As a step towards ubiquitous and mobile computing, a decentralized localization platform allows positioning for objects and persons. The decentralized computation of the position enables to shift the application-level knowledge into a Mobile Station (MS) and avoids the communication with a remote device such as a server. In addition, computing a position on resource-constrained devices is challenging due to the restricted storage, computing capacity, and power supply. Therefore, we propose suitable algorithms to compute unoptimized as well as optimized positions on resource-limited MSs. Algorithms for unoptimized positions will be analyzed with respect to the stability, complexity, and memory requirements. The calculated positions are optimized by using the Gauss-Newton (GNM) or Levenberg-Marquardt methods (LVMs). We analyze and compare the GNM with two variants of the LVM algorithm. Furthermore, we develop an adaptive algorithm for the position optimization, which is based on the Singular Value Decomposition (SVD), LVM algorithm, and the Dilution of Precision. This method allows an adaptive selection mechanism for the LVM algorithm. The influence and choice of the right parameter combination of the LVM algorithm will be analyzed and discussed. Finally, we design and evaluate a method to reduce multipath errors on the MS.