Speed testing IMUs

Dependencies:   MadgwickAHRS mbed

Fork of IMU_serial by Patrick Ciccone

Revision:
0:80a695ae3cc3
Child:
3:c1902ecb30a7
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/MPU9250.h	Wed Sep 28 23:59:57 2016 +0000
@@ -0,0 +1,1030 @@
+/*
+TODO:
+add configuration function:
+loop through mux
+if imu
+    append imu to a list
+    ...
+    ...
+if list > 0
+    return something good
+
+add config output function
+
+
+
+*/
+
+
+#ifndef MPU9250_H
+#define MPU9250_H
+
+#include "mbed.h"
+#include "math.h"
+#include "MadgwickAHRS.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 0
+#if ADO
+#define MPU9250_ADDRESS 0x69<<1  // Device address when ADO = 1
+#else
+#define MPU9250_ADDRESS 0x68<<1  // Device address when ADO = 0
+#endif
+
+// Set initial input parameters
+enum Ascale {
+    AFS_2G = 0,
+    AFS_4G,
+    AFS_8G,
+    AFS_16G
+};
+
+enum Gscale {
+    GFS_250DPS = 0,
+    GFS_500DPS,
+    GFS_1000DPS,
+    GFS_2000DPS
+};
+
+enum Mscale {
+    MFS_14BITS = 0, // 0.6 mG per LSB
+    MFS_16BITS      // 0.15 mG per LSB
+};
+
+uint8_t Ascale = AFS_2G;     // AFS_2G, AFS_4G, AFS_8G, AFS_16G
+uint8_t Gscale = GFS_250DPS; // GFS_250DPS, GFS_500DPS, GFS_1000DPS, GFS_2000DPS
+uint8_t Mscale = MFS_16BITS; // MFS_14BITS or MFS_16BITS, 14-bit or 16-bit magnetometer resolution
+uint8_t Mmode = 0x06;        // Either 8 Hz 0x02) or 100 Hz (0x06) magnetometer data ODR
+float aRes, gRes, mRes;      // scale resolutions per LSB for the sensors
+
+//Set up I2C, (SDA,SCL)
+I2C i2c(I2C_SDA, I2C_SCL);
+
+DigitalOut myled(LED1);
+
+// Pin definitions
+int intPin = 12;  // These can be changed, 2 and 3 are the Arduinos ext int pins
+
+float SelfTest[6];
+
+int delt_t = 0; // used to control display output rate
+int count = 0;  // used to control display output rate
+
+// parameters for 6 DoF sensor fusion calculations
+float PI = 3.14159265358979323846f;
+float GyroMeasError = PI * (60.0f / 180.0f);     // gyroscope measurement error in rads/s (start at 60 deg/s), then reduce after ~10 s to 3
+//float beta = sqrt(3.0f / 4.0f) * GyroMeasError;  // compute beta
+float GyroMeasDrift = PI * (1.0f / 180.0f);      // gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
+float 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
+#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
+
+
+
+class MPU9250
+{
+
+protected:
+
+public:
+    int16_t accelCount[3];  // Stores the 16-bit signed accelerometer sensor output
+    int16_t gyroCount[3];   // Stores the 16-bit signed gyro sensor output
+    int16_t magCount[3];    // Stores the 16-bit signed magnetometer sensor output
+    float ax, ay, az, gx, gy, gz, mx, my, mz; // variables to hold latest sensor data values
+    float magCalibration[3];
+    float magbias[3];  // Factory mag calibration and mag bias
+    float gyroBias[3];
+    float accelBias[3]; // Bias corrections for gyro and accelerometer
+    int16_t tempCount;   // Stores the real internal chip temperature in degrees Celsius
+    float temperature;
+    float pitch, yaw, roll;
+    float deltat;                             // integration interval for both filter schemes
+    int lastUpdate;
+    int firstUpdate;
+    int Now;    // used to calculate integration interval
+    float q[4];           // vector to hold quaternion
+    float eInt[3];              // vector to hold integral error for Mahony method
+    uint32_t checksum;
+
+    MPU9250() {
+        ax=ay=az=gx=gy=gz=mx=my=mz=0.0;
+        for (int i = 0; i < 3; i++) {
+            magCalibration[i] = 0.0;
+            magbias[i] = 0.0;
+            gyroBias[i] = 0.0;
+            accelBias[i] = 0.0;
+            eInt[i] = 0.0f;
+        } // end of for
+        q[0] = 1.0f;
+        q[1] = 0.0f;
+        q[2] = 0.0f;
+        q[3] = 0.0f;
+        lastUpdate = 0, firstUpdate = 0, Now = 0;
