Nonnegative variance component estimation in GPS position time series

To estimate the unknown parameters in a linear model in which the observations are linear functions of the unknowns, one of the conventional methods is the least-square estimation. The best linear unbiased estimation (BLUE) is achieved when the inverse of the variancecovariance matrix of the observables is considered as the weight matrix in the estimation process. Therefore having a realistic assessment of the precision of the observations is an important issue. One of the methods to reach this goal is the use of the least-square variance component estimation (LS-VCE). However, in this method, it is not impossible to estimate negative variances. But, they are not acceptable from the statistical point of view. In this paper, numerical methods such as genetic algorithm and also iterative methods based on LS-VCE are presented for non-negative estimation of variance components. By using non-negative variance components estimation methods not only one guarantees the non-negative variance components but also one can investigate to incorporate different noise components into the stochastic model. Those components that are not likely present are automatically estimated zeros. In this paper, using the above-mentioned methods, we assess the noise characteristics of time series of GPS permanent stations. The data used in this research are the coordinates of IGS stations located in Mehrabad-Tehran and also two other stations in Ahvaz and Mashhad (2005-2010). To deal with this amount of data, the iterative methods are superior over the numerical methods such as the genetic algorithm. The results indicate the noise of GPS position time series are a combination of white noise plus flicker noise, and in some cases combined with random walk noise.