Wireless sensor networks (WSNs) represent a critical research domain within the Internet of Things (IoT) technology. The distributed Kalman filter (DKF) has garnered significant attention as an information fusion method for WSNs. However, effectively handling non-Gaussian environments remains a crucial challenge for DKF. This paper proposes a solution by partitioning the noise distribution into multiple Gaussian components, thereby approximating the measurement model with sub-models. We introduce a model fusion distributed Kalman filter (MFDKF) that combines sub-models by assuming independent random processes for the model's transition probabilities. The expectation maximization (EM) algorithm is employed to estimate the relevant parameters. To address specific requirements in WSNs that demand high consensus or have limited communication, two derivative algorithms, namely consensus MFDKF (C-MFDKF) and simplified MFDKF (S-MFDKF), are proposed based on consensus theory. The convergence of MFDKF and its derivative algorithms is analyzed. A series of simulations demonstrate the effectiveness of MFDKF and its derivative algorithms. This paper has been accepted and published in IEEE Internet of Things Journal (Early Access), DOI: https://doi.org/10.1109/JIOT.2025.3526240