Least-Squares and Minimum-Variance Estimates for Linear Time-Invariant Systems

2003 ◽  
pp. 155-204
Keyword(s):  
Least Squares ◽  
Linear Time ◽  
Minimum Variance ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Variance Estimates ◽  
Time Invariant

scholarly journals A new unbiased minimum variance observer for stochastic LTV systems with unknown inputs

2019 ◽  
Vol 37 (2) ◽  
pp. 475-496 ◽  
Author(s):  
Luc Meyer ◽  
Dalil Ichalal ◽  
Vincent Vigneron
Keyword(s):  
Unbiased Estimator ◽  
Linear Time ◽  
Stability Result ◽  
Error Variance ◽  
Minimum Variance ◽  
Rank Condition ◽  
Input Estimation ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Abstract This paper is devoted to the state and input estimation of a linear time varying system in the presence of an unknown input (UI) in both state and measurement equations, and affected by Gaussian noises. The classical rank condition used in this kind of approach is relaxed in order to be able to be used in a wider range of systems. A state observer, that is an unbiased estimator with minimum error variance, is proposed. Then a UI observer is constructed, in order to be a best linear unbiased estimator, it follows a unique construction whether the direct feedthrough matrix is null or not. In a sense the proposed approach, generalizes and unifies the existing ones. Besides, a stability result is given for linear time invariant systems, which is a novelty for unbiased minimum variance observers relaxing the classical rank condition.

Complete moment convergence for the dependent linear processes with application to the state observers of linear-time-invariant systems

2020 ◽  
Vol 65 (4) ◽  
pp. 725-745
Author(s):  
Chao Lu ◽  
Chao Lu ◽  
Xuejun J Wang ◽  
Xuejun J Wang ◽  
Yi Wu ◽  
...  
Keyword(s):  
Linear Time ◽  
The State ◽  
Complete Moment Convergence ◽  
Linear Processes ◽  
Linear Time Invariant ◽  
Moment Convergence ◽  
State Observers ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Пусть $X_t=\sum_{j=-\infty}^{\infty}A_j\varepsilon_{t-j}$ - зависимый линейный процесс, где $\{\varepsilon_n, n\in \mathbf{Z}\}$ - последовательность $m$-обобщенных отрицательно зависимых ($m$-END) случайных величин с нулевым средним, которая стохастически доминируется случайной величиной $\varepsilon$, и пусть $\{A_n, n\in \mathbf{Z}\}$ - другая последовательность случайных величин с нулевым средним, обладающая свойством $m$-END. При подходящих условиях установлена полная моментная сходимость для зависимых линейных процессов. В частности, приведены достаточные условия полной моментной сходимости. В качестве приложения исследуется сходимость наблюдателей состояния для линейных стационарных систем.

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