Multiscale Statistical Signal Processing: Stochastic Processes Indexed by Trees [chapter]

M. Basseville, A. Benveniste, K. C. Chou, A. S. Willsky
1990 Realization and Modelling in System Theory  
Motivated by the recently-developed theory of multiscale signal models and wavelet transforms, we introduce stochastic dynamic models evolving on homogeneous trees. In particular we introduce and investigate both AR and state models on trees. Our analysis yields generalizations of Levinson and Schur recursions and of Kalman filters, Riccati equations, and Rauch-Tung-Striebel smoothing.
doi:10.1007/978-1-4612-3462-3_31 fatcat:gefeq6yqmvcltgizvsjyr62jtu