+        deltat = 0.0f;
+    } // end of initalizer
+
+//===================================================================================================================
+//====== Set of useful function to access acceleratio, gyroscope, and temperature data
+//===================================================================================================================
+
+    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);
+    }
+
+
+    void selfTest(Serial &pc , bool show = false) {
+        resetMPU9250(); // Reset registers to default in preparation for device calibration
+        MPU9250SelfTest(SelfTest); // Start by performing self test and reporting values
+        if (show) {
+            pc.printf("x-axis self test: acceleration trim within : %f % of factory value\n\r", SelfTest[0]);
+            pc.printf("y-axis self test: acceleration trim within : %f % of factory value\n\r", SelfTest[1]);
+            pc.printf("z-axis self test: acceleration trim within : %f % of factory value\n\r", SelfTest[2]);
+            pc.printf("x-axis self test: gyration trim within : %f % of factory value\n\r", SelfTest[3]);
+            pc.printf("y-axis self test: gyration trim within : %f % of factory value\n\r", SelfTest[4]);
+            pc.printf("z-axis self test: gyration trim within : %f % of factory value\n\r", SelfTest[5]);
+        }
+        //calibrateMPU9250(gyroBias, accelBias); // Calibrate gyro and accelerometers, load biases in bias registers
+        if(show) {
+            pc.printf("x gyro bias = %f\n\r", gyroBias[0]);
+            pc.printf("y gyro bias = %f\n\r", gyroBias[1]);
+            pc.printf("z gyro bias = %f\n\r", gyroBias[2]);
+            pc.printf("x accel bias = %f\n\r", accelBias[0]);
+            pc.printf("y accel bias = %f\n\r", accelBias[1]);
+            pc.printf("z accel bias = %f\n\r", accelBias[2]);
+        }
+    }
+
+
+    void config(Serial &pc, bool show = false) {
+        initMPU9250();
+        if (show)
+            pc.printf("MPU9250 initialized for active data mode....\n\r"); // Initialize device for active mode read of acclerometer, gyroscope, and temperature
+        initAK8963(magCalibration);
+        if(show) {
+            pc.printf("AK8963 initialized for active data mode....\n\r"); // Initialize device for active mode read of magnetometer
+            pc.printf("Accelerometer full-scale range = %f  g\n\r", 2.0f*(float)(1<<Ascale));
+            pc.printf("Gyroscope full-scale range = %f  deg/s\n\r", 250.0f*(float)(1<<Gscale));
+            if(Mscale == 0) pc.printf("Magnetometer resolution = 14  bits\n\r");
+            if(Mscale == 1) pc.printf("Magnetometer resolution = 16  bits\n\r");
+            if(Mmode == 2) pc.printf("Magnetometer ODR = 8 Hz\n\r");
+            if(Mmode == 6) pc.printf("Magnetometer ODR = 100 Hz\n\r");
+            pc.printf("mag calibration: \r\nx:\t%f\r\ny:\t%f\r\nz:\t%f\r\n", magbias[0], magbias[1], magbias[2]);
+        }
+    }
+
+
+    void sensitivity(Serial &pc, bool show = false) {
+        getAres(); // Get accelerometer sensitivity
+        getGres(); // Get gyro sensitivity
+        getMres(); // Get magnetometer sensitivity
+        if (show) {
+            pc.printf("Accelerometer sensitivity is %f LSB/g \n\r", 1.0f/aRes);
+            pc.printf("Gyroscope sensitivity is %f LSB/deg/s \n\r", 1.0f/gRes);
+            pc.printf("Magnetometer sensitivity is %f LSB/G \n\r", 1.0f/mRes);
+        }
+    }
+
+
+    char readByte(uint8_t address, uint8_t subAddress) {
+        char data[1]; // `data` will store the register data
+        char data_write[1];
+        data_write[0] = subAddress;
+        i2c.write(address, data_write, 1, 1); // no stop
+        i2c.read(address, data, 1, 0);
+        return data[0];
+    }
+
+
