This paper is concerned with the set-membership filtering problem for a class of linear time-varying systems with norm-bounded noises and impulsive measurement outliers. A new representation is proposed to model the measurement outlier by an impulsive signal whose minimum interval length (i.e., the minimum duration between two adjacent impulsive signals) and minimum norm (i.e., the minimum of the norms of all impulsive signals) are larger than certain thresholds that are adjustable according to engineering practice. In order to guarantee satisfactory filtering performance, a so-called parameter-dependent set-membership filter is put forward that is capable of generating a time-varying ellipsoidal region containing the true system state. First, a novel outlier detection strategy is developed, based on a dedicatedly constructed input-output model, to examine whether the received measurement is corrupted by an outlier. Then, through the outcome of the outlier detection, the gain matrix of the desired filter and the corresponding ellipsoidal region are calculated by solving two recursive difference equations. Furthermore, the ultimate boundedness issue on the time-varying ellipsoidal region is thoroughly investigated. Finally, a simulation example is provided to demonstrate the effectiveness of our proposed parameter-dependent set-membership filtering strategy.

中文翻译：

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集成员过滤受脉冲测量异常值的影响：递归算法

本文涉及一类具有范数界噪声和脉冲测量离群值的线性时变系统的集合成员滤波问题。提出了一种新的表示形式，通过其最小间隔长度（即，两个相邻脉冲信号之间的最小持续时间）和最小范数（即，所有脉冲信号的范数的最小值）大于一定值的脉冲信号来对测量离群值建模阈值可根据工程实践进行调整。为了保证令人满意的滤波性能，提出了一种所谓的参数相关的集合成员滤波器，其能够产生包含真实系统状态的时变椭圆形区域。首先，根据专门构建的输入输出模型，开发了一种新颖的异常值检测策略，检查收到的测量值是否被异常值破坏。然后，通过离群值检测的结果，通过求解两个递归差方程来计算所需滤波器的增益矩阵和相应的椭球区域。此外，对时变椭球区域上的极限有界问题进行了深入研究。最后，提供了一个仿真示例来证明我们提出的参数相关的集合成员资格过滤策略的有效性。彻底研究了时变椭球区域上的极限有界问题。最后，提供了一个仿真示例来证明我们提出的参数相关的集合成员资格过滤策略的有效性。彻底研究了时变椭球区域上的极限有界问题。最后，提供了一个仿真示例来证明我们提出的参数相关的集合成员资格过滤策略的有效性。