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Table of Contents
Elements of Quaternion Algebra
Quaternion Definitions
Quaternion Multiplication
Useful Identities
Properties of the quaternion multiplication matrices L and R
Properties of the cross product skew-symmetric matrix
Properties of the matrix
Properties of the matrix
Relationship between Quaternion and Rotational Matrix
Quaternion Time Derivative
Quaternion Integration
Zeroth Order Quaternion Integrator
First Order Quaternion Integrator
Attitude Propagation
Gyro Noise Model
The State Equation
Error and Covariance Representation
Continuous Time Error State Equations
Discrete Time Error State Equations
The State Transition Matrix
The Noise Covariance Matrix Qd
Propagation Equations
Update
Measurement Models
Sun Sensor
Kalman Filter Update