For the linear stochastic descriptor system with random one-step measurement delay and uncertain-variance correlated noises, the robust estimation problem is addressed. Applying the singular value decomposition method, augmented state approach and fictitious noise approach, the original descriptor system is transformed to new standard system only with uncertain-variance fictitious noises. Based on Kalman filtering and the minimax robust estimation principle, the actual Kalman estimator for the proposed standard system with actual measurement and the upper bounds of the variances is presented, including the Kalman predictor, filter, smoother and white noise deconvolution estimator. According to the relation of the new standard system and the original system, the actual estimator of original state of descriptor system and actual estimation error variance are presented. Further, the robustness of the actual estimator is proved by the Lyapunov equation approach, that is, the actual estimation error variance is guaranteed to have minimal upper bound for all admissible uncertainties. A simulation example about circuits system verifies the correctness and effectiveness of the proposed results.

中文翻译：

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具有随机一步测量延迟的描述符系统的鲁棒时变估计器

针对具有随机单步测量延迟和不确定方差相关噪声的线性随机描述符系统，解决了鲁棒估计问题。应用奇异值分解方法、增广状态方法和虚拟噪声方法，将原始描述符系统转换为仅具有不确定方差虚拟噪声的新标准系统。基于卡尔曼滤波和极小极大鲁棒估计原理，给出了具有实际测量和方差上限的标准系统的实际卡尔曼估计器，包括卡尔曼预测器、滤波器、平滑器和白噪声解卷积估计器。根据新标准体系与原体系的关系，给出了描述符系统原始状态的实际估计量和实际估计误差方差。此外，实际估计量的鲁棒性由李雅普诺夫方程方法证明，即保证实际估计误差方差对于所有可容许的不确定性具有最小的上限。电路系统仿真实例验证了所提结果的正确性和有效性。