| Abstract: | The statistics of the residuals are used in this paper to perform a quality assessment of the solutions from space geodesy data analysis. With the stochastic estimation and the relatively arbitrary empirical parameters being employed to absorb unmodelled errors, it has long been noticed that different estimate combinations or analysis strategies may achieve the same level of fitting yet result in significantly different solutions. Based on the postulate that no conceivable signals should remain in the residuals, solutions of the same level of root mean square error (RMS) and variance–covariance may be differentiated in the sense that for reasonable solutions, the residuals are virtually identical with noise. While it is possible to develop complex noise models, the Gaussian white noise model simplifies the solution interpretation and implies the unmodelled errors have been smoothed out. Statistical moments of the residuals as well as the Pearson chi-square are computed in this paper to measure the discrepancies between the residuals and Gaussian white noise. Applying to both satellite laser ranging (SLR) and global positioning system (GPS) data analysis, we evaluate different parameter estimate combinations and/or different strategies that would be hardly discriminated by the level of fitting. Unlike most solution assessment methods broadly termed as external comparison, no information independent of the data analyzed is required. This makes the immediate solution assessment possible and easy to carry out. While the external comparison is the best and most convincing quality assessment of the solution, the statistics of the residuals provide important information on the solutions and, in some cases as discussed in this paper, can be supported with external comparison. |
