Revision 0:264ee5acfe00, committed 2018-03-02

Comitter:

MarijnJ

Date:

Fri Mar 02 10:29:51 2018 +0000

Commit message:

bla

Changed in this revision

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/MPU9250-common.h	Fri Mar 02 10:29:51 2018 +0000
@@ -0,0 +1,177 @@
+#ifndef MPU9250_COMMON_H
+#define MPU9250_COMMON_H
+
+/*
+	See also MPU-9250 Register Map and Descriptions, Revision 4.0, RM-MPU-9250A-00,
+	Rev. 1.4, 9/9/2013 for registers not listed in above document. The MPU9250
+	and MPU9150 are virtually identical but the latter has a different register map.
+*/
+
+// Magnetometer Registers
+#define AK8963_ADDRESS		0x0C<<1
+#define WHO_AM_I_AK8963		0x00	// should return 0x48
+#define INFO				0x01
+#define AK8963_ST1			0x02	// data ready status bit 0
+#define AK8963_XOUT_L		0x03	// data
+#define AK8963_XOUT_H		0x04
+#define AK8963_YOUT_L		0x05
+#define AK8963_YOUT_H		0x06
+#define AK8963_ZOUT_L		0x07
+#define AK8963_ZOUT_H		0x08
+#define AK8963_ST2			0x09	// Data overflow bit 3 and data read error status bit 2
+#define AK8963_CNTL			0x0A	// Power down (0000), single-measurement (0001), self-test (1000) and Fuse ROM (1111) modes on bits 3:0
+#define AK8963_ASTC			0x0C	// Self test control
+#define AK8963_I2CDIS		0x0F	// I2C disable
+#define AK8963_ASAX			0x10	// Fuse ROM x-axis sensitivity adjustment value
+#define AK8963_ASAY			0x11	// Fuse ROM y-axis sensitivity adjustment value
+#define AK8963_ASAZ			0x12	// Fuse ROM z-axis sensitivity adjustment value
+
+#define SELF_TEST_X_GYRO	0x00
+#define SELF_TEST_Y_GYRO	0x01
+#define SELF_TEST_Z_GYRO	0x02
+
+/*
+#define X_FINE_GAIN			0x03	// [7:0] fine gain
+#define Y_FINE_GAIN			0x04
+#define Z_FINE_GAIN			0x05
+#define XA_OFFSET_H			0x06	// User-defined trim values for accelerometer
+#define XA_OFFSET_L_TC		0x07
+#define YA_OFFSET_H			0x08
+#define YA_OFFSET_L_TC		0x09
+#define ZA_OFFSET_H			0x0A
+#define ZA_OFFSET_L_TC		0x0B
+*/
+
+#define SELF_TEST_X_ACCEL	0x0D
+#define SELF_TEST_Y_ACCEL	0x0E
+#define SELF_TEST_Z_ACCEL	0x0F
+
+#define SELF_TEST_A			0x10
+
+#define XG_OFFSET_H			0x13		// User-defined trim values for gyroscope
+#define XG_OFFSET_L			0x14
+#define YG_OFFSET_H			0x15
+#define YG_OFFSET_L			0x16
+#define ZG_OFFSET_H			0x17
+#define ZG_OFFSET_L			0x18
+#define SMPLRT_DIV			0x19
+#define CONFIG				0x1A
+#define GYRO_CONFIG			0x1B
+#define ACCEL_CONFIG		0x1C
+#define ACCEL_CONFIG2		0x1D
+#define LP_ACCEL_ODR		0x1E
+#define WOM_THR				0x1F
+
+#define MOT_DUR				0x20		// Duration counter threshold for motion interrupt generation, 1 kHz rate, LSB = 1 ms
+#define ZMOT_THR			0x21		// Zero-motion detection threshold bits [7:0]
+#define ZRMOT_DUR			0x22		// Duration counter threshold for zero motion interrupt generation, 16 Hz rate, LSB = 64 ms
+
+#define FIFO_EN				0x23
+#define I2C_MST_CTRL		0x24
+#define I2C_SLV0_ADDR		0x25
+#define I2C_SLV0_REG		0x26
+#define I2C_SLV0_CTRL		0x27
