A geoid is a reference surface for orthometric height computed by the Stokes integral, and the error caused by truncating the integral into a limit area can be regarded as a bias. Early on, Molodensky modified the Stokes formula by decreasing the numerical size of the truncation coefficient to reduce the bias, and Evans and Featherstone accelerated the bias convergence. In comparison, spectral combination and least-squares modification (LSM) account for terrestrial gravity and Earth gravity model (EGM) errors as a variance in modifying the Stokes formula. However, the spectral combination and unbiased LSM (ULSM) poorly consider the bias when minimizing the variance, and this issue can be overcome by introducing the two bias-reducing methods. A theorem, proven in this study, accelerates the convergence of the truncation coefficient and improves the Molodensky-type modification. The proposed spectral combination with reducing bias (SCRB) and variance-minimizing ULSM with reducing bias (VURB) mitigate the errors of terrestrial gravity and EGMs, and the bias converges faster by the theorem. Considering the internal correlation of gravity anomaly error, the regional solution is also derived for SCRB and VURB for local geoid determination. Additionally, two regularizers introduced in this study avoid the ill-conditioned problems of the coefficient matrices.

大地水准面是斯托克斯积分计算出的正高的参考面，将积分截断到极限区域所产生的误差可以视为偏差。早期，Molodensky 通过减小截断系数的数值大小来修改 Stokes 公式以减少偏差，而 Evans 和 Featherstone 则加速了偏差收敛。相比之下，光谱组合和最小二乘修正 (LSM) 将地球重力和地球重力模型 (EGM) 误差解释为修正斯托克斯公式的方差。然而，谱组合和无偏LSM（ULSM）在最小化方差时很少考虑偏差，这个问题可以通过引入两种偏差减少方法来克服。本研究证明的定理加速了截断系数的收敛并改进了 Molodensky 型修正。所提出的具有减少偏差的谱组合（SCRB）和具有减少偏差的方差最小化ULSM（VURB）减轻了地球重力和EGM的误差，并且根据定理偏差收敛得更快。考虑到重力异常误差的内在相关性，还推导了SCRB和VURB的区域解，用于局部大地水准面的确定。此外，本研究中引入的两个正则化器避免了系数矩阵的病态问题。