Abstract In this paper, we study the centralized fusion (CF) and weighted measurement fusion (WMF) robust steady-state Kalman filtering problem for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, two-step random delays, missing measurements, and uncertain noise variances. By using a model transformation approach consisting 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. By introducing an augmented state vector, and applying the weighted least squares (WLS) algorithm, the CF and WMF systems are obtained. According to the minimax robust estimation principle, based on the worst-case fusion systems with conservative upper bounds of uncertain noise variances, the CF and WMF robust steady-state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved by using a combination method consisting of augmented noise approach, matrix representation approach of quadratic form, and Lyapunov equation approach, the so-called robustness is concerned with the design of a filter such that for all admissible uncertainties, the actual fused 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 (AR) signal processing is proposed, which shows that the robust fusion signal estimation problems can be solved by the robust fusion state estimation method. Simulation example shows the effectiveness and correctness of the proposed method.

中文翻译：

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具有随机两步传输延迟和丢失测量的多传感器网络系统的稳健测量融合稳态估计器设计

摘要 在本文中，我们研究了一类具有混合不确定性的多传感器网络系统的集中融合 (CF) 和加权测量融合 (WMF) 鲁棒稳态卡尔曼滤波问题，包括乘法噪声、两步随机延迟、丢失测量、和不确定的噪声方差。通过使用由增广法、去随机化法和虚拟噪声法组成的模型转换方法，将研究中的原始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。通过引入增强状态向量，并应用加权最小二乘 (WLS) 算法，获得了 CF 和 WMF 系统。根据极小极大鲁棒估计原理，基于具有不确定噪声方差的保守上限的最坏情况融合系统，CF 和 WMF 稳健稳态卡尔曼估计器（预测器、滤波器和平滑器）在统一框架中呈现。通过使用由增广噪声法、二次型矩阵表示法和李雅普诺夫方程法组成的组合方法证明了它们的鲁棒性，所谓的鲁棒性与滤波器的设计有关，使得对于所有可接受的不确定性，实际融合估计量的稳态估计误差方差保证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。提出了一个应用于自回归 (AR) 信号处理的示例，这表明鲁棒融合状态估计方法可以解决鲁棒融合信号估计问题。仿真实例表明了该方法的有效性和正确性。