+#define I2C_SLV1_ADDR		0x28
+#define I2C_SLV1_REG		0x29
+#define I2C_SLV1_CTRL		0x2A
+#define I2C_SLV2_ADDR		0x2B
+#define I2C_SLV2_REG		0x2C
+#define I2C_SLV2_CTRL		0x2D
+#define I2C_SLV3_ADDR		0x2E
+#define I2C_SLV3_REG		0x2F
+#define I2C_SLV3_CTRL		0x30
+#define I2C_SLV4_ADDR		0x31
+#define I2C_SLV4_REG		0x32
+#define I2C_SLV4_DO			0x33
+#define I2C_SLV4_CTRL		0x34
+#define I2C_SLV4_DI			0x35
+#define I2C_MST_STATUS		0x36
+#define INT_PIN_CFG			0x37
+#define INT_ENABLE			0x38
+#define DMP_INT_STATUS		0x39		// Check DMP interrupt
+#define INT_STATUS			0x3A
+#define ACCEL_XOUT_H		0x3B
+#define ACCEL_XOUT_L		0x3C
+#define ACCEL_YOUT_H		0x3D
+#define ACCEL_YOUT_L		0x3E
+#define ACCEL_ZOUT_H		0x3F
+#define ACCEL_ZOUT_L		0x40
+#define TEMP_OUT_H			0x41
+#define TEMP_OUT_L			0x42
+#define GYRO_XOUT_H			0x43
+#define GYRO_XOUT_L			0x44
+#define GYRO_YOUT_H			0x45
+#define GYRO_YOUT_L			0x46
+#define GYRO_ZOUT_H			0x47
+#define GYRO_ZOUT_L			0x48
+#define EXT_SENS_DATA_00	0x49
+#define EXT_SENS_DATA_01	0x4A
+#define EXT_SENS_DATA_02	0x4B
+#define EXT_SENS_DATA_03	0x4C
+#define EXT_SENS_DATA_04	0x4D
+#define EXT_SENS_DATA_05	0x4E
+#define EXT_SENS_DATA_06	0x4F
+#define EXT_SENS_DATA_07	0x50
+#define EXT_SENS_DATA_08	0x51
+#define EXT_SENS_DATA_09	0x52
+#define EXT_SENS_DATA_10	0x53
+#define EXT_SENS_DATA_11	0x54
+#define EXT_SENS_DATA_12	0x55
+#define EXT_SENS_DATA_13	0x56
+#define EXT_SENS_DATA_14	0x57
+#define EXT_SENS_DATA_15	0x58
+#define EXT_SENS_DATA_16	0x59
+#define EXT_SENS_DATA_17	0x5A
+#define EXT_SENS_DATA_18	0x5B
+#define EXT_SENS_DATA_19	0x5C
+#define EXT_SENS_DATA_20	0x5D
+#define EXT_SENS_DATA_21	0x5E
+#define EXT_SENS_DATA_22	0x5F
+#define EXT_SENS_DATA_23	0x60
+#define MOT_DETECT_STATUS	0x61
+#define I2C_SLV0_DO			0x63
+#define I2C_SLV1_DO			0x64
+#define I2C_SLV2_DO			0x65
+#define I2C_SLV3_DO			0x66
+#define I2C_MST_DELAY_CTRL	0x67
+#define SIGNAL_PATH_RESET	0x68
+#define MOT_DETECT_CTRL		0x69
+#define USER_CTRL			0x6A	// Bit 7 enable DMP, bit 3 reset DMP
+#define PWR_MGMT_1			0x6B	// Device defaults to the SLEEP mode
+#define PWR_MGMT_2			0x6C
+#define DMP_BANK			0x6D	// Activates a specific bank in the DMP
+#define DMP_RW_PNT			0x6E	// Set read/write pointer to a specific start address in specified DMP bank
+#define DMP_REG				0x6F	// Register in DMP from which to read or to which to write
+#define DMP_REG_1			0x70
+#define DMP_REG_2			0x71
+#define FIFO_COUNTH			0x72
+#define FIFO_COUNTL			0x73
+#define FIFO_R_W			0x74
+#define WHO_AM_I_MPU9250	0x75	// Should return 0x71
+#define XA_OFFSET_H			0x77
+#define XA_OFFSET_L			0x78
+#define YA_OFFSET_H			0x7A
+#define YA_OFFSET_L			0x7B
+#define ZA_OFFSET_H			0x7D
+#define ZA_OFFSET_L			0x7E
+
+// Using the MSENSR-9250 breakout board, ADO is set to 0
+// Seven-bit device address is 110100 for ADO = 0 and 110101 for ADO = 1
+// mbed uses the eight-bit device address, so shift seven-bit addresses left by one!
