Inertial Navigation System (INS)

spreadsheet of data:
https://docs.google.com/spreadsheets/d/1SMg0OuFvwoGWqhNJKjKyEFaudhpbxwleUFlkU9-4UDw/edit?usp=sharing

INS Intertial Navigation System - Sensors, processors, and software to estimate position.

3D cartesian space - a cube, 3 dimensions: x,y,z

A vehicle exists in 3D cartesian space. It can be measured in three dimensions, such as width, height, and depth.

The movement of a vehicle can also be measured in 3 dimensions: x, y, and z.

• The x-axis runs the length of the vehicle, from nose to tail.
• The y-axis runs from side to side, from wingtip to wingtip.
• The z-axis runs up and down, from the center of the earth on up.

Motion sensors measure the movement of a vehicle along the three axes.

• accelerometer - measures linear motion along an axis.
• gyroscope - measures rotational motion around an axis.

• magnetometer - measures the strength of the magnetic fields operating on a vehicle.
• barometer/altimeter - measures air pressure, which can be used to calculate altitude above sea level.

A collection of 3 accelerometers and 3 gyroscopes. This device gives us six numbers: linear motion along each of the x,y,z axes, and rotational motion around each of the x,y,z axes. This gives us the complete picture of inertial motion of the vehicle.

It is not enough to measure motion. We also need to know our current position, or orientation, or attitude.

Imagine we experienced an acceleration along the x-axis for two seconds. During that two seconds we went from standing still to moving upwards at 8 meters per second squared. Now where are we

???? does the accelerometer measure acceleration or motion ?

3 types of accelerometer: mems, piezo electric, piezo resistive https://youtu.be/To7JagpPDwY

velocity vs acceleration

per Steppe School youtubes:

bias, aka offset, must be removed from each measurement

• accelerometer
  • measures linear acceleration, not velocity
  • unit: mg, 1g = 9.8 m/s2, 1mg = 1 thousandth of a g
  • has bias, but not so critical as gyroscope and magnetometer
  • gravity is an acceleration of 1g or 1000mg. This acceleration is always acting on the sensor.
  • the upright and at-rest measurement should be x:0, y:0, z:1000.
  • as the sensor is rotated the acceleration due to gravity is distributed among the x,y,z axes.
• gyroscope
  • gyroscope measures angular velocity, not acceleration
  • gyroscope unit: degrees per second
  • at rest, gyroscope returns the bias
  • by subtracting the bias from a readingd, the at rest measurement is x:0, y:0, z:1000
  • calibration is done at rest for some seconds, the average of readings is the bias
  • 20948 chip has “offset” registers that we can set with the 3 bias values, each divided by 4
• magnetometer
  • no registers, so we must keep variables and do the subtraction from each measurement
  • calibration is done during 3D rotation for some seconds
  • ((max - min) / 2) should be zero, so the actual value during calibration is the bias
  • in addition to the bias, we also have an adjustment for declination, to convert magnetic north to true north

localization = changing reference system from the body of the sensor to the earth

• sensor readings give data relative to the body, the vehicle
• ahrs values give data relative to the earth

units:

• linear velocity: meters per second
• linear acceleration: meters per second squared
• angular velocity: degrees per second, radians per second
• angular acceleration: ?
• rotation velocity: hertz, cycles per second
• 10-6 one millionth, μ, micro * 10-3 one thousandth, m, milli

accelerometer and gyroscope measure motion we know that the z-axis is pointing straight up, but the x and y-axes are relative to some random or arbitrary starting point by adding a magnetometer, we can fix the x axis relative to north-south, and the y-axis relative to east-west

the magnetometer measures the strength of magnetic fields acting on the sensor the most significant magnetic field is that of the earth

naming absurdities:

• IMU inertial measurement unit
  • does not measure inertia. It's components measure accleration, velocity, and magnetic field strenth.
  • is not a unit of measurement
• 6-axis imu or 9-axis imu. There are only three axes: x,y,z.
• 6dof or 9dof. A sensor does not have degrees of freedom.

AHRS - Attitude and Heading Reference System -

Attitude - the orientation of a vehicle in cartesian space. Pitch, roll, yaw.

Heading - the direction a vehicle is facing, the x-axis, in compass degrees.

Dead reckoning - estimate current position of a vehicle by keeping track of changes in speed and direction over time.

IMU Kalman Filter, a type of sensor fusion Low Pass Filter GPS - 1 meter accuracy at best, 3 meter average in position. No heading info. Sensor Fusion DMP

RTK - two gps: base station plus rover, triangulate, to get position with 1 cm accuracy Compassing - two gps to get heading

Odometer - wheel odometer Cameras Lidar

IMU - 3×3 sensors AHRS - use kalman filter to fuse sensor data and output roll, pitch, and yaw INS - add gps input and dead reckoning to the Kalman Filter, for position and heading

Commercial company, explaining sensor types intermd of their product offering https://youtu.be/4CZQQ0VLCG8?si=CiCEKmKsOqWOa6bP

Hideakitai library, esp32 + mpu9250 for heading output https://github.com/hideakitai/MPU9250

9250 obsolete, replace with ICM-20948 https://youtu.be/Oen3HqUbctM?si=3UnWGo-XOvs3ZwCZ

video by very creepy guy using adafruit bno055, but no compass heading, source code on screen but not downloadable https://www.youtube.com/watch?v=uJVzkl73A74

quaternion

  4 numbers, 0 to 1, w,x,y,z

euler angles

  3 numbers, 0 to 360, x,y,z, pitch, roll, yaw
  susceptible to gimbal lock at 90 degrees
  over 45 degrees, not so smooth

sparkfun 9dof imu https://learn.sparkfun.com/tutorials/sparkfun-9dof-imu-icm-20948-breakout-hookup-guide library for arduino https://github.com/sparkfun/SparkFun_ICM-20948_ArduinoLibrary/archive/main.zip

Kris Winer, see github examples for MPU9250

In general, start search in github, as opposed to youtube or google.