+    void readBytes(uint8_t address, uint8_t subAddress, uint8_t count, uint8_t * dest) {
+        char data[14];
+        char data_write[1];
+        data_write[0] = subAddress;
+        i2c.write(address, data_write, 1, 1); // no stop
+        i2c.read(address, data, count, 0);
+        for(int ii = 0; ii < count; ii++) {
+            dest[ii] = data[ii];
+        }
+    }
+
+
+    void 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 = 10.0*4219.0/8190.0; // Proper scale to return milliGauss
+                break;
+            case MFS_16BITS:
+                mRes = 10.0*4219.0/32760.0; // Proper scale to return milliGauss
+                break;
+        }
+    }
+
+
+    void 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 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 readAccelData() {
+        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
+        ax = (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ;  // Turn the MSB and LSB into a signed 16-bit value
+        ay = (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
+        az = (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
+    }
+
+    void readGyroData() {
+        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
+        gx = (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ;  // Turn the MSB and LSB into a signed 16-bit value
+        gy = (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
+        gz = (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
+    }
+
+    void readMagData() {
+        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
+                mx = (int16_t)(((int16_t)rawData[1] << 8) | rawData[0]) ;  // Turn the MSB and LSB into a signed 16-bit value
+                my = (int16_t)(((int16_t)rawData[3] << 8) | rawData[2]) ;  // Data stored as little Endian
+                mz = (int16_t)(((int16_t)rawData[5] << 8) | rawData[4]) ;
+            }
+        }
+    }
+
+    void readimu() {
+        readAccelData();
+        ax = ax*aRes - accelBias[0];
+        ay = ay*aRes - accelBias[1];
+        az = az*aRes - accelBias[2];
+
+        readGyroData();
+        gx = gx*gRes - gyroBias[0];
+        gy = gy*gRes - gyroBias[1];
+        gz = gz*gRes - gyroBias[2];
+
+        // Calculate the magnetometer values in milliGauss
+        // Include factory calibration per data sheet and user environmental corrections
+        readMagData();
+        mx = mx*mRes*magCalibration[0] - magbias[0];
+        my = my*mRes*magCalibration[1] - magbias[1];
+        mz = mz*mRes*magCalibration[2] - magbias[2];
+        
+        checksum = 0;
+        checksum += int(1000*ax) + int(1000*ay) + int(1000*az) +int(gx) + int(gy) + int(gz) +int(mx) + int(my) + int(mz);
+
+    }// end of read IMUData()
+
+    int16_t 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)(((int16_t)rawData[0]) << 8 | rawData[1]) ;  // Turn the MSB and LSB into a 16-bit value
+    }
+
+
+    void resetMPU9250() {
+        // reset device
+        writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x80); // Write a one to bit 7 reset bit; toggle reset device
+        wait(0.1);
+    }
+
+    void initAK8963(float * destination) {
+        // First extract the factory calibration for each magnetometer axis
+        uint8_t rawData[3];  // x/y/z gyro calibration data stored here
+        writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00); // Power down magnetometer
+        wait(0.01);
+        writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x0F); // Enter Fuse ROM access mode
+        wait(0.01);
+        readBytes(AK8963_ADDRESS, AK8963_ASAX, 3, &rawData[0]);  // Read the x-, y-, and z-axis calibration values
+        destination[0] =  (float)(rawData[0] - 128)/256.0f + 1.0f;   // Return x-axis sensitivity adjustment values, etc.
