Gauss Markov

Gauss-Markov models, characterized by their linear relationships and Gaussian noise assumptions, are fundamental tools for time series analysis and state estimation. Current research focuses on improving computational efficiency for high-dimensional applications, particularly through Kalman filtering and smoothing advancements and novel model architectures like Markovian Gaussian Processes, which combine the flexibility of Gaussian Processes with the computational efficiency of Linear Dynamical Systems. These improvements are impacting diverse fields, from neuroscience (analyzing brain region communication) to robotics (visual navigation) and climate modeling, by enabling more accurate and scalable inference in complex systems. Furthermore, extensions of the Gauss-Markov theorem are being explored to enhance linear estimation techniques, particularly in overparameterized settings.