Revisiting Force Model Error Modeling in GRACE Gravity Field Recovery

Improved GRACE‐FO Gravity Field Solution by Combining Different Accelerometer Transplant Products

“…In general, weights of different ACT products are comparable in both cases, while those derived from empirical noise estimation show larger fluctuations with the JPL‐ACH getting the largest weights. The relatively consistent weights, that is, close to 1.0, estimated in the VCE case are within our expectation, because we have applied stochastic modeling in the construction of individual NEQ, which already takes into account data heterogeneity via fully‐populated observation weight matrices (Brockmann et al., 2021; Nie et al., 2022a). Moreover, as VCE is mainly driven by the internal (or formal) precision of the parameter estimation system, any deviation from the truth in stochastic modeling cannot be self‐calibrated (Lerch, 1991).…”

“…The combination is carried out at the level of NEQ instead of SH coefficients to fully consider correlations among parameters (Meyer et al., 2019), which reads $$$\left(\sum\limits _{i=1}^{3}{w}_{i}{\boldsymbol{N}}_{i}\right)\widehat{\boldsymbol{x}}=\left(\sum\limits _{i=1}^{3}{w}_{i}{\boldsymbol{b}}_{i}\right)$$$ where $$\widehat{\boldsymbol{x}}$$ is the vector of gravity field parameters to be estimated, N i and b i are normal matrix and right‐hand‐side vector of NEQ, the construction of which is detailed in Nie et al. (2022a, 2022b). Three groups of NEQ are derived from JPL‐ACT, JPL‐ACH, and TUG‐ACT, respectively, and they are weighted based on corresponding factors w i .…”

“…where (⋅) T denotes the transpose operator, l i is the reduced observation data vector, and P i is the weight matrix determined from the filtering approach in this study (Nie et al, 2022a); n i is the number of observations reduced by local parameters, for example, initial states and accelerometer calibration parameters, and t i is contribution number of each solution to the joint estimation of x, which is computed as (Nie, Shen, Pail, & Chen, 2022)…”

“…Instead of estimating empirical parameters, either in the form of accelerations or range-rate parameters, stochastic modeling is employed (Nie et al, 2022a). In stochastic modeling, an autoregressive model-based filtering approach is adopted to properly model colored noise in the data during the weighted least-squares parameter estimation process, detailed in Nie et al (2022a). Additionally, relative weights between different observation groups are determined based on the variance component estimation (VCE) (Koch & Kusche, 2002;Kusche, 2003), which is realized by an efficient algorithm developed by Nie, Shen, Pail, and Chen (2022).…”

“…The differences mainly come from their specific L1B data processing strategies, in particular their methods of noise modeling as elaborated in Nie et al. (2022a).…”