Robust Estimation Peculiarity Of Robust Estimation Methods In Observations To Obey Generalized Gaussian Distribution

Robust estimation is formally proposed since the1960s, and has more than50years. Now, robust estimation methods in many fields have been widely used, and is still expanding range of applications, including measurement field is a very important aspect, It can effectively eliminate or weaken the influence of gross error of parameter estimation. The proposed robust estimation is associated with gross errors. Gross error refers outlier error by mistake, observation mode error and distribution pattern error, it actually inevitable.The observation mode error is locality, global system error.There is no effective method.At present, theapproachto process the observations contained grosserrors is generallydividedintotwo categories:one is to view the contaminated observations as abnormal expectation by statistical test first, then to process the remaining data; another is to view the contaminated observations as abnormal variance, then to use robust estimation methods to process. The earliest attention is the statistical test, and its essence is attributed to gross error handling function model, the main methods are B-test, t-test and t-test ect.If there are multiple gross error, and when the poor system configuration, this approach has significant limitations.Robust estimation is the gross error is inevitable in the circumstances, choose the appropriate estimation method, so as to reduce its valuation parameters affect the normal mode and the optimal or near-optimal parameter estimation. When the presence of gross errors in the observations, robust estimation method can get closer than the actual results of the least squares method.As we all know, the least squares method can eliminate the impact of errors, but the difference will be assigned to all of the crude residuals. In addition, the role of lever point differential protection, it is easy to exclude a good observation, leaving a bad observations. Robust estimation location is also positioned by the size of the residual of gross errors,however, this is anti-poor residuals of the residuals, the accuracy is not affected by gross errors.A measure of robust estimation method is robust capabilities from two aspects to consider:1. Qualitative and quantitative robust;2.Local robust and entirty robust. Adjustment is a traditional measurement from the observed space to the parameter space of transformation, meaning that based on observations obtained by the unknown parameters and variance adjustment model valuations obtained. Robust estimation is also a transformation,with traditional surveying adjustment is robust estimation of different transformation function is continuous bounded,however, the least squares estimation method is unbounded. This continuous transformation sector there is robust estimation of qualitative robust. But no way to determine qualitatively robust anti robust estimation method merits of poor capacity, which requires a quantitative point of view from the robust capabilities of robust estimation methods.In this paper, observations obey the generalized Gaussian distribution network and three measuring three standard side-nettingfor example, the use of simulation methods, Focuses on14kinds of robust estimation methods for measuring the standard network and network adjustment of side effects,through the14kinds of commonly used robust estimation methods were analyzed and compared to determine the level of network and test the edge network adjustment is relatively more efficient robust estimation methods.The simulation results show:On observations obey generalized Gaussian distribution in terms of the level of network,both the observations contained in the5.0σ0gross errors, or contained in the10.0σ0gross errors,robust of L1、 Danish method、German-McClure method、IGGIII program and SBWLS method to other robust estimation method,it better able to eliminate or weaken the impact on gross error parameter estimation. On observations obey generalized Gaussian distribution in terms of measuring the side-netting,both the observations contained in the5.0σ0gross errors, or contained in the10.0σ0gross errors,robust of L1、Danish method、German-McClure method、 IGGⅢ program and SBWLS method to other robust estimation method,it better able to eliminate or weaken the impact on gross error parameter estimation.