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11.
12.
Two different goals in fitting straight lines to data are to estimate a true linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating true straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal—predicting the dependent variable—OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples. 相似文献
13.
Michael Commer Stefan L. Helwig reas Hördt Carsten Scholl Bülent Tezkan 《Geophysical Journal International》2006,167(3):1172-1187
14.
航天INSAR复影像对的自动快速匹配 总被引:3,自引:0,他引:3
针对航天INSAR主、辅影像数据的特点,提出了加大匹配窗口、加大锚点间隔的匹配策略,以提高匹配的可靠性和速度。在匹配过程中,综合利用轨道参数和强度影像金字塔进行粗匹配,并对强度影像采用相关系数与最小二乘相结合的双向匹配方案,实现了自动、快速、高可靠性和高精度的航天INSAR复影像匹配。最后总结了航天INSAR复影像匹配的特点。 相似文献
15.
航空影像分割的最小二乘支持向量机方法 总被引:5,自引:0,他引:5
将最小支持向量机LS-SVM用于航空影像的分割,讨论了不同核函数对分割结果的影响和稀疏化处理对决策函数的影响。试验表明了LS-SVM方法用于航空影像分割的可行性。 相似文献
16.
Investigating the propagation mechanism of unmodelled systematic errors on coordinate time series estimated using least squares 总被引:6,自引:8,他引:6
The propagation of unmodelled systematic errors into coordinate time series computed using least squares is investigated,
to improve the understanding of unexplained signals and apparent noise in geodetic (especially GPS) coordinate time series.
Such coordinate time series are invariably based on a functional model linearised using only zero and first-order terms of
a (Taylor) series expansion about the approximate coordinates of the unknown point. The effect of such truncation errors is
investigated through the derivation of a generalised systematic error model for the simple case of range observations from
a single known reference point to a point which is assumed to be at rest by the least squares model but is in fact in motion.
The systematic error function for a one pseudo-satellite two-dimensional case, designed to be as simple but as analogous to
GPS positioning as possible, is quantified. It is shown that the combination of a moving reference point and unmodelled periodic
displacement at the unknown point of interest, due to ocean tide loading, for example, results in an output coordinate time
series containing many periodic terms when only zero and first-order expansion terms are used in the linearisation of the
functional model. The amplitude, phase and period of these terms is dependent on the input amplitude, the locations of the
unknown point and reference point, and the period of the reference point's motion. The dominant output signals that arise
due to truncation errors match those found in coordinate time series obtained from both simulated data and real three-dimensional
GPS data. 相似文献
17.
EFG法在土体固结中的应用 总被引:4,自引:0,他引:4
EFGM作为一种新的数值计算方法,具有只需节点信息而无段单元的特性,故在解固结方程方面有很大的优势。在计算分析中,此法容易构造固结方程的EFGM刚度矩阵和处理不同边界条件。对单面排水等条件的计算结果表明,EFGM在解决固结变形问题上,精度较高,处理边界准确。 相似文献
18.
Method of Data Reduction and Uncertainty Estimation for Platinum-Group Element Data Using Inductively Coupled Plasma-Mass Spectrometry 总被引:1,自引:0,他引:1
A data reduction method is described for determining platinum-group element (PGE) abundances by inductively coupled plasma-mass spectrometry (ICP-MS) using external calibration or the method of standard addition. Gravimetric measurement of volumes, the analysis of reference materials and the use of procedural blanks were all used to minimise systematic errors. Internal standards were used to correct for instrument drift. A linear least squares regression model was used to calculate concentrations from drift-corrected counts per second (cps). Furthermore, mathematical manipulations also contribute to the uncertainty estimates of a procedure. Typical uncertainty estimate calculations for ICP-MS data manipulations involve: (1) Carrying standard deviations from the raw cps through the data reduction or (2) calculating a standard deviation from multiple final concentration calculations. It is demonstrated that method 2 may underestimate the uncertainty estimate of the calculated data. Methods 1 and 2 do not typically include an uncertainty estimate component from a regression model. As such models contribute to the uncertainty estimates affecting the calculated data, an uncertainty estimate component from the regression must be included in any final error calculations. Confidence intervals are used to account for uncertainty estimates from the regression model. These confidence intervals are simpler to calculate than uncertainty estimates from method 1, for example. The data reduction and uncertainty estimation method described here addresses problems of reporting PGE data from an article in the literature and addresses both precision and accuracy. The method can be applied to any analytical technique where drift corrections or regression models are used. 相似文献
19.
在水分析计算中,经常涉及到变量之间的线性或非线性拟合,而在拟合各种特性曲线时,通常应用以实测资料与拟合曲线间的误差平方和最小作为目标函数的方法——最小二乘法,但这种方法忽视了所有实测点应与拟合曲线间的相对误差尽量不超过某一百分比的原则,为了达到上述要求,提出了非线性的加权最小二乘法及线性相关方程的最小距离平方和法,探讨改进了传统的最小二乘法达到优化的效果。最小距离平方和法与常用的图解法相比,本法所得成果较为客观;与传统的单方向(x或y方向)最小二乘回归法相比,所求线性方程不会因坐标系的选取而改变。最后应用算例进行了初步讨论。 相似文献
20.
S. H. Ju 《地震工程与结构动力学》2003,32(9):1431-1442
This paper discusses how to use the three‐dimensional (3D) time‐domain finite‐element method incorporating the least‐squares method to calculate the equivalent foundation mass, damping and stiffness matrices. Numerical simulations indicate that the accuracy of these equivalent matrices is acceptable when the applied harmonic force of 1+sine is used. Moreover, the accuracy of the least‐squares method using the 1+sine force is not sensitive to the first time step for inclusion of data. Since the finite‐element method can model problems flexibly, the equivalent mass, damping and stiffness matrices of very complicated soil profiles and foundations can be established without difficulty using this least‐squares method. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献