+#define ADO 1
+#if ADO
+#define MPU9250_ADDRESS 0x69<<1 // Device address when ADO = 1
+#else
+#define MPU9250_ADDRESS 0x68<<1 // Device address when ADO = 0
+#endif
+
+#define PI 3.14159265358979323846f
+#define Kp 2.0f * 5.0f		// these are the free parameters in the Mahony filter and fusion scheme, Kp for proportional feedback, Ki for integral
+#define Ki 0.0f
+
+#define CORRECT_WHO_AM_I 0x71
+
+#define DEG2RAD(x) (x * PI / 180.0f)
+#define RAD2DEG(x) (x / PI * 180.0f)
+
+#endif

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/MPU9250.h	Fri Mar 02 10:29:51 2018 +0000
@@ -0,0 +1,1012 @@
+#ifndef MPU9250_H
+#define MPU9250_H
+
+#include "mbed.h"
+#include "math.h"
+#include "MPU9250-common.h"
+
+
+// Set initial input parameters
+enum Ascale {
+	AFS_2G = 0,
+	AFS_4G = 1,
+	AFS_8G = 2,
+	AFS_16G = 3
+};
+
+enum Gscale {
+	GFS_250DPS = 0,
+	GFS_500DPS = 1,
+	GFS_1000DPS = 2,
+	GFS_2000DPS = 3
+};
+
+enum Mscale {
+	MFS_14BITS = 0, 	// 0.6 mG per LSB
+	MFS_16BITS			// 0.15 mG per LSB
+};
+
+
+
+class MPU9250 {
+public:
+
+// The sufficientMeasurements boolean is used to indicate that the sensor has
+// gathered enough measurements to do future sensor measurements reliably.
+// After roughly 10 seconds of full speed measuring, it should be accurate
+// enough (with the filter updates), so this can then be set to true.
+bool sufficientMeasurements;
+
+I2C *i2c;
+float beta, zeta;
+float deltat;			// integration interval for both filter schemes
+float q[4];				// vector to hold quaternion
+float eInt[3];			// vector to hold integral error for Mahony method
+
+const uint8_t Ascale;	// AFS_2G, AFS_4G, AFS_8G, AFS_16G
+const uint8_t Gscale;	// GFS_250DPS, GFS_500DPS, GFS_1000DPS, GFS_2000DPS
+const uint8_t Mscale;	// MFS_14BITS or MFS_16BITS, 14-bit or 16-bit magnetometer resolution
+const uint8_t Mmode;	// Either 8 Hz 0x02) or 100 Hz (0x06) magnetometer data ODR
+
+float aRes, gRes, mRes;	// Resolution scales for accelerometer, gyro, magnetometer
+
+float accelCalibration[3];
+float accelBias[3];
+
+float gyroCalibration[3];
+float gyroBias[3];
+
+float magCalibration[3];
+float magBias[3];
+
+
+MPU9250(I2C *i2cConnection) : i2c(i2cConnection), Ascale(AFS_8G),
+							Gscale(GFS_1000DPS), Mscale(MFS_16BITS), Mmode(0x06) {
+	// Gyroscope measurement error in rads/s (start at 60 deg/s),
+	// then reduce after ~10 s to 3
+	float GyroMeasError = PI * (60.0f / 180.0f);
+	beta = sqrt(3.0f / 4.0f) * GyroMeasError;
+
+	// Gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
+	float GyroMeasDrift = PI * (1.0f / 180.0f);
+
+	// Other free parameter zeta in the Madgwick scheme usually set to a small or zero value
+	zeta = sqrt(3.0f / 4.0f) * GyroMeasDrift;
+
+	// Integration interval for both filter schemes
+	deltat = 0.0f;
+
+	q[0] = 1.0f;
+	q[1] = q[2] = q[3] = 0.0f;
+
+	eInt[0] = eInt[1] = eInt[2] = 0.0f;
+
+	// Get resolution scales
+	aRes = getAres();
+	gRes = getGres();
+	mRes = getMres();
+
+	// Set initial calibration stuff all to 0.0f
+	accelCalibration[0] = accelCalibration[1] = accelCalibration[2] = 0.0f;
+	accelBias[0] = accelBias[1] = accelBias[2] = 0.0f;
+	gyroCalibration[0] = gyroCalibration[1] = gyroCalibration[2] = 0.0f;
+	gyroBias[0] = gyroBias[1] = gyroBias[2] = 0.0f;
+	magCalibration[0] = magCalibration[1] = magCalibration[2] = 0.0f;
+
+	// User environmental xyz-axes correction in milliGauss, should be automatically calculated
+	magBias[0] = 470.0f;
+	magBias[1] = 120.0f;
+	magBias[2] = 125.0f;
+
+	// We haven't done enough measurements to get accurate values yet!
