A platform architecture for positioning systems is essential for the realization of a flexible localization system, which interacts with other systems and supports various positioning technologies and algorithms. The decentralized processing of a position enables to push the application-level knowledge into a mobile station and avoids the communication with a central unit such as a server or a base station. In addition, the calculation of the position on low-cost and resource-constrained devices presents a challenge due to the limited computing and storage capacity as well as power supply. Therefore, this thesis proposes a platform architecture which allows for the design of a system with the following advantages: reusability of the components, extensibility (e.g., with other positioning technologies) and interoperability. Furthermore, the position is computed on-the-fly on a low-cost device such as a microcontroller, which simultaneously performs additional tasks such as data collecting or preprocessing based on an operating system. The platform architecture is designed, implemented, and evaluated based on two systems: a time-of-arrival and a field strength-based positioning system. These systems use Ultra-Wideband (UWB) and Direct Current (DC)-pulsed magnetic signals, respectively. Suitable algorithms are proposed to compute an unoptimized position (start position). These algorithms will be analyzed and compared with respect to the stability, efficiency, complexity, and memory requirements. An adaptive algorithm is developed for the optimization of the position, which is based on the Singular Value Decomposition (SVD), Levenberg–Marquardt (LVM) algorithm, and the Position Dilution of Precision (PDOP). This algorithm allows an adaptive selection mechanism for the LVM algorithm. This adaptive algorithm enables saving of resources such as memory, computing time, and energy on resource-constrained devices. Furthermore, two variants of the LVM algorithms are used: the Dahmen-Reusken LVM and Madsen LVM, which are analyzed and compared with the Gauss-Newton algorithm. All the algorithms are derived in a convenient form for resource-constrained devices. Since the parameters of the LVM algorithm impact the accuracy as well as the required iteration number, the influence and the choice of the right parameter combination will be determined, analyzed and discussed. Finally, a method is designed and evaluated to reduce multipath errors on the mobile station. This method allows an accurate localization in non-line-of-sight scenarios.