This paper presents non-iterative cooperative/parallel Kalman filtering algorithms for decentralized network navigation, in which mobile nodes cooperate in both spatial and temporal domains to infer their positions. We begin by presenting an augmented minimum-mean-square error (MMSE) estimator for centralized navigation network, and then decouple it into a set of local sub-ones each corresponding to a mobile node; all these sub-estimators work in parallel and cooperatively — with the state estimates exchanging between neighbors — to provide results similar to those obtained by the augmented one. After that, we employ the approximation methods that adopted in the conventional nonlinear Kalman filters to calculate the second-order terms involved in these sub-estimators, and propose a decentralized cooperative/parallel Kalman filtering based network navigation framework. Finally, upon the framework, we present two cooperative/parallel Kalman filtering algorithms corresponding to the extended and unscented Kalman filters respectively, and compare them with conventional decentralized methods by simulations to show the superiority.