When a single-epoch observation set is processed, an instantaneous, precise GNSS positioning is an ill-posed problem. To deal with this ill-posed positioning problem, the integer-valued ambiguity parameters can be resolved in the coordinate domain to reduce the dimension of a search space. The ill-posed problem is then smoothed because the unknowns of n -dimensional search space are implicitly expressed in the constant three-dimensional space. So, the number of redundant data can now be large enough to perform integer ambiguity resolution. One of the methods which resolve integer ambiguities in the coordinate domain is the Modified Ambiguity Function Approach. This method searches discreetly for optimal integer-valued ambiguity parameters in the constant threedimensional space using the coordinate function. Due to the ill-conditioning of the single-epoch GNSS mathematical model, the weak approximate GNSS position and its variance-covariance matrix of poor properties still present the problem for well-performing instantaneous integer ambiguity resolution in the coordinate domain. The issue is stabilizing the single-epoch math model by regularization to improve localizing and shaping the search region in the three-dimensional space to contain the actual GNSS position more frequently, representing optimal ambiguities in the sense of integer-least squares principle. The innovation of this contribution is to improve the properties of a single-epoch approximate GNSS position and its variance-covariance matrix in the sense of meansquared error by regularizing real-valued ambiguity parameters. Thus, the float baseline solution conditioned on regularized float ambiguities is an indirectly regularized approximate GNSS position with the variance-covariance matrix of better precision. A regularized approximate position is promising because its overall accuracy increases thanks to the successful variance reduction. Despite the indirect regularization, an improved initial position is biased, resulting from the biased least-squares estimation. However, the optimal RP values obtained within the quality-based Mean-Squared Error criterion properly govern the contribution of variance reduction in the solution with the regularized bias. In the presence of bias, the regularized single-epoch integer least-squares estimator performs well in the context of correct integer ambiguity resolution in the coordinate domain.