For 2 decades, meteor radars have been routinely used to monitor atmospheric temperature around 90 km altitude. A common method, based on a temperature gradient model, is to use the height dependence of meteor decay time to obtain a height-averaged temperature in the peak meteor region. Traditionally this is done by fitting a linear regression model in the scattered plot of ${\log }_{\mathrm{10}}(\mathrm{1}/\mathit{\tau })$ and height, where τ is the half-amplitude decay time of the received signal. However, this method was found to be consistently biasing the slope estimate. The consequence of such a bias is that it produces a systematic offset in the estimated temperature, thus requiring calibration with other co-located measurements. The main reason for such a biasing effect is thought to be due to the failure of the classical regression model to take into account the measurement error in τ and the observed height. This is further complicated by the presence of various geophysical effects in the data, as well as observational limitation in the measuring instruments. To incorporate various error terms in the statistical model, an appropriate regression analysis for these data is the errors-in-variables model. An initial estimate of the slope parameter is obtained by assuming symmetric error variances in normalised height and ${\log }_{\mathrm{10}}(\mathrm{1}/\mathit{\tau })$. This solution is found to be a good prior estimate for the core of this bivariate distribution. Further improvement is achieved by defining density contours of this bivariate distribution and restricting the data selection process within higher contour levels. With this solution, meteor radar temperatures can be obtained independently without needing any external calibration procedure. When compared with co-located lidar measurements, the systematic offset in the estimated temperature is shown to have reduced to 5 % or better on average.

中文翻译：

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估计流星峰高度温度的改进方法

20 年来，流星雷达通常用于监测 90 公里高度附近的大气温度。一种常用的方法是基于温度梯度模型，利用流星衰减时间的高度依赖性来获得流星峰值区域的高度平均温度。传统上，这是通过在散点图中拟合线性回归模型来完成的${\mathrm{日志}}_{\mathrm{10}}(\mathrm{1}/\mathit{\tau })$和高度，其中τ是接收信号的半幅衰减时间。然而，这种方法被发现始终偏向斜率估计。这种偏差的结果是它会在估计的温度中产生系统偏移，因此需要与其他同位测量值进行校准。这种偏差效应的主要原因被认为是由于经典回归模型未能考虑τ 中的测量误差和观察到的高度。由于数据中存在各种地球物理效应，以及测量仪器的观测限制，这进一步复杂化。为了在统计模型中加入各种误差项，对这些数据进行适当的回归分析是变量误差模型。斜率参数的初始估计是通过假设标准化高度的对称误差方差和${\mathrm{日志}}_{\mathrm{10}}(\mathrm{1}/\mathit{\tau })$. 发现该解决方案是该双变量分布核心的良好先验估计。通过定义这种二元分布的密度等高线并将数据选择过程限制在更高的等高线级别内，可以实现进一步的改进。使用此解决方案，无需任何外部校准程序即可独立获取流星雷达温度。与协同定位的激光雷达测量相比，估计温度的系统偏移平均降低至 5% 或更好。