In this paper a novel partition-based state prediction method is proposed for interconnected stochastic systems using sensor networks. Each sensor locally computes a prediction of the state of the monitored subsystem based on the knowledge of the local model and the communication with neighboring nodes of the sensor network. The prediction is performed in a distributed way, not requiring a centralized coordination or the knowledge of the global model. Weights and parameters of the state prediction are locally optimized in order to minimise at each time-step bias and variance of the prediction error by means of a multi-objective Pareto optimization framework. Individual correlations between the state, the measurements, and the noise components are considered, thus assuming to have in general unequal weights and parameters for each different state component. No probability distribution knowledge is required for the noise variables. Simulation results show the effectiveness of the proposed method.