Building an efficient node localization system in wireless sensor networks is facing several challenges. For example, calculating the square root consumes computational resources and utilizing flooding techniques to broadcast nodes location wastes bandwidth and energy. Reducing computational complexity and communication overhead is essential to reduce the power consumption, extend the life time of the battery operated nodes, and improve the performance of the limited computational resources of these sensor nodes. Localization algorithms can be classified as range-free or range-based Algorithms. Range-based algorithms are more accurate but also more computationally complex. However, in applications such as target tracking, localization accuracy is important. In this paper, we revise the mathematical model,the analysis and the simulation experiments of the basic Trigonometric based Ad-hoc Localization System (TALS), a range-based localization system presented previously. A better picture on the overall behavior of TALS is drown. Furthermore, the study is extended, and a new technique to optimize the system is proposed. A deep analysis and an extensive simulation for the optimized TALS is presented showing its cost, accuracy, efficiency, and deducing the impact of its parameters on the performance. Thus, the contribution of this work can be summarized as follows: 1) Extending and optimizing the basic TALS that reduces the computational overhead by eliminating the need of solving a linear system of equations via least square methods and its variants or the need to any square root operations. 2) Revision of the system formulas and providing correct and accurate equations 3) Deeply analyzing, and extensively simulating the optimized TALS showing its cost, accuracy, efficiency, and deducing the impact of its parameters, such as the initial anchors density, the number of considered localizing neighbors aiding in the localization process, the transmission noise, and noisy measurements, on the performance. 4) Ensuring a very good accuracy with less complexity than the basic TALS by proposing and using a novel modified Manhattan distance in the elimination process. Through the mathematical analysis and intensive simulation, the optimized TALS has presented superior performance and accuracy results compared to other localization techniques.