This module contains a Kalman filter implementation and simulation of the rotation dynamics of solid bodies in 2D & 3D.

This module is written to gain an understanding of how a Kalman filter for attitude estimation works.

There are unit tests for most of the essential components. They are in the *_test.m files. To run the unit tests simply run the matlab command clear classes; runtests.

For live visualization run the script run_visualization.m in matlab.

To run the simulation and show a plot afterwards run the script run_graph.m in matlab. This script does multiple runs (each with random initialization) and shows the estimation error plot for rate and attitude.

math subroutines:

• quatconj.m : conjugate of quaternion
• quatmult.m : quaternion multiplication
• rotate_by_quaternion.m : rotate a 3D vector by a quaternion
• rotation_matrix_from_quat.m : generate a rotation matrix from a quaternion
• quat_rand.m : generate a random quternion with uniform probability
• quat_from_two_vect.m : compute a quaternion that rotates a vector to another vector
• cross_prod_matrix : build the cross product matrix from a vector

Kalman filter:

• ExtendedKalmanFilter.m : generic EKF implementation
• KalmanFilter.m : generic KF implementation (there is no constistent distinction in variable naming between F (continuous time) and Phi (discrete time), this should be changed someday)
• EKF3DConstMomentum.m : simple EKF for 3D body assuming constant momentum
• EKF3DConstMomentumSymbolicDerivation.m : symbolic derivations for the above
• MEKF3DConstMomentum.m : Multiplicative EKF with constant momentum model
• MEKF3DConstMomentumSymbolicDerivation.m : symbolic derivations for the above
• MEKF3DGyro.m : Multiplicative EKF with gyroscope input
• MEKF3DGyroSymbolicDerivation.m : symbolic derivations for the above

Simulation:

• RotationBody3D.m : simulates 3d rotation dynamics & sensor readings
• Simulation3DBody.m : runs the kalman together with 3d body simulation

Plotting:

• run_visualization.m : run the simulation and visualize 3d cube
• cube_plot.m : draw a cube, used in run_visualization.m
• run_graph.m : run multiple simulations and plot error graphs

Simple 2d KF example: (this is just a toy example of a linear Kalman filter)

• runPosVel2DSystem.m : set up and run 2d Kalman
• RotationBody2D.m : simulates 2d rotation dynamics & sensor readings
• plot_KF_results.m : 2d graphs with error bar