We present a new generation version of $\texttt{DIFMAP}$ ($\texttt{ngDIFMAP}$) to model and fit interferometric closure quantities. $\texttt{ngDIFMAP}$ uses a global optimization algorithm based on simulated annealing, which results in more accurate parameter estimation especially when the number of parameters is high. Using this package we demonstrate the ramifications of amplitude and phase errors, and loss of $u-v$ coverage on estimated parameters, in terms of variance, bias and correlations between parameters. In addition to increasing correlations, we find that amplitude and phase errors can cause significant increase in variance and bias for all parameters for a simple jet model, and we provide prescriptions to take this into account in reporting errors on best-fit model parameters. This software serves as the pillar to our new program called the `Catalogue of proper motions in extragalactic jets from Active galactic Nuclei with Very large Array Studies' or CAgNVAS, designed with the objective of using archival and new VLA observations to measure proper motions of jets on kpc scales. Since this objective requires extremely high accuracy in component localization, and very robust understanding of source structure, $\texttt{ngDIFMAP}$ is ideally suited for this purpose. Our results are, in general, a pathway to understanding noisy interferometric data more accurately than ever before.