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首页> 外文期刊>IEEE Transactions on Automatic Control >Convergence of Optimal Linear Estimator With Multiplicative and Time-Correlated Additive Measurement Noises
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Convergence of Optimal Linear Estimator With Multiplicative and Time-Correlated Additive Measurement Noises

机译：具有乘法和时间相关的相加测量噪声的最优线性估计的收敛性

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摘要

In this paper, the problem of convergence for the optimal linear estimator of discrete-time linear systems with multiplicative and time-correlated additive measurement noises is studied. By defining a new random vector that consists of the innovation, error, and part of the noise in the new measurement obtained from the measurement differencing method, we obtain convergence conditions of the optimal linear estimator by equivalently studying the convergence of the expectation of a random matrix where the random matrix is the product of the new vector and its transpose. It is also shown that the state error covariance matrix of the optimal linear estimator converges to a unique fixed point under appropriate conditions and, moreover, this fixed point can be obtained by solving a set of matrix equations.
机译：本文研究了具有时间相关的乘积和测量噪声的离散时间线性系统的最优线性估计的收敛性问题。通过定义一个新的随机矢量，该矢量由测量差分方法获得的新测量中的创新，误差和部分噪声组成，我们通过等效研究随机期望的收敛性来获得最优线性估计的收敛条件。矩阵，其中随机矩阵是新矢量及其转置的乘积。还表明最佳线性估计器的状态误差协方差矩阵在适当的条件下收敛到唯一的固定点，此外，可以通过求解一组矩阵方程来获得该固定点。

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