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Bilinear equation method for unbiased identification of linear FIR systems in the presence of input and output noises

机译：输入和输出噪声存在下用于线性FIR系统的无偏辨识的双线性方程法

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摘要

The presence of contaminating noises in both the input and output of an FIR system usually results in a biased least squares (LS) parameter estimate. The total least squares (TLS) methods are known to be efficient in achieving unbiased estimation, if the ratio of the input noise variance to the output noise variance (NNR) is known. However, when the NNR is unknown, a simple analysis shows that the classical LS and TLS estimation methods usually have such insufficient degree of freedom that they can achieve the unbiased solution. In this paper, it is shown by analyzing the algebraic structure of the correlation matrix that the unbiased estimate of FIR parameters can be obtained by solving a special bilinear equation. Then we develop a bilinear equation method (BEM) for solving the bilinear equation associated with the unbiased solution of the FIR system or filtering under the unknown NNR. Unlike the available unbiased estimators, the main advantage is that the proposed method exploits much sufficiently the special structure of the correlation matrix and obtains much accurate estimation for FIR filtering in the presence of input and output noises. Two simulation examples are presented that show the good performance of the proposed method, including its superiority over the classical LS and TLS approaches, and the instrumental variable methods.
机译：FIR系统的输入和输出中都存在污染噪声，通常会导致偏差最小二乘（LS）参数估计。如果已知输入噪声方差与输出噪声方差（NNR）之比，则总最小二乘法（TLS）方法可有效实现无偏估计。但是，当NNR未知时，简单分析表明，经典的LS和TLS估计方法通常具有如此低的自由度，以至于它们可以实现无偏解。本文通过分析相关矩阵的代数结构表明，可以通过求解特殊的双线性方程来获得FIR参数的无偏估计。然后，我们开发了一种双线性方程方法（BEM），用于求解与FIR系统的无偏解或在未知NNR下进行滤波的双线性方程有关。与可用的无偏估计器不同，主要优点是，所提出的方法充分利用了相关矩阵的特殊结构，并在存在输入和输出噪声的情况下获得了对FIR滤波的非常准确的估计。给出了两个仿真示例，显示了所提方法的良好性能，包括与经典LS和TLS方法相比的优越性以及工具变量法。

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