+        destination[1] =  (float)(rawData[1] - 128)/256.0f + 1.0f;
+        destination[2] =  (float)(rawData[2] - 128)/256.0f + 1.0f;
+        writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00); // Power down magnetometer
+        wait(0.01);
+        // Configure the magnetometer for continuous read and highest resolution
+        // set Mscale bit 4 to 1 (0) to enable 16 (14) bit resolution in CNTL register,
+        // and enable continuous mode data acquisition Mmode (bits [3:0]), 0010 for 8 Hz and 0110 for 100 Hz sample rates
+        writeByte(AK8963_ADDRESS, AK8963_CNTL, Mscale << 4 | Mmode); // Set magnetometer data resolution and sample ODR
+        wait(0.01);
+    }
+
+
+    void initMPU9250() {
+        // Initialize MPU9250 device
+        // wake up device
+        writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00); // Clear sleep mode bit (6), enable all sensors
+        wait(0.1); // Delay 100 ms for PLL to get established on x-axis gyro; should check for PLL ready interrupt
+
+        // get stable time source
+        writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x01);  // Set clock source to be PLL with x-axis gyroscope reference, bits 2:0 = 001
+
+        // Configure Gyro and Accelerometer
+        // Disable FSYNC and set accelerometer and gyro bandwidth to 44 and 42 Hz, respectively;
+        // DLPF_CFG = bits 2:0 = 010; this sets the sample rate at 1 kHz for both
+        // Maximum delay is 4.9 ms which is just over a 200 Hz maximum rate
+        writeByte(MPU9250_ADDRESS, CONFIG, 0x03);
+
+        // Set sample rate = gyroscope output rate/(1 + SMPLRT_DIV)
+        writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x04);  // Use a 200 Hz rate; the same rate set in CONFIG above
+
+        // Set gyroscope full scale range
+        // Range selects FS_SEL and AFS_SEL are 0 - 3, so 2-bit values are left-shifted into positions 4:3
+        uint8_t c =  readByte(MPU9250_ADDRESS, GYRO_CONFIG);
+        writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c & ~0xE0); // Clear self-test bits [7:5]
+        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
+
+        // Set accelerometer configuration
+        c =  readByte(MPU9250_ADDRESS, ACCEL_CONFIG);
+        writeByte(MPU9250_ADDRESS, 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, and clear on read of INT_STATUS, enable I2C_BYPASS_EN so additional chips
+        // can join the I2C bus and all can be controlled by the Arduino as master
+        writeByte(MPU9250_ADDRESS, INT_PIN_CFG, 0x22);
+        writeByte(MPU9250_ADDRESS, INT_ENABLE, 0x01);  // Enable data ready (bit 0) interrupt
+    }
+
+    //void calibrateMag(float * dest1, float * dest2, Serial &pc)
+    void calibrateMag(Serial &pc) {
+        uint16_t ii = 0, sample_count = 0;
+        //int32_t mag_bias[3] = {0, 0, 0};
+        int32_t mag_scale[3] = {0, 0, 0};
+        int16_t mag_max[3] = {0x8000, 0x8000, 0x8000};
+        int16_t mag_min[3] = {0x7FFF, 0x7FFF, 0x7FFF};
+        int16_t mag_temp[3] = {0, 0, 0};
+        pc.printf("Pre-Mag Calibration: \r\nx:\t%f\r\ny:\t%f\r\nz:\t%f\r\n", magbias[0], magbias[1], magbias[2]);
+        pc.printf("Mag Calibration: Wave device in a figure eight until done!\n");
+        wait(4);
+
+        sample_count = 500;
+        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];
+            }// end of inner for
+            wait(.035);  // at 8 Hz ODR, new mag data is available every 125 ms
+            pc.printf("%d\t%d\t%d\r\n", mag_temp[0], mag_temp[1], mag_temp[2]);
+        }// end of outer for
