Link to paper by Bernard Levy, Milton Adam, and Alan Willsky (1990).
This paper considers the problem of estimation of random fields on lattice which statisfy an autoregressive model such that the estimate of each point depends on its neighbors and is driven by white noise. They show example of how these systems are common when one discretized differential equations to get a discrete representation of the system. There solution to estimation is to stack the columns of the field and show that the columns satisfy a second order difference equation – which they refer to as two point boundary valued descriptor system (TPBVDs). Then, they use known theory on deriving smoothing algorithms using TPNVDs.
Tags: nearest neighbor models, random fields, reciprocal process, recursive estimation
