Using Additive Robust Modeling and Fault Simulation for Laser Ranging Measurements

Abstract

© 2020 IEEE. This paper is focusing on the application of the regression modeling for analyzing highly accurate observations. In the study, the lunar laser ranging (LLR) measurements were assessed by robust analysis. Nowadays, statistical methods are applied in many branches of computer and information technology (astronomy, geology, ecology, geophysics, etc.). The use of the regression modeling (RM) allows producing not only reliable assessments for the parameters desired but also performing works on predicting the behavior of a system under consideration. Such investigations are conducted using both calculation algorithms of regression modeling (ARM) and the method of least squares (MLS) for assessing the quality of models. It is worth noting that the single use of the classic regression modeling method has certain disadvantages. The main problem is that the assumptions influence on the modeling results is not tested. As a result, the regression model may not correspond to the observations. The classic solution for this problem is checking the regression modeling conditions in case they are violated, one should apply other mathematic algorithms. This work suggests solving the problem described above by the additive dynamic regression modeling (ADRM). We developed the special software for ADRM which allows automatic checking the conditions reliability for RM-MLS systems and also conducting adaptation procedures if the conditions are not observed. To assess the model of observations, we use the method of simultaneous accounting of the presence of multicollinearity and violations of the normal error distribution. As a result, we produced assessments for the desired parameters with the minimum eliminating of erroneous observations. It should be noted that a significant performance loss is possible even at the limited eliminating of erroneous observations. To investigate the efficiency of LLR measurements, we produced the parameters as follows: percentage of erroneous observations eliminated, the standard value of the adaptation error, multi-parameter correlation, robust estimations of the ridge, its regression and stability.