A Recursive Method for Estimating Missing Data in Spatio-Temporal Applications

Missing data is a major data reliability problem in spatio-temporal (ST) applications. This article proposes an online method for estimating missing data in case of a network of
$n$
sensors. The true sensor value at a specific location is expressed using an integro-difference equation. The Karhunen–Loéve Expansion of the spatial process allows one to represent the ST field values at
$n$
locations in the form of a linear state-space model. The parameters of the model are identified using the maximum likelihood method. The parameters are updated in a rolling window approach. Whenever missing data are encountered, the algorithm predicts the missing observations based on the constrained solution of state evolution equation. The constrained solution is obtained by representing the optimal state as the orthogonal sum decomposition of a deterministic and a stochastic component. The utility of the algorithm is presented on two sensor network datasets.