+	sufficientMeasurements = false;
+}
+
+void 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 readByte(uint8_t address, uint8_t subAddress) {
+	// `data` will store the register data
+	char data[1];
+	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 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];
+	}
+}
+
+float getMres() {
+	switch (Mscale) {
+		// Possible magnetometer scales (and their register bit settings) are:
+		// 14 bit resolution (0) and 16 bit resolution (1)
+		case MFS_14BITS:
+			return 10.0 * 4219.0 / 8190.0; // Proper scale to return milliGauss
+		case MFS_16BITS:
+			return 10.0 * 4219.0 / 32760.0; // Proper scale to return milliGauss
+	}
+
+	return -1.0f;
+}
+
+
+float 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:
+			return 250.0/32768.0;
+		case GFS_500DPS:
+			return 500.0/32768.0;
+		case GFS_1000DPS:
+			return 1000.0/32768.0;
+		case GFS_2000DPS:
+			return 2000.0/32768.0;
+	}
+
+	return -1.0f;
+}
+
+
+float 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:
+			return 2.0 / 32768.0;
+		case AFS_4G:
+			return 4.0 / 32768.0;
+		case AFS_8G:
+			return 8.0 / 32768.0;
+		case AFS_16G:
+			return 16.0 / 32768.0;
+	}
+
+	return -1.0f;
+}
+
+uint8_t hasNewData() {
+	return readByte(MPU9250_ADDRESS, INT_STATUS) & 0x01;
+}
+
+uint8_t getWhoAmI() {
+	return readByte(MPU9250_ADDRESS, WHO_AM_I_MPU9250);
+}
+
+
+void readAccelData(float *ax, float *ay, float *az) {
+	// x/y/z accel register data stored here
+	uint8_t rawData[6];
+
+	// Read the six raw data registers into data array
+	readBytes(MPU9250_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]);
+
+	// Turn the MSB and LSB into a signed 16-bit value
+	int16_t axTemp = (int16_t) (((int16_t) rawData[0] << 8) | rawData[1]);
+	int16_t ayTemp = (int16_t) (((int16_t) rawData[2] << 8) | rawData[3]);
+	int16_t azTemp = (int16_t) (((int16_t) rawData[4] << 8) | rawData[5]);
+
+	// "Return" ax, ay and az in actual g's, depending on resolution
+	*ax = (float) axTemp * aRes - accelBias[0];
+	*ay = (float) ayTemp * aRes - accelBias[1];
+	*az = (float) azTemp * aRes - accelBias[2];
+}
+
+void readGyroData(float *gx, float *gy, float *gz) {
+	// x/y/z gyro register data stored here
+	uint8_t rawData[6];
+
+	// Read the six raw data registers sequentially into data array
+	readBytes(MPU9250_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]);
+
+	// Turn the MSB and LSB into a signed 16-bit value
+	int16_t gxTemp = (int16_t) (((int16_t) rawData[0] << 8) | rawData[1]);
+	int16_t gyTemp = (int16_t) (((int16_t) rawData[2] << 8) | rawData[3]);
+	int16_t gzTemp = (int16_t) (((int16_t) rawData[4] << 8) | rawData[5]);
+
+	// "Return" gx, gy and gz in actual deg/s, depending on scale
+	*gx = (float) gxTemp * gRes - gyroBias[0];
+	*gy = (float) gyTemp * gRes - gyroBias[1];
+	*gz = (float) gzTemp * gRes - gyroBias[2];
+}
+
+void readMagData(float *mx, float *my, float *mz) {
+	// x/y/z gyro register data, ST2 register stored here, must read ST2 at end of data acquisition
+	uint8_t rawData[7];
+
+	// Wait for magnetometer data ready bit to be set
+	if (readByte(AK8963_ADDRESS, AK8963_ST1) & 0x01) {
+		// Read the six raw data and ST2 registers sequentially into data array
+		readBytes(AK8963_ADDRESS, AK8963_XOUT_L, 7, &rawData[0]);
+		uint8_t c = rawData[6]; // End data read by reading ST2 register
+
+		// Check if magnetic sensor overflow set, if not then report data
+		if (!(c & 0x08)) {
+			// Turn the MSB and LSB into a signed 16-bit value
+			// Data stored as little Endian
+			int16_t mxTemp = (int16_t) (((int16_t) rawData[1] << 8) | rawData[0]);
+			int16_t myTemp = (int16_t) (((int16_t) rawData[3] << 8) | rawData[2]);
+			int16_t mzTemp = (int16_t) (((int16_t) rawData[5] << 8) | rawData[4]);
+
+			// Calculate the magnetometer values in milliGauss. Include factory
+			// calibration per data sheet and user environmental corrections