+        wait(1);
+        pc.printf("%d\t%d\t%d\t%d\t%d\t%d\r\n", mag_min[0], mag_max[0], mag_min[1], mag_max[1], mag_min[2], mag_max[2]);
+        wait(10);
+        // Get hard iron correction
+        magbias[0]  = (mag_max[0] + mag_min[0])/2;  // get average x mag bias in counts
+        magbias[1]  = (mag_max[1] + mag_min[1])/2;  // get average y mag bias in counts
+        magbias[2]  = (mag_max[2] + mag_min[2])/2;  // get average z mag bias in counts
+
+        //dest1[0] = (float) mag_bias[0]*mRes*MPU9250magCalibration[0];  // save mag biases in G for main program
+        //dest1[1] = (float) mag_bias[1]*mRes*MPU9250magCalibration[1];
+        //dest1[2] = (float) mag_bias[2]*mRes*MPU9250magCalibration[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]);
+        pc.printf("Post-Mag Calibration: \r\nx:\t%f\r\ny:\t%f\r\nz:\t%f\r\n", magbias[0], magbias[1], magbias[2]);
+        pc.printf("Mag Calibration done!\n");
+    }// end of calibrateMag
+
+    // 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(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(MPU9250_ADDRESS, PWR_MGMT_1, 0x80); // Write a one to bit 7 reset bit; toggle reset device
+        wait(0.1);
+
+        // get stable time source
+        // Set clock source to be PLL with x-axis gyroscope reference, bits 2:0 = 001
+        writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x01);
+        writeByte(MPU9250_ADDRESS, PWR_MGMT_2, 0x00);
+        wait(0.2);
+
+        // Configure device for bias calculation
+        writeByte(MPU9250_ADDRESS, INT_ENABLE, 0x00);   // Disable all interrupts
+        writeByte(MPU9250_ADDRESS, FIFO_EN, 0x00);      // Disable FIFO
+        writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00);   // Turn on internal clock source
+        writeByte(MPU9250_ADDRESS, I2C_MST_CTRL, 0x00); // Disable I2C master
+        writeByte(MPU9250_ADDRESS, USER_CTRL, 0x00);    // Disable FIFO and I2C master modes
+        writeByte(MPU9250_ADDRESS, USER_CTRL, 0x0C);    // Reset FIFO and DMP
+        wait(0.015);
+
+        // Configure MPU9250 gyro and accelerometer for bias calculation
+        writeByte(MPU9250_ADDRESS, CONFIG, 0x01);      // Set low-pass filter to 188 Hz
+        writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x00);  // Set sample rate to 1 kHz
+        writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 0x00);  // Set gyro full-scale to 250 degrees per second, maximum sensitivity
+        writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0x00); // Set accelerometer full-scale to 2 g, maximum sensitivity
+
+        uint16_t  gyrosensitivity  = 131;   // = 131 LSB/degrees/sec
+        uint16_t  accelsensitivity = 16384;  // = 16384 LSB/g
+
+        // Configure FIFO to capture accelerometer and gyro data for bias calculation
+        writeByte(MPU9250_ADDRESS, USER_CTRL, 0x40);   // Enable FIFO
+        writeByte(MPU9250_ADDRESS, FIFO_EN, 0x78);     // Enable gyro and accelerometer sensors for FIFO (max size 512 bytes in MPU-9250)
+        wait(0.04); // accumulate 40 samples in 80 milliseconds = 480 bytes
+
+        // At end of sample accumulation, turn off FIFO sensor read
+        writeByte(MPU9250_ADDRESS, FIFO_EN, 0x00);        // Disable gyro and accelerometer sensors for FIFO
+        readBytes(MPU9250_ADDRESS, FIFO_COUNTH, 2, &data[0]); // read FIFO sample count
+        fifo_count = ((uint16_t)data[0] << 8) | data[1];
+        packet_count = fifo_count/12;// How many sets of full gyro and accelerometer data for averaging
+
