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首页> 外文期刊>Signal processing >Making linear prediction perform like maximum likelihood in Gaussian autoregressive model parameter estimation
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Making linear prediction perform like maximum likelihood in Gaussian autoregressive model parameter estimation

机译：使线性预测像高斯自回归模型参数估计中的最大似然一样执行

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摘要

A two-stage method for the parameter estimation of Gaussian autoregressive models is proposed. The proposed first stage is an improved version of the conventional forward-backward prediction method and can be interpreted as its weighted version with the weights derived from the arithmetic mean of the log-likelihood functions for different conditioning cases. The weighted version is observed to perform better than the conventional forward-backward prediction method and other linear prediction based methods (correlation method, covariance method, Burg's method etc.) in terms of attained likelihood value. The proposed second stage uses the estimate of the first stage as the initial condition and approximates the highly non-linear log-likelihood function with a quadratic function around the initial estimate. The optimization of the quadratic cost function yields the optimal perturbation vector that locally maximizes the likelihood in the vicinity of the initial condition. The proposed method is compared with other methods and it has been observed that the likelihood value attained at the end of two-stages is almost identical to the value attained by higher complexity numerical-search based optimization tools in a wide range of experiments. The maximum likelihood-like performance at a significantly lower implementation cost makes the proposed method especially valuable for the applications with short data-records and limited computational resources. (C) 2019 Elsevier B.V. All rights reserved.
机译：提出了一种两阶段的高斯自回归模型参数估计方法。所提出的第一阶段是常规向前-向后预测方法的改进版本，可以解释为其加权版本，其中权重是从对数似然函数的算术平均值中得出的，用于不同条件的情况。就获得的似然值而言，观察到加权版本比常规的前后预测方法和其他基于线性预测的方法（相关方法，协方差方法，Burg方法等）表现更好。提议的第二阶段将第一阶段的估计值用作初始条件，并在初始估计值附近用二次函数来近似高度非线性对数似然函数。二次成本函数的优化产生了最佳扰动向量，该向量在初始条件附近局部最大化了似然性。将该方法与其他方法进行了比较，并且发现在两个阶段的末尾获得的似然值几乎与在更高范围的实验中基于更高复杂度的基于数值搜索的优化工具所获得的似然值相同。以极低的实现成本获得最大似然性能，使得该方法对于数据记录短，计算资源有限的应用特别有价值。 （C）2019 Elsevier B.V.保留所有权利。

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