+			// "Return" gx, gy and gz in actual deg/s, depending on scale
+			*mx = (float) mxTemp * mRes * magCalibration[0] - magBias[0];
+			*my = (float) myTemp * mRes * magCalibration[1] - magBias[1];
+			*mz = (float) mzTemp * mRes * magCalibration[2] - magBias[2];
+		}
+	}
+}
+
+int16_t readTempData() {
+	// x/y/z gyro register data stored here
+	uint8_t rawData[2];
+
+	// Read the two raw data registers sequentially into data array
+	readBytes(MPU9250_ADDRESS, TEMP_OUT_H, 2, &rawData[0]);
+
+	// Turn the MSB and LSB into a 16-bit value
+	return (int16_t) (((int16_t) rawData[0]) << 8 | rawData[1]);
+}
+
+float getTemperature() {
+	int16_t tempData = readTempData();
+	return ((float) tempData) / 333.87f + 21.0f;	// In Celsius
+}
+
+
+void getYawPitchRoll(float *yaw, float *pitch, float *roll, float declination) {
+	// 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]);
+
+	// Quaternion q is in deg, so convert it to radian
+	*pitch = RAD2DEG(*pitch);
+	*yaw = RAD2DEG(*yaw)- declination;
+	*roll = RAD2DEG(*roll);
+}
+
+
+void resetMPU9250() {
+	// Write a one to bit 7 reset bit; toggle reset device
+	writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x80);
+	wait(0.1);
+}
+
+void initAK8963() {
+	// First extract the factory calibration for each magnetometer axis
+	// x/y/z gyro calibration data stored here
+	uint8_t rawData[3];
+
+	// Power down magnetometer
+	writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00);
+	wait(0.01);
+
+	// Enter Fuse ROM access mode
+	writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x0F);
+	wait(0.01);
+
+	// Read the x-, y-, and z-axis calibration values
+	readBytes(AK8963_ADDRESS, AK8963_ASAX, 3, &rawData[0]);
+
+	// Return x-axis sensitivity adjustment values, etc.
+	magCalibration[0] = (float)(rawData[0] - 128) / 256.0f + 1.0f;
+	magCalibration[1] = (float)(rawData[1] - 128) / 256.0f + 1.0f;
+	magCalibration[2] = (float)(rawData[2] - 128) / 256.0f + 1.0f;
+
+	// Power down magnetometer
+	writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00);
+	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
+	// Set magnetometer data resolution and sample ODR
+	writeByte(AK8963_ADDRESS, AK8963_CNTL, Mscale << 4 | Mmode);
+	wait(0.01);
+}
+
+
+void initMPU9250() {
+	// Initialize MPU9250 device
+	// Wake up device
+	// Clear sleep mode bit (6), enable all sensors
+	writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00);
+
+	// Delay 100 ms for PLL to get established on x-axis gyro
+	// Should check for PLL ready interrupt
+	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);
+
+	// 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)
+	// Use a 200 Hz rate; the same rate set in CONFIG above
+	writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x04);
+
+	// 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);
+
+	// Clear self-test bits [7:5]
+	writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c & ~0xE0);
+
+	// Clear AFS bits [4:3]
+	writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c & ~0x18);
+
+	// Set full scale range for the gyro
+	writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c | Gscale << 3);
+
+	// Set accelerometer configuration
+	c =	readByte(MPU9250_ADDRESS, ACCEL_CONFIG);
+
+	// Clear self-test bits [7:5]
+	writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c & ~0xE0);
+
+	// Clear AFS bits [4:3]
+	writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c & ~0x18);
+
+	// Set full scale range for the accelerometer
+	writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c | Ascale << 3);
+
+	// 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);
+
+	// Clear accel_fchoice_b (bit 3) and A_DLPFG (bits [2:0])
+	writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, c & ~0x0F);
+
+	// Set accelerometer rate to 1 kHz and bandwidth to 41 Hz
+	writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, c | 0x03);
+
