In this article, the robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties. The uncertainties include state‐dependent and noise‐dependent multiplicative noises, missing measurements, packet dropouts, and uncertain noise variances, the phenomena of missing measurements and packet dropouts occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, de‐randomization approach and fictitious noise approach, the original multisensor system under study is converted into a multi‐model multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of non‐negative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive moving average (ARMA) signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.

中文翻译：

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具有数据包丢失和丢失测量的网络随机不确定系统的鲁棒融合稳态估计器

在本文中，针对一类具有混合不确定性的多传感器网络系统，研究了鲁棒的融合稳态滤波问题。不确定性包括状态相关和噪声相关的乘法噪声，丢失的测量值，数据包丢失和不确定的噪声方差，丢失的测量值和数据包丢失的现象以随机方式发生，并由两个已知条件的伯努利分布随机变量来描述。概率。使用包括增强方法，去随机化方法和虚拟噪声方法的模型转换方法，将原始正在研究的多传感器系统转换为仅具有不确定噪声方差的多模型多传感器系统。根据minimax鲁棒估计原理，基于具有不确定噪声方差的保守上限的最坏情况子系统，在统一框架中给出了鲁棒的局部稳态卡尔曼估计器（预测器，滤波器和平滑器）。应用矩阵加权的最优融合算法，为所考虑的系统推导了鲁棒的分布式加权状态融合稳态卡尔曼估计器。通过使用包括增加噪声方法，非负定矩阵的分解方法，二次形式的矩阵表示方法和Lyapunov方程方法的组合方法，证明了所提出估计量的鲁棒性，从而对于所有可允许的不确定性，实际稳定估计量的状态估计误差方差具有相应的最小上限。证明了鲁棒局部和融合稳态卡尔曼估计量之间的精度关系。提出了一个以自回归移动平均（ARMA）信号处理为例的例子，表明状态估计问题可以解决鲁棒的局部和融合信号估计问题。仿真实例验证了所提出结果的有效性和正确性。