Multi-Sensor Filtering Fusion With Parametric Uncertainties and Measurement Censoring: Monotonicity and Boundedness

This paper is concerned with the Tobit Kalman fusion estimation problem for a class of multi-sensor systems subject to parametric uncertainties and measurement censoring. The parametric uncertainty is characterized by the multiplicative noise appearing in both state and observation equations, and the measurement censoring is governed by the Tobit observation model. The fusion estimation is implemented via two stages: at the first stage, each sensor sends its observations to the local estimator and, at the second stage, the local estimates are then transmitted to the fusion center so as to generate the fused estimate. The local estimator realizes a Tobit Kalman filtering algorithm which is devised in accordance with a modified regression model, whilst the fusion center carries out the fusion estimation by resorting to the federated fusion rule. Furthermore, the monotonicity of the fused error covariance with respect to the censoring threshold is discussed and, subsequently, the boundedness property is also examined where both lower and upper bounds are acquired for the fused error covariance. The validity of the fusion estimator is finally shown via two numerical examples.