and Jacobian
		f1 = _2q2 * q4 - _2q1 * q3 - ax;
		f2 = _2q1 * q2 + _2q3 * q4 - ay;
		f3 = 1.0f - _2q2 * q2 - _2q3 * q3 - az;
		J_11or24 = _2q3;
		J_12or23 = _2q4;
		J_13or22 = _2q1;
		J_14or21 = _2q2;
		J_32 = 2.0f * J_14or21;
		J_33 = 2.0f * J_11or24;

		// Compute the gradient (matrix multiplication)
		hatDot1 = J_14or21 * f2 - J_11or24 * f1;
		hatDot2 = J_12or23 * f1 + J_13or22 * f2 - J_32 * f3;
		hatDot3 = J_12or23 * f2 - J_33 *f3 - J_13or22 * f1;
		hatDot4 = J_14or21 * f1 + J_11or24 * f2;

		// Normalize the gradient
		norm = sqrt(hatDot1 * hatDot1 + hatDot2 * hatDot2 + hatDot3 * hatDot3 + hatDot4 * hatDot4);
		hatDot1 /= norm;
		hatDot2 /= norm;
		hatDot3 /= norm;
		hatDot4 /= norm;

		// Compute estimated gyroscope biases
		gerrx = _2q1 * hatDot2 - _2q2 * hatDot1 - _2q3 * hatDot4 + _2q4 * hatDot3;
		gerry = _2q1 * hatDot3 + _2q2 * hatDot4 - _2q3 * hatDot1 - _2q4 * hatDot2;
		gerrz = _2q1 * hatDot4 - _2q2 * hatDot3 + _2q3 * hatDot2 - _2q4 * hatDot1;

		// Compute and remove gyroscope biases
		gbiasx += gerrx * dt * zeta;
		gbiasy += gerry * dt * zeta;
		gbiasz += gerrz * dt * zeta;
//           gx -= gbiasx;
//           gy -= gbiasy;
//           gz -= gbiasz;

		// Compute the quaternion derivative
		qDot1 = -_halfq2 * gx - _halfq3 * gy - _halfq4 * gz;
		qDot2 =  _halfq1 * gx + _halfq3 * gz - _halfq4 * gy;
		qDot3 =  _halfq1 * gy - _halfq2 * gz + _halfq4 * gx;
		qDot4 =  _halfq1 * gz + _halfq2 * gy - _halfq3 * gx;

		// Compute then integrate estimated quaternion derivative
		q1 += (qDot1 -(beta * hatDot1)) * dt;
		q2 += (qDot2 -(beta * hatDot2)) * dt;
		q3 += (qDot3 -(beta * hatDot3)) * dt;
		q4 += (qDot4 -(beta * hatDot4)) * dt;

		// Normalize the quaternion
		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;

}


	float MPU6050::invSqrt(float x)
	{
		float xhalf = 0.5f * x;
		int i = *(int*)&x;         // evil floating point bit level hacking
		i = 0x5f3759df - (i >> 1);  // what the fuck?
		x = *(float*)&i;
		x = x*(1.5f-(xhalf*x*x));

		return x;
	}