+	// 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);
+
+	// Enable data ready (bit 0) interrupt
+	writeByte(MPU9250_ADDRESS, INT_ENABLE, 0x01);
+}
+
+// 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 calibrateMPU9250() {
+	// Data array to hold accelerometer and gyro x, y, z, data
+	uint8_t data[12];
+	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
+	// Write a one to bit 7 reset bit; toggle reset device
+	writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x80);
+	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
+	// Disable all interrupts
+	writeByte(MPU9250_ADDRESS, INT_ENABLE, 0x00);
+
+	// Disable FIFO
+	writeByte(MPU9250_ADDRESS, FIFO_EN, 0x00);
+
+	// Turn on internal clock source
+	writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00);
+
+	 // Disable I2C master
+	writeByte(MPU9250_ADDRESS, I2C_MST_CTRL, 0x00);
+
+	// Disable FIFO and I2C master modes
+	writeByte(MPU9250_ADDRESS, USER_CTRL, 0x00);
+
+	// Reset FIFO and DMP
+	writeByte(MPU9250_ADDRESS, USER_CTRL, 0x0C);
+	wait(0.015);
+
+	// Configure MPU9250 gyro and accelerometer for bias calculation
+	// Set low-pass filter to 188 Hz
+	writeByte(MPU9250_ADDRESS, CONFIG, 0x01);
+
+	// Set sample rate to 1 kHz
+	writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x00);
+
+	// Set gyro full-scale to 250 degrees per second, maximum sensitivity
+	writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 0x00);
+
+	// Set accelerometer full-scale to 2 g, maximum sensitivity
+	writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0x00);
+
+	// = 131 LSB/degrees/sec
+	uint16_t gyrosensitivity = 131;
+
+	// = 16384 LSB/g
+	uint16_t accelsensitivity = 16384;
+
+	// Configure FIFO to capture accelerometer and gyro data for bias calculation
+	// Enable FIFO
+	writeByte(MPU9250_ADDRESS, USER_CTRL, 0x40);
+
+	// Enable gyro and accelerometer sensors for FIFO (max size 512 bytes in MPU-9250)
+	writeByte(MPU9250_ADDRESS, FIFO_EN, 0x78);
+
+	// accumulate 40 samples in 80 milliseconds = 480 bytes
+	wait(0.04);
+
+	// At end of sample accumulation, turn off FIFO sensor read
+	// Disable gyro and accelerometer sensors for FIFO
+	writeByte(MPU9250_ADDRESS, FIFO_EN, 0x00);
+
+	// read FIFO sample count
+	readBytes(MPU9250_ADDRESS, FIFO_COUNTH, 2, &data[0]);
+	fifo_count = ((uint16_t) data[0] << 8) | data[1];
+
+	// How many sets of full gyro and accelerometer data for averaging
+	packet_count = fifo_count/12;
+
+	for (ii = 0; ii < packet_count; ii++) {
+		int16_t accel_temp[3] = {0, 0, 0}, gyro_temp[3] = {0, 0, 0};
+
+		// read data for averaging
+		readBytes(MPU9250_ADDRESS, FIFO_R_W, 12, &data[0]);
+
+		// Form signed 16-bit integer for each sample in FIFO
+		accel_temp[0] = (int16_t) (((int16_t)data[0] << 8) | data[1]);
+		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]);
+
+		// Sum individual signed 16-bit biases to get accumulated signed 32-bit biases
+		accel_bias[0] += (int32_t) accel_temp[0];
+		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];
+	}
+
+	// Normalize sums to get average count biases
+	accel_bias[0] /= (int32_t) packet_count;
+	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;
+
+	// Remove gravity from the z-axis accelerometer bias calculation
+	if (accel_bias[2] > 0L) {
+		accel_bias[2] -= (int32_t) accelsensitivity;
+	} 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. Divide by 4 to get
+	// 32.9 LSB per deg/s to conform to expected bias input format
+	data[0] = (-gyro_bias[0]/4	>> 8) & 0xFF;
+
+	// Biases are additive, so change sign on calculated average gyro biases
+	data[1] = (-gyro_bias[0]/4) & 0xFF;
+	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]);
+	*/
+	// Construct gyro bias in deg/s for later manual subtraction
+	gyroBias[0] = (float) gyro_bias[0]/(float) gyrosensitivity;
+	gyroBias[1] = (float) gyro_bias[1]/(float) gyrosensitivity;
+	gyroBias[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.
