This paper presents a noise-robust mobile positioning system based on received signal strength (RSS) estimators, particle filters and a convex optimization processor. The positioning system uses a code-aided noise cancellation technique to refine the (RSS) signals and improve the positioning accuracy. This study also presents a virtual basestation transform (VBST) and convex optimization algorithm to deal with the none-light-of-sight (NLOS) travelling problem of the microwave transmission. The proposed positioning processor consists of four code-aided SNR/RSS estimators and four latency-reduced particle filters to refine the RSS signals from four base stations and estimate their distances to the mobile station. Then, the estimated distances are delivered to a convex optimization processor with the VBST algorithm to locate the mobile station. This work implemented the positioning algorithm on Xilinx Virtex-4 FPGA and RF modules to verify the positioning performance. The measurement and analysis results show that the proposed convex-optimized positioning system reduces 20 % RMSE in the mixed NLOS/LOS environment compared to the sole particle filtering approach. The RSS estimator can further improve the positioning performance in the noisy environments.