This paper considers Kalman filtering for mass-spring systems. The aim is a scalable distributed implementation where nodes communicate in a sparse pattern and the state estimate for each node is available locally and usable for control. The focus is on translation invariant systems, to make use of the powerful results available based on Fourier transform methods. In this case it is known that Kalman filters will have a coupling that asymptotically falls off exponentially with distance. Examples are shown where the Kalman filter gains can be truncated very narrowly with small performance loss even though the coupling falls off more slowly. A step towards spatially varying systems is taken in analyzing a system with periodically placed sensors, and it is shown that the original design is insensitive to this spatial variation.