+	// A place to hold the factory accelerometer trim biases
+	int32_t accel_bias_reg[3] = {0, 0, 0};
+
+	// Read factory accelerometer trim values
+	readBytes(MPU9250_ADDRESS, XA_OFFSET_H, 2, &data[0]);
+	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];
+
+	// Define mask for temperature compensation bit 0 of lower byte of
+	// accelerometer bias registers
+	uint32_t mask = 1uL;
+
+	// Define array to hold mask bit for each accelerometer bias axis
+	uint8_t mask_bit[3] = {0, 0, 0};
+
+	for (ii = 0; ii < 3; ii++) {
+		// If temperature compensation bit is set, record that fact in mask_bit
+		if (accel_bias_reg[ii] & mask) {
+			mask_bit[ii] = 0x01;
+		}
+	}
+
+	// Construct total accelerometer bias, including calculated average
+	// accelerometer bias from above. Subtract calculated averaged
+	// accelerometer bias scaled to 2048 LSB/g (16 g full scale)
+	accel_bias_reg[0] -= (accel_bias[0]/8);
+	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;
+
+	// Preserve temperature compensation bit when writing back to accelerometer bias registers
+	data[1] = data[1] | mask_bit[0];
+	data[2] = (accel_bias_reg[1] >> 8) & 0xFF;
+	data[3] = (accel_bias_reg[1]) & 0xFF;
+
+	// Preserve temperature compensation bit when writing back to accelerometer bias registers
+	data[3] = data[3] | mask_bit[1];
+	data[4] = (accel_bias_reg[2] >> 8) & 0xFF;
+	data[5] = (accel_bias_reg[2]) & 0xFF;
+
+	// Preserve temperature compensation bit when writing back to accelerometer bias registers
+	data[5] = data[5] | mask_bit[2];
+
+	// 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
+	accelBias[0] = (float)accel_bias[0] / (float)accelsensitivity;
+	accelBias[1] = (float)accel_bias[1] / (float)accelsensitivity;
+	accelBias[2] = (float)accel_bias[2] / (float)accelsensitivity;
+}
+
+
+// Accelerometer and gyroscope self test; check calibration wrt factory settings
+void 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;
+
+	// Set gyro sample rate to 1 kHz
+	writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x00);
+
+	// Set gyro sample rate to 1 kHz and DLPF to 92 Hz
+	writeByte(MPU9250_ADDRESS, CONFIG, 0x02);
+
+	// Set full scale range for the gyro to 250 dps
+	writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 1<<FS);
+
+	// Set accelerometer rate to 1 kHz and bandwidth to 92 Hz
+	writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, 0x02);
+
+	// Set full scale range for the accelerometer to 2 g
+	writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 1<<FS);
+
+	// Get average current values of gyro and acclerometer
+	for (int ii = 0; ii < 200; ii++) {
+		// Read the six raw data registers into data array
+		readBytes(MPU9250_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]);
+
+		// Turn the MSB and LSB into a signed 16-bit value
+		aAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]);
+		aAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]);
+		aAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]);
+
+		// Read the six raw data registers sequentially into data array
+		readBytes(MPU9250_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]);
+
+		// Turn the MSB and LSB into a signed 16-bit value
+		gAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]);
+		gAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]);
+		gAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]);
+	}
+
+	// Get average of 200 values and store as average current readings
+	for (int ii = 0; ii < 3; ii++) {
+		aAvg[ii] /= 200;
+		gAvg[ii] /= 200;
+	}
+
+	// Configure the accelerometer for self-test
+	// Enable self test on all three axes and set accelerometer range to +/- 2 g
+	writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0xE0);
+
+	// Enable self test on all three axes and set gyro range to +/- 250 degrees/s
+	writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 0xE0);
+
+	// Delay a while to let the device stabilize
+	wait(0.1);
+
+	// Get average self-test values of gyro and acclerometer
+	for (int ii = 0; ii < 200; ii++) {
+		// Read the six raw data registers into data array
+		readBytes(MPU9250_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]);
