A regularization algorithm for improving the reliability of TRF datum parameters

The parameter estimation of the adjustment model of the Terrestrial Reference Frame (TRF) can be regarded as a rank-deficient problem. However, traditional internal constraints potentially treat the identity matrix I and the numerical value 1 as the regularization matrix and parameter, respectively. This may introduce some biases in the estimation and accuracy evaluation of TRF datum parameters. To improve the reliability of TRF datum parameter estimation and accuracy evaluation, we propose a regularization algorithm for improving the reliability of the TRF datum. This method constructs the regularization matrix and parameter based on the error propagation law, and uses the least squares variance component estimation (LS-VCE) technique for necessary updates. To verify the effectiveness of the proposed method, we use simulated data for illustration. The results indicated that the proposed method can significantly improve the bias between the estimated and defined values for the datum parameters, thereby enhancing their total accuracy. Compared with traditional methods, the proposed approach has reduced the datum bias on the X-axis, Y-axis, and Z-axis by 93.61%, 95.24%, and 85.82%, respectively. The total accuracy on the X-axis, Y-axis, and Z-axis has been improved by 94.24%, 95.94%, and 87.43%, respectively. This indicates that reliable TRF datum parameters estimation should consider the error characteristics of the regularization matrix and parameter. We applied the proposed approach to the 2005–2014 International global navigation satellites systems service (IGS) 2nd data reprocessing campaign (repro2) daily TRF time series and conducted a comparative analysis with traditional methods to test the actual performance of the proposed method. The final measured data showed similar results to those of the simulation experiment. This indicates that reliable TRF datum parameters estimation should consider the error characteristics of the regularization matrix and parameter.