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.

中文翻译：

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具有参数不确定性和测量审查的多传感器滤波融合：单调性和有界性


本文关注一类受参数不确定性和测量删失影响的多传感器系统的托比特卡尔曼融合估计问题。参数不确定性的特征是状态方程和观测方程中都出现乘性噪声，测量删失由 Tobit 观测模型控制。融合估计通过两个阶段实现：在第一阶段，每个传感器将其观测值发送到局部估计器，在第二阶段，然后将局部估计传输到融合中心以生成融合估计。局部估计器实现了根据改进的回归模型设计的托比特卡尔曼滤波算法，而融合中心则利用联邦融合规则进行融合估计。此外，讨论了融合误差协方差相对于审查阈值的单调性，随后还检查了有界性属性，其中获取了融合误差协方差的下限和上限。最后通过两个数值例子证明了融合估计器的有效性。