Source localization is the process of finding the source of an unknown scalar field using a sensor-equipped autonomous agent. It finds application in search and rescue, chemical/pollutant leakage detection, Radio source localization, etc. The problem of source localization has been explored using various methods, among which switched turn-based methods prove promising for single-agent source localization. To this end, this work provides enhancements and mathematical analysis for Maxima Turn Switching (MTS) and Gradient-Augmented MTS (GAMTS) algorithms. Since MTS and GAMTS are inherently more susceptible to sensor noise, a novel switched turn Algorithm, `Gradient Direction Turn Switching (GDTS),' utilizes robust gradient estimation and switching strategy to achieve faster and more reliable localization. Analysis of the convergence of GDTS to the source is detailed. Existing switched-turn methods perform gradient climbing to seek the source; faster localization is expected by utilizing Hessian information of the scalar field. Most of the literature utilizes multi-agent systems to estimate Hessian information. Due to the limitation of multi-agent systems, a novel single-agent switched trajectory-based method is developed, `Trust region-based method (TRM),' which estimates local Hessian and gradient information of the field to obtain optimal steps toward the source. Extensive realistic Software-In-The-Loop simulation studies are conducted to validate the developed methods and verify their superior performance. An application of these methods for localizing an Avalanche beacon is also explored.