Distributed Pareto-optimal state estimation using sensor networks

A novel model-based dynamic distributed state estimator is proposed using sensor networks. The estimator consists of a filtering step - which uses a weighted combination of information provided by the sensors - and a model-based predictor of the system's state. The filtering weights and the model-based prediction parameters jointly minimize - at each time-step - the bias and the variance of the prediction error in a Pareto optimization framework. The simultaneous distributed design of the filtering weights and of the model-based prediction parameters is considered, differently from what is normally done in the literature. It is assumed that the weights of the filtering step are in general unequal for the different state components, unlike existing consensus-based approaches. The state, the measurements, and the noise components are allowed to be individually correlated, but no probability distribution knowledge is assumed for the noise variables. Each sensor can measure only a subset of the state variables. The convergence properties of the mean and of the variance of the prediction error are demonstrated, and they hold both for the global and the local estimation errors at any network node. Simulation results illustrate the performance of the proposed method, obtaining better results than state of the art distributed estimation approaches.