Localization algorithms are traditionally developed to minimize the impact of observation errors on accurate positioning by considering the errors in observations obtained from the target. When dealing with a moving sensor, navigation systems provide reports on the sensor's locations. Consequently, the localization methods in this approach need to be modified to incorporate the navigation errors along with the erroneous target observations in the equations, with the aim of reducing the impact of these errors on positioning accuracy. This paper focuses on utilizing passive positioning methods with moving sensors and presents an analysis and design of a method to enhance the speed and accuracy of positioning algorithms, while also updating the error estimates in observations and navigation reports. Simulation results demonstrate that the single-stage generalized least squares algorithm consistently yields the most accurate results across all scenarios and is suitable for real-world conditions. Additionally, an algorithm based on adaptive filters has been devised to expedite convergence speed. Moreover, the factors influencing convergence speed have been analyzed, and a solution to enhance convergence speed has been proposed. By examining Kramer Rao's bound in various methods, a novel framework has been developed. In this article, the intersection and rotation algorithm is employed to combine orientation-based and time-based energy transmission methods. These algorithms are characterized by their high accuracy, low computational overhead, and resilience to measurement noise. Simulation-based evaluations have been conducted, demonstrating the superior performance of the proposed method compared to existing approaches in terms of quality and effectiveness.