The strength of the GNSS precise positioning model degrades in cases of a lack of visible satellites, poor satellite geometry or uneliminated atmospheric delays. The least-squares solution to a weak GNSS model may be unreliable due to a large mean squared error (MSE). Recent studies have reported that Tikhonov’s regularization can decrease the solution’s MSE and improve the success rate of integer ambiguity resolution (IAR), as long as the regularization matrix (or parameter) is properly selected. However, there are two aspects that remain unclear: (i) the optimal regularization matrix to minimize the MSE and (ii) the IAR performance of the regularization method. This contribution focuses on these two issues. First, the “optimal” Tikhonov’s regularization matrix is derived conditioned on an assumption of prior information of the ambiguity. Second, the regularized integer least-squares (regularized ILS) method is compared with the integer least-squares (ILS) method in view of lattice theory. Theoretical analysis shows that regularized ILS can increase the upper and lower bounds of the success rate and reduce the upper bound of the LLL reduction complexity and the upper bound of the search complexity. Experimental assessment based on real observed GPS data further demonstrates that regularized ILS (i) alleviates the LLL reduction complexity, (ii) reduces the computational complexity of determinate-region ambiguity search, and (iii) improves the ambiguity fixing success rate.

在缺少可见卫星、卫星几何形状不佳或未消除的大气延迟的情况下，GNSS 精确定位模型的强度会降低。由于较大的均方误差 (MSE)，弱 GNSS 模型的最小二乘解可能不可靠。最近的研究表明，只要正确选择正则化矩阵（或参数），Tikhonov 正则化可以降低解的 MSE 并提高整数模糊度解析 (IAR) 的成功率。然而，有两个方面仍不清楚：（i）最小化 MSE 的最佳正则化矩阵和（ii）正则化方法的 IAR 性能。本文主要关注这两个问题。首先，“最优”Tikhonov 的正则化矩阵是基于对模糊性的先验信息的假设得出的。第二，正则化整数最小二乘法（regularized ILS）从格理论的角度与整数最小二乘法（ILS）法进行了比较。理论分析表明，正则化ILS可以提高成功率的上下界，降低LLL归约复杂度的上界和搜索复杂度的上界。基于实际观测 GPS 数据的实验评估进一步表明，正则化 ILS (i) 减轻了 LLL 减少复杂度，(ii) 降低了确定区域模糊度搜索的计算复杂度，以及 (iii) 提高了模糊度修复成功率。