We describe a distributed and iterative approach to perform the unitary transformations in the square root information filter implementation of the Kalman filter, providing an alternative to the common QR factorization-based approaches. The new approach is useful in approximate computation of filtered estimates for temporally evolving random fields defined by local interactions and observations. Using several examples motivated by computer vision applications, we demonstrate that near-optimal estimates can be computed for problems of practical importance using only a small number of iterations, which can be performed in a finely parallel manner over the spatial domain of the random field.