For telemetry data processing systems, estimating the bit error probability of received data is important in terms of data quality. For systems in which the number of allowable errors in an $M$ -bit frame syncword (FS) of a telemetry data frame is $K$ and the numbers of FSs with no error, one error, $\dots$ , $K$ errors, and more than $K$ errors are given, respectively, it is known from the literature that conventional methods, including the maximum-likelihood estimator (MLE), are not generally presented as a closed-form expression excluding specific cases. This article proposes a weighted least squares estimator (WLSE) by taking the ratios of the observed FS error rates to minimize the squared discrepancies between the observed and the predicted values, and the WLSE is obtained by straightforward calculation. We analyze the characteristics of the bias and the variance and derive optimal weights that minimize the variance considering that the mean squared error (MSE) of the proposed estimator depends on the variance rather than the bias. Based on the derived optimal weights, a method is proposed to sequentially obtain the weights close to optimum. The analytical and simulation results verify that the MSE of the proposed estimator is only slightly larger or even less than those of the existing methods, while the proposed estimator has a significantly lower computational complexity than those of the conventional schemes.

中文翻译：

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根据帧同步字误码率的加权最小二乘法估计 BEP

对于遥测数据处理系统来说，估计接收数据的误码概率对于数据质量来说很重要。对于系统中允许的错误数百万美元 遥测数据帧的位帧同步字 (FS) 是 $K$ 和没有错误的FS的数量，一个错误， $\点$ , $K$ 错误，并且超过 $K$错误分别给出，从文献中可以看出，包括最大似然估计（MLE）在内的传统方法通常不作为封闭形式的表达式呈现，排除特定情况。本文提出了一种加权最小二乘估计（WLSE），通过取观察到的FS错误率的比率来最小化观察值和预测值之间的平方差异，并且通过直接计算得到WLSE。我们分析了偏差和方差的特征，并考虑到所提出的估计量的均方误差 (MSE) 取决于方差而不是偏差，得出使方差最小的最佳权重。基于导出的最优权重，提出了一种依次获取接近最优权重的方法。