Abstract—Accurate Global Positioning System (GPS) positioning is critical for numerous applications, yet traditional navigation algorithms such as Gradient Descent (GD), Least Squares (LS), and Weighted Least Squares (WLS) often face challenges in terms of convergence speed, computational complexity, and robustness, especially under conditions of low satellite visibility. This paper proposes a new navigation solution, the Levenberg (LVB) algorithm, designed to address these challenges. The LVB algorithm integrates the strengths of GD and LS, using an adaptive learning coefficient to provide optimal estimates without encountering the inverse problems associated with LS. We evaluated the performance of LVB alongside GD, LS, and WLS using real GPS receiver data collected from the Indian Institute of Science (IISc) in Bangalore. Our results demonstrate that LVB outperforms the traditional methods, delivering more accurate and reliable GPS position estimates, particularly in scenarios with limited satellite visibility, which is beneficial for users in the Indian subcontinent.