+        for (ii = 0; ii < packet_count; ii++) {
+            int16_t accel_temp[3] = {0, 0, 0}, gyro_temp[3] = {0, 0, 0};
+            readBytes(MPU9250_ADDRESS, FIFO_R_W, 12, &data[0]); // read data for averaging
+            accel_temp[0] = (int16_t) (((int16_t)data[0] << 8) | data[1]  ) ;  // Form signed 16-bit integer for each sample in FIFO
+            accel_temp[1] = (int16_t) (((int16_t)data[2] << 8) | data[3]  ) ;
+            accel_temp[2] = (int16_t) (((int16_t)data[4] << 8) | data[5]  ) ;
+            gyro_temp[0]  = (int16_t) (((int16_t)data[6] << 8) | data[7]  ) ;
+            gyro_temp[1]  = (int16_t) (((int16_t)data[8] << 8) | data[9]  ) ;
+            gyro_temp[2]  = (int16_t) (((int16_t)data[10] << 8) | data[11]) ;
+
+            accel_bias[0] += (int32_t) accel_temp[0]; // Sum individual signed 16-bit biases to get accumulated signed 32-bit biases
+            accel_bias[1] += (int32_t) accel_temp[1];
+            accel_bias[2] += (int32_t) accel_temp[2];
+            gyro_bias[0]  += (int32_t) gyro_temp[0];
+            gyro_bias[1]  += (int32_t) gyro_temp[1];
+            gyro_bias[2]  += (int32_t) gyro_temp[2];
+
+        }
+        accel_bias[0] /= (int32_t) packet_count; // Normalize sums to get average count biases
+        accel_bias[1] /= (int32_t) packet_count;
+        accel_bias[2] /= (int32_t) packet_count;
+        gyro_bias[0]  /= (int32_t) packet_count;
+        gyro_bias[1]  /= (int32_t) packet_count;
+        gyro_bias[2]  /= (int32_t) packet_count;
+
+        if(accel_bias[2] > 0L) {
+            accel_bias[2] -= (int32_t) accelsensitivity;   // Remove gravity from the z-axis accelerometer bias calculation
+        } else {
+            accel_bias[2] += (int32_t) accelsensitivity;
+        }
+
+        // Construct the gyro biases for push to the hardware gyro bias registers, which are reset to zero upon device startup
+        data[0] = (-gyro_bias[0]/4  >> 8) & 0xFF; // Divide by 4 to get 32.9 LSB per deg/s to conform to expected bias input format
+        data[1] = (-gyro_bias[0]/4)       & 0xFF; // Biases are additive, so change sign on calculated average gyro biases
+        data[2] = (-gyro_bias[1]/4  >> 8) & 0xFF;
+        data[3] = (-gyro_bias[1]/4)       & 0xFF;
+        data[4] = (-gyro_bias[2]/4  >> 8) & 0xFF;
+        data[5] = (-gyro_bias[2]/4)       & 0xFF;
+
+        /// Push gyro biases to hardware registers
+        /*  writeByte(MPU9250_ADDRESS, XG_OFFSET_H, data[0]);
+          writeByte(MPU9250_ADDRESS, XG_OFFSET_L, data[1]);
+          writeByte(MPU9250_ADDRESS, YG_OFFSET_H, data[2]);
+          writeByte(MPU9250_ADDRESS, YG_OFFSET_L, data[3]);
+          writeByte(MPU9250_ADDRESS, ZG_OFFSET_H, data[4]);
+          writeByte(MPU9250_ADDRESS, ZG_OFFSET_L, data[5]);
+        */
+        dest1[0] = (float) gyro_bias[0]/(float) gyrosensitivity; // construct gyro bias in deg/s for later manual subtraction
+        dest1[1] = (float) gyro_bias[1]/(float) gyrosensitivity;
+        dest1[2] = (float) gyro_bias[2]/(float) gyrosensitivity;
+
+        // Construct the accelerometer biases for push to the hardware accelerometer bias registers. These registers contain
+        // factory trim values which must be added to the calculated accelerometer biases; on boot up these registers will hold
+        // non-zero values. In addition, bit 0 of the lower byte must be preserved since it is used for temperature
+        // compensation calculations. Accelerometer bias registers expect bias input as 2048 LSB per g, so that
+        // the accelerometer biases calculated above must be divided by 8.
