Trajectory Kalman Filter with Enhanced State Estimation

This program provides a Kalman filter simulation specifically designed for target trajectory estimation. A key implementation difference from previous versions is the inclusion of velocity and acceleration components in the observation signals, requiring appropriate state vector augmentation. The information matrix has been extended to three dimensions to accommodate the enhanced measurement model. The implementation employs standard Kalman filter equations while demonstrating proper handling of multi-dimensional data structures. Code architecture includes separate modules for prediction and update cycles, with matrix operations optimized for real-time performance. The program contains complete validation checks and error handling mechanisms. This robust implementation serves as an excellent educational resource for colleagues beginning their study of Kalman filters. Beyond the core functionality, we provide detailed usage documentation, comprehensive code comments explaining algorithmic choices, and implementation notes covering state transition models and measurement updates. These resources help users better understand both the theoretical principles and practical implementation aspects of Kalman filtering for motion tracking applications. The code structure clearly demonstrates key elements including state initialization, process noise configuration, measurement processing, and covariance management. Particular attention is given to the implementation of the three-dimensional information matrix operations and their integration with the standard filter equations.