+
+		// Turn the MSB and LSB into a signed 16-bit value
+		aSTAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]);
+		aSTAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]);
+		aSTAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]);
+
+		// Read the six raw data registers sequentially into data array
+		readBytes(MPU9250_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]);
+
+		// Turn the MSB and LSB into a signed 16-bit value
+		gSTAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]);
+		gSTAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]);
+		gSTAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]);
+	}
+
+	// Get average of 200 values and store as average self-test readings
+	for (int ii = 0; ii < 3; ii++) {
+		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 a while to let the device stabilize
+	wait(0.1);
+
+	// Retrieve accelerometer and gyro factory Self-Test Code from USR_Reg
+	selfTest[0] = readByte(MPU9250_ADDRESS, SELF_TEST_X_ACCEL);
+	selfTest[1] = readByte(MPU9250_ADDRESS, SELF_TEST_Y_ACCEL);
+	selfTest[2] = readByte(MPU9250_ADDRESS, SELF_TEST_Z_ACCEL);
+	selfTest[3] = readByte(MPU9250_ADDRESS, SELF_TEST_X_GYRO);
+	selfTest[4] = readByte(MPU9250_ADDRESS, SELF_TEST_Y_GYRO);
+	selfTest[5] = readByte(MPU9250_ADDRESS, SELF_TEST_Z_GYRO);
+
+	// Retrieve factory self-test value from self-test code reads
+	// FT[Xa] factory trim calculation, and FT[Ya], FT[Xg], etc
+	factoryTrim[0] = (float) (2620 / 1<<FS) * (pow(1.01, ((float) selfTest[0] - 1.0)));
+	factoryTrim[1] = (float) (2620 / 1<<FS) * (pow(1.01, ((float) selfTest[1] - 1.0)));
+	factoryTrim[2] = (float) (2620 / 1<<FS) * (pow(1.01, ((float) selfTest[2] - 1.0)));
+	factoryTrim[3] = (float) (2620 / 1<<FS) * (pow(1.01, ((float) selfTest[3] - 1.0)));
+	factoryTrim[4] = (float) (2620 / 1<<FS) * (pow(1.01, ((float) selfTest[4] - 1.0)));
+	factoryTrim[5] = (float) (2620 / 1<<FS) * (pow(1.01, ((float) selfTest[5] - 1.0)));
+
+	// 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++) {
+		// Report percent differences
+		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];
+	}
+}
+
+
+
+// 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 MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy,
+							float gz, float mx, float my, float mz) {
+	// Short name local variable for readability
+	float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];
+	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);
+
+	// Handle NaN
+	if (norm == 0.0f) {
+		return;
+	}
+
+	norm = 1.0f / norm;
+	ax *= norm;
+	ay *= norm;
+	az *= norm;
+
+	// Normalise magnetometer measurement
+	norm = sqrt(mx * mx + my * my + mz * mz);
+
+	// Handle NaN
+	if (norm == 0.0f) {
+		return;
+	}
+
+	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 descent 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);
+
+	// Normalise step magnitude
+	norm = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4);
+	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;
+
+	// 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;
+}
+
+
+// Similar to Madgwick scheme but uses proportional and integral filtering on
+// the error between estimated reference vectors and measured ones.
+void MahonyQuaternionUpdate(float ax, float ay, float az, float gx, float gy,
+							float gz, float mx, float my, float mz) {
+	// short name local variable for readability
+	float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];
+	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);
+
+	// Handle NaN
+	if (norm == 0.0f) {
+		return;
+	}
+
+	// Use reciprocal for division
+	norm = 1.0f / norm;
+	ax *= norm;
+	ay *= norm;
+	az *= norm;
+
+	// Normalise magnetometer measurement
+	norm = sqrt(mx * mx + my * my + mz * mz);
+
+	// Handle NaN
+	if (norm == 0.0f) {
+		return;
+	}
+
+	// Use reciprocal for division
+	norm = 1.0f / norm;
+	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) {
+		// Accumulate integral error
+		eInt[0] += ex;
+		eInt[1] += ey;
+		eInt[2] += ez;
+	} else {
+		// Prevent integral wind up
+		eInt[0] = 0.0f;
+		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;
+}
+
+};
+
+#endif