I. Introduction  
II. Background on Filters  
A. Attitude Estimation Filters and Inertial Systems  
B. Development History  
III. Aided Inertial Navigation Systems  
A. Applications of Inertial Navigation Systems  
IV. Coordinate Frames and Transformations  
A. Coordinate Frames  
B. Transformations  
V. Applied Inertial Navigation  
A. Gyro Bias Corrections  
B. Coning Correction  
C. Sculling Compensation  
D. Velocity Increments Transformation  
E. Quaternion Integration  
F. Normalizing Quaternion Parameters  
G. Direction Cosine Matrix Computation  
VI. Principles of Inertial Navigation  
A. Navigation Equations  
B. Error Dynamic Equations  
VII. Kalman Filter  
A. Components of the Kalman Filter  
B. Kalman Filter Algorithm  
VIII. Filter Insights  
A. Inverse Matrix Calculation  
B. Error Dynamics Approximations  
C. Error-State Kalman Filter  
D. System Model Error Sources  
E. IMU and GNSS Time Synchronization  
IX. Other Attitude Filters  
X. Summary