scholarly journals Improved method of estimating temperatures at meteor peak heights

2020 ◽  
Author(s):  
Emranul Sarkar ◽  
Alexander Kozlovsky ◽  
Thomas Ulich ◽  
Ilkka Virtanen ◽  
Mark Lester ◽  
...  
Keyword(s):  
Regression Model ◽  
Decay Time ◽  
Analytic Solution ◽  
Calibration Procedure ◽  
Meteor Radar ◽  
Slope Estimate ◽  
Lidar Measurements ◽  
Height Dependence ◽  
Error Terms ◽  
Line Fitting

Abstract. For two decades meteor radars have been routinely used to monitor temperatures around the 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 log10(1 / τ) 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 bias is that it produces a systematic offset in the estimated temperature, and thus requiring calibration with other colocated 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 or the observed height. This is further complicated by the presence of various geophysical effects in the data, which are not taken into account in the physical model. The effect of such biasing is discussed on both theoretical and experimental grounds. An alternative regression method that incorporates various error terms in the statistical model is used for line fitting. This model is used to construct an analytic solution for the bias-corrected slope coefficient for this data. With this solution, meteor radar temperatures can be obtained independently without using any external calibration procedure. When compared with colocated lidar measurements, the temperature estimated using this method is found to be accurate within 7 % or better and without any systematic offset.

Solving the long-standing problem of estimating the atmospheric temperature at 90 km altitude with meteor radar

2021 ◽  
Author(s):  
Emranul Sarkar ◽  
Thomas Ulich ◽  
Ilkka Virtanen ◽  
Mark Lester ◽  
Bernd Kaifler
Keyword(s):  
Regression Model ◽  
Decay Time ◽  
Selection Process ◽  
Calibration Procedure ◽  
Atmospheric Temperature ◽  
Bivariate Distribution ◽  
Measuring Instruments ◽  
Meteor Radar ◽  
Lidar Measurements ◽  
Height Dependence

<p>For two decades meteor radars have been routinely used to monitor atmospheric temperatures around the 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<sub>10</sub>(1/tau) and height, where ’tau’ 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 bias is that it produces a  systematic offset in the estimated temperature, and thus requiring calibration with other colocated 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 decay time or 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. We demonstrate an alternative regression method that incorporates various error terms in the statistical model. An initial estimate of the slope parameter is obtained by assuming symmetric error variances in normalised height and log<sub>10</sub>(1/tau). This solution is found to be a good prior solution for the core of this bivariate distribution. However, depending on the data selection process the error variances may not be exactly equal. A first-order correction is then carried out to address the biasing effect due to asymmetric error variances. This allows to construct an analytic solution for the bias-corrected slope coefficient for this data. With this solution, meteor radar temperatures can be obtained independently without using any external calibration procedure. When compared with colocated lidar measurements, the temperature estimated using this method is found to be accurate within 7% or better and without any systematic offset.</p>

scholarly journals Improved method of estimating temperatures at meteor peak heights

2021 ◽  
Vol 14 (6) ◽  
pp. 4157-4169
Author(s):  
Emranul Sarkar ◽  
Alexander Kozlovsky ◽  
Thomas Ulich ◽  
Ilkka Virtanen ◽  
Mark Lester ◽  
...  
Keyword(s):  
Regression Model ◽  
Decay Time ◽  
Selection Process ◽  
Calibration Procedure ◽  
Atmospheric Temperature ◽  
Bivariate Distribution ◽  
Measuring Instruments ◽  
Lidar Measurements ◽  
Prior Estimate ◽  
Height Dependence

Abstract. 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⁡10(1/τ) 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⁡10(1/τ). 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.

Using The Fully Modified M Method In Estimating The Effect Of Cultivated Area On Barley Production In Iraq For The Period 1970-2018

2020 ◽  
Vol 2020 (66) ◽  
pp. 101-110
Author(s):  
. Azhar Kadhim Jbarah ◽  
Prof Dr. Ahmed Shaker Mohammed
Keyword(s):  
Regression Model ◽  
Moving Average ◽  
Estimation Method ◽  
Estimation Methods ◽  
Autoregressive Moving Average ◽  
Moving Average Models ◽  
Error Terms ◽  
Relationship Of ◽  
The Relationship ◽  
Barley Crop

The research is concerned with estimating the effect of the cultivated area of barley crop on the production of that crop by estimating the regression model representing the relationship of these two variables. The results of the tests indicated that the time series of the response variable values is stationary and the series of values of the explanatory variable were nonstationary and that they were integrated of order one ( I(1) ), these tests also indicate that the random error terms are auto correlated and can be modeled according to the mixed autoregressive-moving average models ARMA(p,q), for these results we cannot use the classical estimation method to estimate our regression model, therefore, a fully modified M method was adopted, which is a robust estimation methods, The estimated results indicate a positive significant relation between the production of barley crop and cultivated area.

scholarly journals A Low-Cost Calibration Method for Low-Cost MEMS Accelerometers Based on 3D Printing

Sensors ◽  
2020 ◽  
Vol 20 (22) ◽  
pp. 6454
Author(s):  
Jesús A. García ◽  
Evangelina Lara ◽  
Leocundo Aguilar
Keyword(s):  
3D Printing ◽  
Low Cost ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Position Accuracy ◽  
Mems Accelerometers ◽  
Sophisticated Equipment ◽  
3D Printed ◽  
Error Terms ◽  
Over Time

A ubiquitous sensor in embedded systems is the accelerometer, as it enables a range of applications. However, accelerometers experience nonlinearities in their outputs caused by error terms and axes misalignment. These errors are a major concern because, in applications such as navigations systems, they accumulate over time, degrading the position accuracy. Through a calibration procedure, the errors can be modeled and compensated. Many methods have been proposed; however, they require sophisticated equipment available only in laboratories, which makes them complex and expensive. In this article, a simple, practical, and low-cost calibration method is proposed. It uses a 3D printed polyhedron, benefiting from the popularisation and low-cost of 3D printing in the present day. Additionally, each polyhedron could hold as much as 14 sensors, which can be calibrated simultaneously. The method was performed with a low-cost sensor and it significantly reduced the root-mean-square error (RMSE) of the sensor output. The RMSE was compared with the reported in similar proposals, and our method resulted in higher performance. The proposal enables accelerometer calibration at low-cost, and anywhere and anytime, not only by experts in laboratories. Compensating the sensor’s inherent errors thus increases the accuracy of its output.

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