Basic_Linear_Library

Intro

• It's an easy C library for linear algebra and control on mcus.
• Contain 4 parts:
  • basic_linear.h
  • Quaternion_C.h
  • Quaternion_Gauss_Newton.h
  • Quaternion_EKF.h
• It should be OK to use this in your C++ project

Feature

• For basic_linear.h
  • 2d matrix initialization
  • add, substract, dot, scaling, transpose
  • matrix inverse
  • Cholesky Decomposition
  • Linear solver for Upper/Lower triangular matrix
• For Quaternion_C.h
  • Quaternion initialization
  • Quaternion add, substract, multiply, inverse, scaling, norm
  • Rodriguez Equation
• For Quaternion_Gauss_Newton.h
  • Calculate orientation in 3D space
  • from accelerometer only or from compass+accerelometer
• For Quaternion_EKF.h
  • Sensor fusion from gyroscope and orientation data
  • Gyro bias estimation
  • Potentially provide orientation with faster response
  • Orientation data can be obtained from Quaternion_Gauss_Newton.h

Usage

• To test this library:
  • You can test it on your linux PC
  • make all to build code
  • make clean to wipe the binary
  • please check out main.c in src/ for examples. The comment should be clear.
    • There are several sections in main.c. Uncomment required part to run different examples
• Simply drag the file to inc/ and src/
  • Please check makefile if there is any linking problem.
  • We currently rely on math.h. Please check if your env. support this.
• Please refer to .h for how to use those functions

Note and Problem

• basic_linear.h
  • Please specify TYPE macro for matrix type.
  • Chelosky Inverse is only applicable on Positive-Definite Matrix
    • However, you can do A^-1=(A^TA)^-1A^T, A can be any kind of matrix (but should be full rank).
    • That is because A^T*A is Positive-Definite
  • no inplace multiplication for matrix, that is, you can't do $A = A \dot B$
  • You should create matrix only once because I use malloc in it.
    • Also it is not recommended to free the matrix, especially on mcus.
• Quaternion_C.h
  • rely on basic_linear.h
• Quaternion_Gauss_Newton.h
  • rely on basic_linear.h
  • Please specify SIX_AXIS(accerelometer, mpu6050) or NINE_AXIS(acc.+compass, mpu9250) macro for different IMU configuration.
  • Use global variables. Try not to use this library from 2 different place.
• Quaternion_EKF.h
  • rely on basic_linear.h
  • Use global variables. Try not to use this library from 2 different place.
  • When the noise covariance is very small (<1e-5), the EKF will go explode

TODO

• basic_linear.h
  • Norm, 2-Norm, inf-Norm...
  • Eigen Value Decomposition
  • Singular Value Decomposition
  • Advance indicing
• Quaternion_EKF.h
  • Consider Velocity and Position data from i.e. GPS sensor

Reference

• Chelosky Decomposition
  • You can check out Cholesky–Banachiewicz and Cholesky–Crout algorithms for turning this into codes
• "An Extended Kalman Filter for Quaternion-Based Orientation Estimation Using MARG Sensors", JoZo Luis Marins et.el., 2001