System state estimation in the presence of noise is critical for control systems, signal processing, and many other applications in a variety of fields. Developed decades ago, the Kalman filter remains an important, powerful tool for estimating the variables in a system in the presence of noise. However, when inundated with theory and vast notation

Signal-Plus-Noise Models. The Fundamental Covariance Structure. Recursions for L and L-1. Forward Recursions. Smoothing. Initialization. Normal Priors. A General State-Space Model. Appendix A: The Cholesky Decomposition. Appendix B: Notation Guide.