This paper addresses the problem of distributed state estimation in a multi-vehicle framework. In the scenario envisioned in this work, each vehicle aims to estimate its own state by implementing a local state observer which relies on locally available measurements and limited communication with other vehicles in the vicinity. The dynamics of the problem are formulated as a more general discrete-time Kalman filtering problem with a sparsity constraint on the gain and, based on this formulation, a method for computation of steady-state observer gains for arbitrary fixed measurement topologies is introduced. The proposed method consists in the optimization of the time-varying distributed Kalman filter over a finite time window to approximate steady-state behavior and compute well-performing steady-state observer gains. To assess the performance of the proposed solution, simulation results are detailed for the practical case of a formation of Autonomous Underwater Vehicles (AUVs).