This article is concerned with the optimal sequential fusion filter design issue for a class of sampled‐data systems subject to random transmission delays and multiplicative noise. The considered delay is modeled as a multistate Markov chain, while the multiplicative noise corrupting the observation measurements is assumed be a white noise sequence with known statistical properties. First, by reorganizing the original measurements, the solvability of the addressed problem is cast into the feasibility of an optimal estimation issue for the hybrid Markovian jump system without delays. Then, an optimal sequential fusion filter is constructed by utilizing a dynamic model with finite jumps on basis of the arrival order of measurements from different sensors, guaranteeing estimation performances both at sampling instants and within the sampling intervals. Moreover, the desired estimator gains can be computed via solving a series of coupled differential Riccati equations with jumps and coupled differential Lyapunov equations. Further, a stationary sequential fusion filter is achieved with the guarantee of the exponentially mean‐square stability. Finally, two simulation examples are provided to verify the validity of the proposed algorithms.

中文翻译：

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具有随机延迟和乘性噪声的采样数据系统的最优顺序融合估计

本文关注一类受随机传输延迟和乘性噪声影响的采样数据系统的最优顺序融合滤波器设计问题。所考虑的延迟被建模为多状态马尔可夫链，而破坏观测测量的乘性噪声被假设为具有已知统计特性的白噪声序列。首先，通过重新组织原始测量，将所解决问题的可解性转化为无延迟混合马尔可夫跳跃系统最优估计问题的可行性。然后，根据不同传感器测量值的到达顺序，利用有限跳跃的动态模型构建最优顺序融合滤波器，保证采样时刻和采样间隔内的估计性能。此外，可以通过求解一系列具有跳跃的耦合微分 Riccati 方程和耦合微分 Lyapunov 方程来计算所需的估计器增益。此外，在保证指数均方稳定性的情况下实现了平稳顺序融合滤波器。最后，提供两个仿真例子来验证所提算法的有效性。