<p>This paper addresses the distributed Kalman filtering problem from a consensus optimization perspective. A novel distributed Kalman filter employing the well-known primal-dual method, in which the primal and dual variables are iteratively updated, is presented. The proposed algorithm consists of a local prediction step and a distributed estimation update with arbitrary sub-iteration steps. In the stability analysis, we establish sufficient conditions on the step size that guarantee the convergence of the estimation error. Compared to existing distributed filtering methods that necessitate a high number of sub-iterations for consensus, the proposed algorithm ensures stability even with a single subiteration, which is crucial for reducing communication overhead. Furthermore, the effectiveness of the algorithm is validated through lab-scale experiments involving the distributed state estimation of a mobile robot via a camera network.</p>