参数互相关下方差分量和协方差分量的拟合推估
发布时间：2018-12-27 09:41
【摘要】：在测量数据处理过程中,我们在进行常规的方差-协方差拟合推估时,通常假定随机信号具有各向同性的随机过程,在进行运算的过程中不考虑随机信号与观测噪声之间的相关性,然而现实中随机信号的各向异性具有普遍性,即随机信号和观测噪声之间也存在着相关联系。如果在进行拟合推估的过程中不考虑其相关性,其运算结果则不是最优的。为了求取最佳估值,本文在考虑随机信号和观测噪声以及已测点信号与未测点信号之间的相关性前提下,选取最小二乘拟合推估法为研究模型来求解参数X和Y的估值,并采用观测噪声和随机信号的方差-协方差估计来确定随机模型。在求得解析式后,本文采用最小范数二次无偏估计法来协调拟合推估模型中观测噪声和随机信号之间的权比,随后运用MATLAB软件进行模型的拟合推估,分别对比观测值互相独立下和参数相关下的拟合结果,分析其差异性,说明该算法的实用性和优越性。
[Abstract]:In the process of measuring data processing, we usually assume that the random signal has isotropic stochastic process when we estimate the normal variance-covariance fitting. The correlation between random signal and observation noise is not considered in the course of operation, but the anisotropy of random signal is universal in reality, that is, there is a correlation between random signal and observation noise. If the correlation is not considered in the process of fitting estimation, the result is not optimal. In order to obtain the best estimation, considering the correlation between the random signal and the observed noise, and the correlation between the measured point signal and the unmeasured point signal, the least square fitting estimation method is selected as the research model to solve the estimation of the parameters X and Y. The random model is determined by variance-covariance estimation of observation noise and random signal. After the analytical formula is obtained, the least norm quadratic unbiased estimation method is used to coordinate the fitting and estimation of the weight ratio between the observed noise and the random signal in the model, and then the fitting estimation of the model is carried out by using MATLAB software. By comparing the fitting results under the condition of independent observation and parameter correlation, the difference of the algorithm is analyzed, and the practicability and superiority of the algorithm are proved.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P207
[Abstract]:In the process of measuring data processing, we usually assume that the random signal has isotropic stochastic process when we estimate the normal variance-covariance fitting. The correlation between random signal and observation noise is not considered in the course of operation, but the anisotropy of random signal is universal in reality, that is, there is a correlation between random signal and observation noise. If the correlation is not considered in the process of fitting estimation, the result is not optimal. In order to obtain the best estimation, considering the correlation between the random signal and the observed noise, and the correlation between the measured point signal and the unmeasured point signal, the least square fitting estimation method is selected as the research model to solve the estimation of the parameters X and Y. The random model is determined by variance-covariance estimation of observation noise and random signal. After the analytical formula is obtained, the least norm quadratic unbiased estimation method is used to coordinate the fitting and estimation of the weight ratio between the observed noise and the random signal in the model, and then the fitting estimation of the model is carried out by using MATLAB software. By comparing the fitting results under the condition of independent observation and parameter correlation, the difference of the algorithm is analyzed, and the practicability and superiority of the algorithm are proved.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P207
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