+
+        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] = (int16_t) ((int16_t)data[0] << 8) | data[1];
+        readBytes(MPU9250_ADDRESS, YA_OFFSET_H, 2, &data[0]);
+        accel_bias_reg[1] = (int16_t) ((int16_t)data[0] << 8) | data[1];
+        readBytes(MPU9250_ADDRESS, ZA_OFFSET_H, 2, &data[0]);
+        accel_bias_reg[2] = (int16_t) ((int16_t)data[0] << 8) | data[1];
+
+        uint32_t mask = 1uL; // Define mask for temperature compensation bit 0 of lower byte of accelerometer bias registers
+        uint8_t mask_bit[3] = {0, 0, 0}; // Define array to hold mask bit for each accelerometer bias axis
+
+        for(ii = 0; ii < 3; ii++) {
+            if(accel_bias_reg[ii] & mask) mask_bit[ii] = 0x01; // If temperature compensation bit is set, record that fact in mask_bit
+        }
+
+        // Construct total accelerometer bias, including calculated average accelerometer bias from above
+        accel_bias_reg[0] -= (accel_bias[0]/8); // Subtract calculated averaged accelerometer bias scaled to 2048 LSB/g (16 g full scale)
+        accel_bias_reg[1] -= (accel_bias[1]/8);
+        accel_bias_reg[2] -= (accel_bias[2]/8);
+
+        data[0] = (accel_bias_reg[0] >> 8) & 0xFF;
+        data[1] = (accel_bias_reg[0])      & 0xFF;
+        data[1] = data[1] | mask_bit[0]; // preserve temperature compensation bit when writing back to accelerometer bias registers
+        data[2] = (accel_bias_reg[1] >> 8) & 0xFF;
+        data[3] = (accel_bias_reg[1])      & 0xFF;
+        data[3] = data[3] | mask_bit[1]; // preserve temperature compensation bit when writing back to accelerometer bias registers
+        data[4] = (accel_bias_reg[2] >> 8) & 0xFF;
+        data[5] = (accel_bias_reg[2])      & 0xFF;
+        data[5] = data[5] | mask_bit[2]; // preserve temperature compensation bit when writing back to accelerometer bias registers
+
+        // Apparently this is not working for the acceleration biases in the MPU-9250
+        // Are we handling the temperature correction bit properly?
+        // Push accelerometer biases to hardware registers
+        /*  writeByte(MPU9250_ADDRESS, XA_OFFSET_H, data[0]);
+          writeByte(MPU9250_ADDRESS, XA_OFFSET_L, data[1]);
+          writeByte(MPU9250_ADDRESS, YA_OFFSET_H, data[2]);
+          writeByte(MPU9250_ADDRESS, YA_OFFSET_L, data[3]);
+          writeByte(MPU9250_ADDRESS, ZA_OFFSET_H, data[4]);
+          writeByte(MPU9250_ADDRESS, ZA_OFFSET_L, data[5]);
+        */
+        // Output scaled accelerometer biases for manual subtraction in the main program
+        dest2[0] = (float)accel_bias[0]/(float)accelsensitivity;
+        dest2[1] = (float)accel_bias[1]/(float)accelsensitivity;
+        dest2[2] = (float)accel_bias[2]/(float)accelsensitivity;
+    }
+
+
+    // 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;
+
+        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
+        wait_ms(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);
+        wait_ms(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 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 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;
+
+    }
+};
+#endif
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