Magnetic-Declination.com

Khon Kaen Khon Kaen Latitude: 16° 26' 48.2“ N Longitude: 102° 49' 58.8” E BAN NONG WAENG Magnetic Declination: -1° 11' Declination is NEGATIVE (WEST) Inclination: 22° 20' Magnetic field strength: 43808.0 nT

18.7966251, 98.9648206 Declination: -1.11° Total Field: 44929.7 nT

Magnetometer calibration hold the sensor level and spin it horizontally the graph of the results should be a perfect circle, and the radius of the circle is the strength of the magnetic field https://youtu.be/MinV5V1ioWg?si=Bh-e9aDgxxzKsm14

Scott Lobdell, on AHRS calculations, specifically the Madgwick Quaternion Update start with 9 measurements from the 3 sensors * 3 axes calibrate the magnetometer using a 3D bias to get corrected values of the 3 magnetometer measurements begin ahrs localize the acceleration vector from [x,y,z] to [north,east,down] convert the 9 measurements into a quaternion convert the quaternion into a 3×3 rotation matrix multiply the acceleration vector times the inverse of the rotation matrix, giving the localized acceleration vector remove the acceleration due to gravity [0,0,1] to [0,0,0] apply the declination offset https://youtu.be/T9jXoG0QYIA?si=HjldywVEFu-QSfJp

Paul McWhorter: 9-axis IMUs with Arduino, youtube
Adafruit Bosch BNO055
26 videos, in particular:
#10: Making a tilt-compensated compass
#21: Visualizing 3D rotations in VPython using Quaternions

Scott Lobdell: How to implement an IMU
no specific chip or code
hand-drawn diagrams and verbal description of calibration and AHRS calculations

MicWro Engr, Michael Wrona: Magnetometer Errors and Calibration
Adafruit Precision NXP 9-DOF Breakout Board - FXOS8700 + FXAS21002
series of youtubes made while developing his custom “Hummingbird” flight controller Magneto calibration software
notes

Steppe School: STM32 and ICM20948 IMU part 1. accelerator and gyroscope https://youtu.be/Oen3HqUbctM?si=SeUm8s62af9PdqDz 3 videos

Arduino-compatible, hobbyist IMU products from sparkfun, adafruit, polulu.

chip: TDK Invensense MPU9250
date: ?
status: EOL as of 2018 (supposedly replaced by ICM20948)
comments: users complain that this product is no longer being manufactured and the market is flooded with fakes that don't work.

board: boards available from adafruit and sparkfun
chip: TDK Invensense MPU9250
date: 2018
datasheet: https://invensense.tdk.com/wp-content/uploads/2024/03/DS-000189-ICM-20948-v1.6.pdf
status: supposedly replaces MPU9250, but registers are different, therefore different driver required
comment: users complain that the DMP is not finished. DMP output is not available in current libraries videos:

• https://invensense.tdk.com/wp-content/uploads/2018/10/AN-000146-v2.0-TDK_Migration_MPU_9250toICM-20948.pdf
• see Paul McWhorter youtubes

libraries:

• https://github.com/adafruit/Adafruit_ICM20X
• https://wolles-elektronikkiste.de/en/icm-20948-9-axis-sensor-part-i

board: Adafruit 9-DOF Absolute Orientation IMU Fusion Breakout, BNO055
chip: Bosch Sensortec BNO055
date: 2014
status: “Not recommended for new designs…You could use BHI260AP…”, (but that has no magnetometer).
datasheet: https://www.bosch-sensortec.com/media/boschsensortec/downloads/datasheets/bst-bno055-ds000.pdf
components:

• Atmel SAM20D processor
• BMA280 accelerometer
• BMI055 gyroscope
• BMM150 magnetometer
• built-in fusion library, closed source:
  • Euler angles
  • quaternion
  • modes: IMU, compass, M4G, NDOF

libraries:

• https://www.arduinolibraries.info/libraries/adafruit-bno055

videos:

• https://www.adafruit.com/product/2472
• video demo, no heading mentioned, euler and quat, quat more accurate, too slow for vehicle
• https://www.youtube.com/watch?v=EsgKAawwT9A&t=731s

board: Polulu #2862 MinIMU-9 v6 Gyro, Accelerometer, and Compass (LSM6DSO and LIS3MDL Carrier) chips: ST LSM6DSO + LIS3MDL, two ST chips combined onto one Polulu board datasheets:

• https://www.st.com/resource/en/datasheet/lsm6dso.pdf
• https://www.st.com/resource/en/datasheet/lis3mdl.pdf

board: made by Redshift Labs, sold by Polulu chip: UM7 description:

• AHRS, includes microcontroller running a Kalman Filter
• expensive 160 USD
• Redshift Labs appears to be out of business